OPTIMIZATION OF BUS SYSTEM CHARACTERISTICS IN URBAN AREAS UNDER NORMAL AND EMERGENCY CONDITIONS. Ioannis Psarros. A Thesis Submitted to the Faculty of

Transcription

1 OPTIMIZATION OF BUS SYSTEM CHARACTERISTICS IN URBAN AREAS UNDER NORMAL AND EMERGENCY CONDITIONS by Ioannis Psarros A Thesis Submitted to the Faculty of The College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Master of Science Florida Atlantic University Boca Raton, Florida May 2012

2 Copyright by Ioannis Psarros 2012 ii

3 OPTIMIZATION OF BUS SYSTEM CHARACTERISTICS IN URBAN AREAS UNDER NORMAL AND EMERGENCY CONDITIONS By Ioannis Psarros This thesis was prepared under the direction of the candidate's thesis advisor, Dr. Evangelos I. Kaisar, Department of Civil, Environmental, and Geomatics Engineering, and has been approved by the members ofhis supervisory committee. It was submitted to the faculty of the College of Engineering and Computer Science and was accepted in partial fulfillment ofthe requirements for the degree ofmasterof Science. Evan os I. Kaisar, Ph.D. Tf7fi«i~.",..J2.~~...k;;- P.~. ~doj/ st-evfu(1j}i/(f Aleksandar Stevanovic, Ph.D., P.E. P.D. Scarlatos, Ph.D.oJ~_; C ir, epartme~t ofcivil,. nmental, and Geomatics Engineering Interim Dea I as, Ph.D. ollege ofengineering and Computer Science ~r~ ;: &~?1-w ;II~ ~/2- Date 111

4 ACKNOWELDGEMENTS I would like to express my deepest gratitude to my advisor Dr. Evangelos Kaisar for his guidance and support throughout the completion of this thesis. I have the deepest respect for Dr. Evangelos Kaisar not only as scientist and educator but also as my friend. In addition, I would like to thank my committee members, Dr. P.D. Scarlatos and Dr. Aleksandar Stevanovic for their encouragement and advice. I would also like to express my special gratitude to Dr. Matthew G. Karlaftis for motivating me to continue with my graduate studies. His wise advice has guided me throughout these years of research. Finally, I would like to thank all my professors and colleagues in the Department of Civil, Environmental and Geomatics Engineering at Florida Atlantic University for their support, patience and cooperation. iv

5 ABSTRACT Author: Ioannis Psarros Title: Thesis Advisor: Optimization of Bus System Characteristics in Urban Areas under Normal and Emergency Conditions Dr. Evangelos I. Kaisar Degree: Master of Science Year: 2012 Catastrophic events in the past revealed the need for more research in the field of emergency evacuation. During such a procedure different problems such as congestion at the related traffic networks because of the large number of the evacuating vehicles can occur. Current best practices, in order to deal with such problems, suggest the further involvement of buses in evacuation operations. On the first part of this study after the accurate development of the related simulation model, the optimization of a selected bus system characteristics focusing on the vehicle routing parameter will follow through the development and the application of a non-linear cost minimization problem. On the second part, the potential use of the regular-everyday bus routes in a no-notice emergency evacuation in order to save time comparing to the time needed so as to assign the actual evacuation routes to the evacuation bus vehicles will be analyzed. v

6 OPTIMIZATION OF BUS SYSTEM CHARACTERISTICS IN URBAN AREAS UNDER NORMAL AND EMERGENCY CONDITIONS LIST OF TABLES... ix LIST OF FIGURES... x 1. Introduction Traffic Congestion Public Transportation Buses Preparedness for Emergency Events Evacuation Evacuation and Transit Operations Problem Statement and Objectives Thesis Outline LITERATURE REVIEW Introduction Research on the Available Simulation Tools Vehicle Routing Problem Optimization of Bus Operations under Normal Conditions Optimization of Bus Operations under Short-Notice Evacuation Optimization of Operations under No-Notice Evacuation Cost Models for Transportation Problems vi

7 2.8 Conclusions METHODOLOGY General Data Collection Simulation Model Development Optimization Procedure Mathematical Model Supplier Cost User Cost Model Constraints Solution Approach Result Analysis Future Demand and Cost Evacuation Analysis CASE STUDY General Simulation Model Development Transportation Bus System Calibration Validation Mathematical Model Optimization Procedure Parameters Values Emergency Conditions Evacuation Existing Evacuation Plans Evacuation Case Study Scenario vii

8 4.4.3 Simulation Model Adjustments RESULTS ANALYSIS Optimization Procedure Cost Results Model Validation Measures of Effectiveness Comparison Evacuation Conditions Results CONCLUSIONS Research Contribution Research Limitations Future Work Recommendations APPENDIX Data Demand Matrix Model Calibration Validation Cost Results Normal Conditions Measures of Effectiveness (MOEs) REFERENCES viii

9 LIST OF TABLES Table 1: Cost Variables Table 2: Parameters Variables - Units for Supplier Cost Table 3: Parameters Variables - Units for User Cost Table 4: Cost Factor Values Table 5: Optimization Procedure Results Table 6: Bus Line Characteristics Table 7: Entry Point Volumes Table 8: Sample of Turning Percentages Table 9: Validation Test 1 Volumes Table 10: Validation Test 2 Volumes Table 11: Validation Test 3 Volumes Table 12: Validation Test 4 Volumes Table 13: Validation Test 5 Volumes Table 14: Validation Test 6 Volumes Table 15: Validation Test 7 Volumes ix

10 LIST OF FIGURES Figure 1: Traffic Congestion Cause (Source: Traffic Congestion & Reliability, 2005)... 1 Figure 2: Methodology Flowchart Figure 3: District of Columbia (Google Earth) Figure 4: Case Study Area (Google Earth) Figure 5: Bus Line Figure 6: Evacuation Routes (dc.gov/dc/) Figure 7: George Washington University (Google Earth) Figure 8: Pickup Points - Safe Zones Figure 9: Line G-8 Updated Route Figure 10: Line 37 Updated Route Figure 11: Line 42 Updated Route Figure 12: Line S1 Updated Route Figure 13: Line 80 Updated Route Figure 14: Line N2 Updated Route Figure 15: Comparison of Average Costs per Line Figure 16: Comparison of Average User Costs per Line Figure 17: Cost Change - Demand Increase Figure 18: Model Validation Figure 19: Travel Time x

11 Figure 20: Bus Vehicle Emissions Figure 21: Fuel Consumption Figure 22: Clearance Time Figure 23: Bus Evacuation Travel Time Figure 24: Calibration Test Figure 25: Calibration Test Figure 26: Calibration Test Figure 27: Calibration Test Figure 28: Calibration Test Figure 29: Calibration Test Figure 30: Calibration Test Figure 31: Costs for a System of 6 Bus Lines Figure 32: User Costs for a System of 6 Bus Lines Figure 33: Delay Figure 34: Vehicles Speed xi

12 1. INTRODUCTION 1.1 Traffic Congestion Population increase today, especially in urban areas and the expansion of the private cars use have created many problems to the transportation networks efficient operations. One of the major transportation problems is congestion management. The term traffic congestion refers to a simultaneous existence of a large number of vehicles on a specific part of a roadway, something which can cause slower vehicle speeds and longer travel times. The main factors that can result in the congestion occurrence are summarized in the following figure: Figure 1: Traffic Congestion Cause (Source: Traffic Congestion & Reliability, 2005) 1

13 The above summarized congestion causes can be relatively categorized. The first category is the traffic influencing events which include the traffic incidents such as vehicle accidents, blocked lanes, etc., the work zones and the weather which can affect the normal traffic conditions. The next category is traffic demand and includes the special cases of demand increase. The last category is called physical highway features and includes the traffic control devices such as the traffic signals and the physical bottlenecks (when demand exceeds capacity). From figure 1 it is obvious that the main causes of traffic congestion in a total of 80% combined are the physical bottlenecks, the traffic incidents and bad weather (Traffic Congestion & Reliability, 2005). The consequences of the increased traffic congestion in the transportation networks can be identified in different areas. The increased travel times due to traffic congestion result in the increased fuel consumption and have major economic consequences in general. The increase at the levels of gas emissions is another major consequence of the traffic congestion which concerns humanity a lot. Therefore, the question is how to deal with congestion increase and face its consequences. A suggested strategy in this direction is the further development and improvement of public transportation in urban areas. 1.2 Public Transportation Buses Federal and State agencies in order to face congestion problems suggest more and more the further development of public transportation. Different transit systems such as rail, metro-rail, buses or shuttle buses can assist in covering the passengers everyday demand. The further use of transit systems can greatly result in reducing the number of 2

14 private cars at the traffic networks. The expansion of transit systems can greatly contribute in congestion management and as a result in reducing trip travel times or delays and develop new Green cities. However, the quality of transit and mainly bus operations is affected by various parameters such as the network size, the route choice, the number of stops or the fleet size. All these bus line characteristics should be precisely identified as they can greatly affect the cost for the bus system operators and users. One of the most important parameters that affect the systems performance is the vehicle routing and especially the optimal route for each bus line. Various examples worldwide verify the importance of the routing parameter. A related example from Seoul, South Korea on 2006 showed that the application of a new routing policy optimization of the downtown area bus lines resulted in a noticeable reduction in the operating cost and the emissions production (Kim, 2006). The development of environmentally friendly public transportation systems is a major topic of research and the identification of the relationship between the vehicle routing and the fuel consumption or the emissions production is a crucial factor. The research on the field of transit operations can be expanded in different areas. More and more agencies such as the Federal Transit Administration (FTA) or the Federal Emergency Management Agency (FEMA) try to investigate the further involvement of the transit systems and especially buses in cases of emergency. 3

15 1.3 Preparedness for Emergency Events Evacuation Large scale disasters such as hurricanes, flood, terrorist attacks, etc. can occur anytime in different places around the world, so the importance of preparedness and emergency management is crucial. Preparedness and planning can protect human life and facilities from damage (Haghani and Afshar, 2009). Emergency management is a concept which refers to dealing and protecting from hazard risks (Haddow and Bullock, 2004). Emergency management is a procedure which includes the preparation before a disaster, then the response phase and finally the recovery from the potential consequences of the disaster to people and facilities (Afshar and Haghani, 2009). In general, emergency management consists of four phases which are the mitigation, the preparedness, then the response and the recovery. The first phase of mitigation includes all the actions that must be developed in order to reduce the potential of a disaster occurrence while the phase of preparedness includes the development of the related plans during an emergency. As far as the phase of response is concerned, this involves the different actions that should take place when a catastrophic event happens such as evacuation operations if needed. The phase of recovery must ensure the return to normal conditions (The Role of Public Transportation in Emergency Evacuation, 2008). In the phase of response, during an emergency event, the evacuation of large scale areas and large number of people is one of most important operations that must be carried out. Evacuation is an extremely important issue that can affect the life of a large part of the population related to an area in danger. Many different parameters should be considered and deeply analyzed in order the effective execution of such operations to be ensured. 4

16 Emergency evacuation can be defined as the transport of people in a safe distance from a danger. Generally, evacuations can be categorized based on two different parameters which are the size and the time. As for the size factor, considering the number of the evacuating people or the size of the evacuated area we can have a small scale evacuation such as from a building because of a fire and a large scale evacuation of a whole region because of a hurricane. As far as the time factor is concerned, an evacuation can be a no-notice or a short notice one. No-notice evacuation refers to cases such as a terrorist attack whereas short notice evacuation exists in cases such as a coming hurricane where there is a prior notification. Especially, in no-notice evacuation events the most crucial aspect is that the exact time of a hazard occurrence is unknown, something which extends the complexity of the problem (Zhang et al., 2010). No-notice disasters can have various catastrophic consequences to human life and infrastructure. However, the research that has been carried out on the specific field of no-notice evacuation until now is relatively limited (Sayyady et al., 2010). In emergency evacuation cases, traffic conditions are modified and congestion levels are extremely high, something which creates the need for more time for the evacuation operations to be completed. In order to deal with such difficulties, current best practices suggest the further use of transit vehicles during evacuation and try to analyze more the potential optimization of these operations 5

17 1.4 Evacuation and Transit Operations Transit systems and especially buses can greatly be involved in all the different phases of emergency management (Sayyady et al., 2010). In the mitigation phase transit can play an important role by ensuring its facilities while in the phase of preparedness, transit authorities should be involved in the plans development. During the response phase transit can be involved in people evacuation and in the recovery phase transit can be involved in the return of the evacuees (The Role of Public Transportation in Emergency Evacuation, 2008). The importance of transit operations is proved in cases where many citizens do not have access to other means of transportation. This fact has been highlighted through many examples as in the catastrophic events of New Orleans where many people were transit evacuated (Wolshon, 2002). Various characteristics of a bus system can result in the extended use of it during an evacuation operation. The advantages of such a system can be identified in different levels. People without different means of transportation, mainly without cars, can be transported. What is more, bus systems can be used for evacuating population with special needs such as disabled and older people (The Role of Public Transportation in Emergency Evacuation, 2008). In addition, another fact is that a bus can transfer a large number of people who otherwise would use cars, something which might have consequences in road congestion. Due to the great advantages, as described before, that some of the characteristics of transit systems can provide, the further use of buses during emergency incidents, should be ensured. However, the performance of transit operations depends on various 6

18 parameters. Different topics such as the vehicle routing problem or the fleet size in order to achieve the optimization of bus operations during an evacuation are only some of the issues that must be further analyzed. 1.5 Problem Statement and Objectives From the previous introductory analysis that was conducted, it is obvious that more research should be carried out in the field of transit operations efficiency. In general, as far as this specific research is concerned, the focus area is the optimization of some aspects of transit operations under normal and emergency evacuation conditions. Especially, different questions had to be answered such as how the potential optimization of a bus systems characteristics (which operates under normal traffic conditions) focusing on the vehicles routing can affect the Measures of Effectiveness (MOEs) of the network. Additionally, another question refers to the cases of emergency and if the evacuation clearance time can be reduced by using the regular bus line routes for evacuation instead of spending time in order to assign to the bus vehicles the specified evacuation routes. Another issue is if a developed cost model can be efficiently applied in order to identify the systems optimal routes in both normal and evacuation conditions. Regarding this research objectives, these can be identified in different areas. The accurate development of a traffic simulation model which can efficiently describe all the special characteristics of the related transportation network must be ensured. In a next phase, the main goal of this study is to deal with the problem of optimizing transit vehicle routes, based on specific parameters considering a bus network that operates under normal everyday conditions. The optimization procedure will be based on the 7

19 application of a cost minimization model. Then, the comparison of the Measures of Effectiveness (MOEs) of the network before and after applying the optimized bus routes, focusing on how vehicle routing affects the emissions production or the fuel consumption will follow. At the last part of this research a potential use of the updated bus routes in cases of no-notice emergency events for people evacuation in contrast to using the existing specified evacuation routes will be evaluated. Additionally, different evacuation strategies will be investigated. 1.6 Thesis Outline As for the outline of this specific study, it consists of 6 major chapters which address all the procedure that was followed for this thesis work accomplishment. The six chapters are presented below: The first one includes introductory information and also presents the basic terminology that will be used in this study. The basic topics of this research work such as the bus operations under normal conditions, the evacuation process or the use of transit during an emergency evacuation, are introduced at a first phase. Then, the problem statement and the main objectives of this specific research are highlighted. What is more, the general outline of this study is presented. Chapter 2 focuses on the literature review results which are thoroughly presented. This chapter includes the methodology and the main conclusions of the most important studies that were conducted worldwide and deal with issues related to the research topic of this thesis work, such as the vehicle routing problem or the optimization of transit operations duration an emergency evacuation. 8

20 In chapter 3, an extended description of the various data that was collected and used during the analysis is carried out. Then the methodology that is proposed through this study regarding the solution approach of the problem is described. In chapter 4, the different characteristics of the selected cases study are presented. All the different parameters that have to be considered are pointed out. Chapter 5 includes all the results that were obtained after carrying out the analysis that was suggested according to the methodology chapter. Various comments regarding the major findings of this research are pointed out. Chapter 6 includes the presentation of the major conclusions that can be extracted from the research that was carried out. Furthermore, the major limitations of this study and various ideas and topics for future research are presented. 9

21 2. LITERATURE REVIEW 2.1 Introduction The main objectives of this research are to carry out an optimization of a bus system routing under normal conditions of operation and then to identify if the updated routes can be efficiently used in cases of emergency evacuation. In order to achieve these objectives, a thorough review of the related literature is carried out and described in the following chapters. The literature that was reviewed is categorized in 6 different fields. The first one refers to the different simulation tools which are used for transportation related research while the second includes the literature related to the vehicle routing problem in general. The third category focuses on the literature which is related to the bus operations and the various optimization procedures regarding bus systems working under normal conditions. Two different categories are developed in order to address the majority of the research executed in the field of how bus systems can be involved in emergency conditions, during an evacuation. Especially, one category refers to short-notice evacuation events, whereas the second one refers to no-notice evacuation events, where various time limitations occur. The last category of the literature review focuses on the various cost models formulations that have been applied for transportation related optimization research. 10

22 2.2 Research on the Available Simulation Tools The first part of the literature review consists of different studies related to the development of the simulation tools for transportation research purposes. One of the first studies in this area was executed from Goode et al., 1956 of the University of Michigan. Goode et al. developed a simulation model for vehicle movements through signalized intersections. In this model the assignment of the vehicles at each intersection was done randomly. Then, M. C. Stark, 1958 produced a different simulation procedure. The author developed a model to simulate one particular Washington, D. C. traffic segment which included ten intersections, seven of which were signalized. This specific study was also one of the first in the area of computer simulation regarding transportation problems. From these first studies, with the extended limitations in the use of simulation tools, conditions have changed. Through time, simulation techniques and modeling have been developed enough in such a great level, that now comprehensive simulation analysis is a key factor to the successful execution of the various transportation related studies worldwide. Nowadays, the available simulation tools can be distinguished in three major categories: microscopic, mesoscopic and macroscopic simulation tools. A forth category can occur with the combination of the previously described tools. Microscopic simulation tools analyze traffic conditions at a detailed level by focusing on the vehicles interaction. On the other hand, macroscopic simulation tools simulate traffic in a more general level, using various equations which are based on hydrodynamic principles, while mesoscopic tools combine various characteristics of both the microscopic and macroscopic tools (Burghout, 2007). 11

23 In order to emphasize the development of the simulation tools throughout history and point out the fact that nowadays a large number of these tools are available, a study by Jayakrishnan et al., 2003 is presented next. The authors tried to address different issues regarding the available simulation tools for transit related research and focuses on the best among these tools. Suggestions for future improvements were also presented. 2.3 Vehicle Routing Problem The Vehicle Routing Problem (VRP) can be translated into identifying the optimal delivery routes from one initial point to a number of different customers, considering various constraints (Laporte, 1992). The Vehicle routing Problem (VRP) as a concept was developed approximately 50 years ago by Dantzig and Ramser as The Truck Dispatching Problem (Laporte, 2009). Since then, the related research that has been carried out in this area is huge and includes the use of different techniques and algorithm formulations in order to get optimal solutions. This chapter of the literature review presents the most important studies executed on the area of Vehicle Routing Problem and focuses on the most current in order to include the latest best practices developed in that specific research field. As it was mentioned before the first study on this topic was executed from Dantzig and Ramser, 1959 who introduced the Vehicle routing Problem as The Truck Dispatching Problem. During the following decades different people tried to analyze the problem, study the various parameters which must be considered and find the potential best solutions. 12

24 Laporte, 1992 conducted an extended literature review which included the majority of the most important algorithms for the vehicle routing problem until this time period. Especially this study focused on reviewing the basic characteristics and formulations of the most productive developed algorithms which included exact algorithms and heuristic algorithms. A main conclusion was that despite the fact that exact algorithms can be mainly used in solving small problems, they can produce relatively accurate results in general. Also it was highlighted the great efficiency of the tabu search methods and the need for more research for the further extension of these specific algorithm solving tools. Desrochers et al., 1992 analyzed another aspect of the routing problem which is the vehicle routing problem with time windows (VRPTW). The concept of the VRPTW consists of the vehicle routing problem under additional time constraints. These constraints require the start of service at specific time periods which are defined by the customer. The methodology that was followed included the formulation of a shortest path problem with time windows and the solution approach was based on the branch-andbound algorithm. Taillard, 1993 focused on the iterative search methods and suggested two techniques for accelerating the solution process for the routing problem. The first model that was formulated could be applied for geometric problems solution (Complex Euclidean problems) whereas the second technique could be used in shortest path problem solution procedures. Another tabu search heuristic solution for the routing problem was proposed from Gendreau et al., The main objective of this study was to develop a new tabu search 13

25 model considering different constraints related to the route length and capacity. The basic conclusion was that tabu search heuristic could provide in many cases the best results among the available solution techniques until this point. Kohl and Madsen, 1995 analyzed the vehicle routing problem with time windows by suggesting a new optimization technique. The major element of the proposed methodology was the Lagrangian relaxation on the related constraints. The solution procedure that the authors followed included the development of a main problem related to the Lagrangian relaxation and a sub-problem which was formulated as a shortest path. The efficiency of the specific methodology was tested out. A different solution approach was used from Shaw, 1998 who applied a local search method for the vehicle routing problem, the Large Neighborhood Search (LNS). The (LNS) method tries to find a better solution for a problem to the large neighborhood of the current solution. After applying the (LNS) technique, it was found that the efficiency of the produced results is at the same level regarding the results produced with the use of meta-heuristic methodologies. An alternative solution procedure to the routing problem was also suggested from Bullnheimer et al., The use of a new ant system algorithm was proposed. After testing the produced results with the development of various benchmark problems, it was concluded that although the results of the ant system model are efficient enough, much more research regarding this methodology should be done. The topic of studying the routing problem but under specific time windows was also analyzed from Cordeau et al., In this study a tabu search heuristic was used for the problem analysis which focused on two major topics: the periodic and the multi-depot 14

26 routing problem. The results test shown that despite the fact that the final solutions may not be the optimal ones in all the different cases, the main advantages of the solution technique that was followed were its simplicity and the minimization of the time needed for reaching the best solutions. Mester and Braysy, 2005 deal with the same problem of vehicle routing problem with specific time windows. As for the methodology point of view, the authors proposed the use of a new meta-heuristic technique for the potential solution of the problem which was developed in two phases. The first one included the identification of a solution in a local level whereas the second phase expands the search in the related neighborhood. Benchmark problem tests proved the validness of the results and the efficiency of that specific method in contrast with different methodologies. From the literature review executed and presented before, it became obvious that the related research on the field of the vehicle routing problem is huge. Laporte, 2009 executed an analytical investigation of the literature regarding the routing problem, trying to analyze the characteristics of the most important methodologies and algorithms. Especially, in this study, a brief presentation of the main optimization techniques was conducted, and some of the conclusions include the difficultness of the solution of the exact algorithms and the complexity of the meta-heuristic techniques. A different aspect of the vehicle routing problem is formulated in cases of multiple using of vehicles. Azi et al., 2010 studied the routing problem not only with multiple vehicles, but also under specific time restrictions. The formulation of the problem is based on a branch-and-price technique and its solution was done in different 15

27 phases. It was concluded that heuristic approach solutions remain the most productive tools for large - scale related problems. The dynamic multi-period vehicle routing problem was analyzed from Wen et al., Some of the main goals of this study included the minimization of the total travel cost and the minimization of the customers waiting time. The methodology included the formulation of a mixed integer linear model, and a heuristic solution approach was applied. Another related study that was conducted from Smith et al., 2010 analyzed the dynamic nature of the routing problem. Especially, the authors introduced the dynamic vehicle routing problem with different classes of vehicles and under priority constraints. The main objective of this study can be addressed as optimizing the routes in such a way in order to minimize the total delay of the system. Meta-heuristics and especially the tabu search algorithm to the vehicle routing problem were applied from Brandao, The specific problem tries to address the different parameters that must be considered when in the specific network under analysis different types of vehicles are included. The main objective of this study was the minimization of the total cost and the results that were produced after the application of the tabu search method were tested with the use of Benchmark Problems. Leung et al., 2011 tried to find a more effective solution for the two-dimensional loading vehicle routing problem. The suggested meta-heuristic methodology was a combination of tabu search and a new heuristic algorithm. The effectiveness of the previously described methodology was proved by using Benchmark testing problems. 16

28 One of the most recent studies in this specific research area was conducted from Gulczynski et al., The major topic was the periodic vehicle routing problem. The solution procedure involved the development of a new heuristic, the main characteristics of which were the use of a record to - record travel algorithm and an integer program. Benchmark method was used for the testing and the validation of the results. The periodic route problem was also analyzed by Nguyen et al., 2011 but in cases where specific time windows exist. In order to address all the different parameters that should be considered, a new hybrid meta-heuristic model was developed Tests and comparisons with the results of similar methodologies certified the effectiveness of the conclusions that were made. 2.4 Optimization of Bus Operations under Normal Conditions The literature review carried out in this field revealed that an extended research on this area has been done. There is a variety of different topics regarding the transit operations optimization that were analyzed such as optimization of headways and time schedules, optimization of number of vehicles used or optimization of the pick up points. However, the aspect that is more closely related to our study is the optimization of the bus system routes, so the literature that was executed, focuses on this specific area. Constantin and Florian, 1995 analyzed the topic of bus line frequencies by trying to provide an optimization methodology. For the problem formulation a nonlinear mixed integer programming model was developed. As a solution it was suggested the use of a sub-gradient algorithm which solves the problem in a lower bound (less constraints and variables). The major points were the fact that the developed algorithm considered the 17

29 different route choice of vehicles and various parameters such as the capacity of the vehicles and also that the proposed methodology could be applied for the analysis of large scale networks. Ichoua et al., 2003 proposed a time dependent model for vehicle routing problem, based on time-dependent travel speeds so as to address the problem of non-constant travel times. The results proved that the time-dependent models can provide better results in contrast with the models with fixed travel times, but the need for more information regarding this problem, was also indicated. Tom and Mohan, 2003 suggested a two phase optimization model for the transit routing problem. The major objective of this study was the minimization of the total systems cost through the application of a Genetic Algorithm. The proposed optimal solutions are found considering the related headways and ensuring the least operating cost and minimization of the number of vehicles that were used. Another study was carried out from Ngamchai and Lovell, 2003 proposed also the application of genetic algorithms for optimizing transit routes. Among others the importance of headway coordination was pointed out. Zhao and Ubaka, 2004 studied also the problem of bus operations optimization and especially the authors focused on optimizing the transit vehicle routes. The suggested methodology included the networks and transit routes representation and the application of the solution approach. The efficiency of the methodology and its results was testified through the comparison with similar solution approaches. From the various research executed in the field of bus vehicles optimization, it was found that generic algorithms is a tool that can produce very efficient results, so 18

30 that s why it is commonly used. In that direction, Fan and Machemehl, 2006 developed a genetic algorithm to address the problem of optimizing bus routes. A non-linear mixed integer model was developed for the specific problem. The results shown, that the increase at the size of the problem leads to the improvement of the suggested solutions. Zhao and Zeng, 2008 studied various aspects of the optimization of the transit operations. Especially the authors developed a meta-heuristic method for optimizing transit vehicle routes and vehicle headway. The main objective of this study was the minimization of the user cost. The results showed that the previously described methodology can be efficiently applied in large optimization problems. Another study at this research area was conducted from Fan et al., 2009 and deals with the urban transit routing problem (UTRP). The main objective of this specific study was the optimization of the bus routing in order to minimize user and operator costs. The methodology that was followed included the use of a multi-objective optimization algorithm. The issue of bus route optimization was also analyzed from Tang et al., This study focused on formulating a mathematical model for bus vehicle route optimization and was based on a Genetic Ant optimization algorithm. 2.5 Optimization of Bus Operations under Short-Notice Evacuation Evacuation can be categorized depending on the time or space factor. In detail, evacuation can be distinguished to no-notice or short notice depending on time factors and to large or small scale depending on space factors. Different aspects that have been analyzed in this area involve issues such as the optimal evacuation of pedestrians from a 19

31 specific area or the optimal evacuation of a large area in danger, in total. So as to meet the needs of this study, the literature focuses on the use of transit during short-notice evacuation and the optimization of the related operations. Elmitiny, 2007 deal with the problem of the efficient involvement of transit in emergency evacuation. The main objective of this study was the optimization of transit evacuation operations through identifying the optimal vehicle routes. The methodology that was followed was based on the use of a traffic simulation model. The major conclusion that was extracted was that traffic rerouting could relatively reduce delay and evacuation clearance time. An evacuation system was developed from Liu et al., 2008 in order to address the different parameters that can influence the efficient execution of an evacuation operation. The methodology that was suggested, considered different parameters such as vehicle routing, traffic condition adjustments and development of bus operations. Song et al., 2009 tried to study the general problem of optimizing the transit operations during an emergency evacuation. The authors suggested an optimization methodology for transit-dependent people in cases of short notice evacuation. The main objective of this study was the minimization of the total evacuation time and the solution approach was based on Genetic Algorithms. One of the latest studies was conducted from Abdelgawad et al., 2010 and focused on the optimization of evacuation operations which are carried out with different modes of transportation (cars, transit). Regarding the transit evacuation operations, the main objectives of this study included the minimization of the in-vehicle travel time and 20

32 the minimization of the waiting time. The problem was generally formulated as a vehicle routing problem and a heuristic approach was followed for the solution of it. 2.6 Optimization of Operations under No-Notice Evacuation As it was described before, no-notice evacuation cases occur when events with no prior notice. The major characteristic of such cases is the great limitations of the time which is provided to people and authorities to respond. As Sayyady and Eksioglu, 2010 mention the related research on the field of no-notice evacuation is limited. One of the latest studies was executed from Sayyady and Eksioglu, 2010 who suggest a methodology for transit dependent people evacuation during no-notice events. The main objective was the minimization of the total evacuation time by identifying the optimal routes for transit vehicles. A mixed-integer linear problem was formulated and a Tabu search algorithm was applied for finding the optimal solutions. Another important study on this field was executed from Zhang et al., 2010 who suggested a two phase optimization strategy regarding a no-notice emergency transit evacuation. The first phase included the identification of the safe zone areas and the pick-up points, whereas in the second phase the optimal identification of the vehicles routes was carried out. Also, Parr and Kaisar, 2010 investigated how transit signal priority to the evacuation vehicles can reduce the evacuation clearance time in a no notice event. Various simulation scenarios were tested through the use of specific simulation platforms and the efficiency of the transit signal priority strategy was identified. 21

33 2.7 Cost Models for Transportation Problems From the literature worldwide, it was obvious that the accurate cost models formulation is a key factor for the efficiency of the transportation related research. Generally, cost models are applied in transportation problems through the format of minimizing the cost of the transportation operations. One of the first studies in this area was conducted from Obeng, 1985 who carried out an extensive research on the transit cost issue. A mathematical formulation was developed in order to precisely estimate the cost of transit operations considering different parameters such as the fuel pricing or the labor cost. Some of the most current studies on the transit cost issue include the research of Feigenbaum et al., 2005 who developed a new cost model for the routing problem. Especially, the authors formulated an updated cost model and came up with a new solution approach which was based on applying modified algorithms. Chien, 2005 carried out an extensive analysis on the transit operations area focusing on optimizing the headway, the fleet size and the route choice parameters. The optimization analysis was based on applying a cost model which could precisely identify the potential values of all the factors that are related with the user and operator cost, in order to minimize the total systems cost in general. Zhao and Zeng, 2007 analyzed also the transit operations cost. The authors thoroughly investigated all the different parameters that can affect the user and the operator cost for a large scale network and tried to come up with an accurate mathematical formulation for transit operations optimization by minimizing the total cost. 22

34 2.8 Conclusions As it was shown from the literature review, there is a lot of research worldwide that has been done on various topics related to the optimization of the various transit operations. Many studies that have been carried out try to identify the characteristics of the bus systems and the principles that guide their operations. That s a way how to more easily point out existing or potential problems which might disrupt the continuity of the operations and find more efficient and feasible solutions regarding the optimization of the transit system operations, in total. However, through the literature review, it was also observed that the majority of the research that has been executed focuses on the analysis and the optimization of the characteristics of a bus system that performs under normal conditions. As for the cases of emergency and the need for evacuation of a large number of people, much research has been done on the field of the short-notice evacuation. However as Sayyady and Eksioglu (2010) point out in their study the research on the field of no-notice evacuation is limited until now. The main goal of this study is to analyze bus operations in both normal and emergency conditions. The objectives which will be tried to be addressed are firstly to apply a cost model which optimizes a bus system characteristics focusing on the routing parameter under normal conditions of operation. On a second phase of this study, the question if the regular bus line routes can be efficiently used in no-notice emergency evacuation will be answered. 23

35 3. METHODOLOGY 3.1 General This chapter is dealing with the methodology that was followed in order to accomplish the different tasks of this research. These tasks can be summarized in developing a cost model which minimizes the cost of a system of different bus lines focusing on the routing parameter and also to identify if the new updated routes can be efficiently applied to normal and emergency conditions of operations. The major sections in which the methodology can be divided are: the development of a simulation model of the selected case study network on a micro/meso-scopic level, the formulation of a cost based model which optimizes the bus routing parameter by minimizing the cost of using a specific bus line route and the modification of the simulation model in order to be applied in emergency conditions where the evacuation of a selected area has to be executed. All the different steps that had to be accomplished are summarized in the flowchart that is described in figure 2 that follows: 24

36 Start Insert data Optimization Procedure Optimal Routes Simulation Model Apply Changes to Initial Model Demand Modeling Simulation with updated bus routes Simulation under normal conditions Are MOEs better? No Model Validation Yes Bus Line in Evacuation Comparison of MOEs 0.9 < R 2 < 1 Yes No Results End Figure 2: Methodology Flowchart As for the various tasks that are involved in the previously described flowchart, the first action included the collection of the related data that had to be used in order to accomplish this specific research. The next step required the development of the simulation model. In order to efficiently develop an accurate simulation model of a transportation network, the 25

37 networks geometry, the demand modeling (private vehicles, bus lines, etc.) and the signal timings import are some of the major tasks that have to be accomplished. Then the model calibration and validation followed. The validation procedure was based on the test, where if the conditions of this test are verified, the next steps of the study can follow however in the opposite case different corrections should be applied to the model in order this to be characterized as valid. After validating the model, the simulation of the traffic characteristics under normal conditions of operation and the identification of the various Measures of Effectiveness (MOEs) of the model (travel time, delay time, speed, fuel, emissions, etc.) were executed. One major component of this research was the optimization procedure that has to take place. The optimization procedure focused on the vehicle routing problem of the buses, which is applied through the development of a cost related model, and tried to minimize the cost of using a specific bus line route, considering different parameters such as the number of buses used, the number of stops in each line, the passenger demand, etc. After executing the optimization procedure which defined the new bus routes of the system, the next step included the simulation analysis of the transportation model and the identification of the related Measures of Effectiveness (MOEs) of the model under different scenarios. The first scenario included the simulation of the network under its current transportation conditions (e.g. existing bus line routes) while the second one included the simulation of the network after applying the new bus line routes that were identified through the optimization procedure. Then the comparison of the models Measures of Effectiveness (MOEs) under the two different scenarios will help us identify the success of the bus routes optimization technique that was applied and mainly 26

38 investigate the relationship between the routing parameter and emissions-fuel consumption. The last part of this study involved the examination of weather the regular bus line routes can be efficiently used in cases of emergency focusing on a no - notice evacuation scenario. The modification of the simulation model in order to be applied in evacuation conditions (demand modeling, incident management lane closure, etc.) is described. Then, the simulation of the model under evacuation conditions followed and comparison of the Measures of effectiveness (MOEs) when the regular bus routes are used in the evacuation operations in contrast with the use of the specified evacuation routes was executed. That s a way which let us know if the regular bus line routes can be applied in both normal and emergency conditions of operation. 3.2 Data Collection In order to carry out this specific research a comprehensive dataset had to be collected. Different information should be acquired so as to be able to consider and analyze different aspects of this research. The data that was collected can be separated into two major categories. The first category refers to the data related to the development of the simulation model, whereas the second one refers to the data related to the formulation of the cost model which was used for the optimization procedure. In order to develop an accurate simulation model, different type of data is needed. The first component of the dataset referred to the basic geometry characteristics of the network which were defined through the use of the related Geographic Information System (GIS) maps. Basic elements of the geometric information included the network s 27

39 link geometry, the intersection geometry, etc. Additional data that should be collected at the initial phase of the model development regarding the network s link characteristics included the link name and type (arterial, freeway, urban road, on/off ramp, etc.), the link maximum speed and capacity, etc. The data needed regarding the network s intersection were various such as the intersection name and type (signalized, non-signalized, uncontrolled, etc.), the related turning movements, etc. After acquiring the traffic signal timings, one of the most important datasets that had to be collected for the model development refer to the actual vehicle volumes for various vehicle modes that use the case study network and also the percentages of the related vehicles turning movements. Additionally, information regarding the various bus lines of the network and their characteristics were acquired. As for the second major category of data selection this refers to the information that was needed in order to precisely develop and apply the cost model for the optimization procedure. The information that had to be gathered at this section included the length of the case study bus line routes and additionally the length of the alternative routes of each bus line. Also, the values of all the different cost parameters that must be considered, the number of intersections at each different route and the corresponding delay of each intersection should be acquired. The last part of the related dataset included the average speed of the bus vehicles and the average walking speed, the average dwell time of the different types of bus vehicles and the average waiting of people at the bus stops and the passenger demand at the different bus stops of the network. 28

40 3.3 Simulation Model Development For the simulation model development, AIMSUN NG 6.1 simulation platform was used. AIMSUN is a complete simulation package which allows the execution of transportation related analysis in microscopic, mesoscopic and macroscopic level. Using AIMSUN simulation platform different transportation related scenarios and conditions can be developed and analyzed as various tools such as link and intersection geometry editors, traffic and signal timings analyze tools or bus systems editors are provided. The simulation model development included among others the network s geometry creation, the signal timings import, the bus lines identification and the demand modeling. As far as the demand modeling development is concerned, the trip generation was based on assigning the real traffic volumes of private cars and heavy vehicles at the entry points (external intersections of the simulation model) of the network according to the demand matrixes that were provided from the related transportation agencies. The provided matrixes also included the route choice of the simulated vehicles in the format of turning percentages at each intersection. However, the final produced volumes from the model s simulation were modified due to the dynamic traffic assignment strategy of AIMSUN simulation platform (e.g. consideration of congestion impact at the traffic conditions). This fact created the need for the model calibration and validation in order the simulated vehicle volumes to match with real life traffic conditions. A last task to be completed before the model to be ready for use was the calibration and validation of the model. The calibration of the model was based on adjusting different parameters such as the lane changing or the car following model so as 29

41 to more accurately represent real life traffic conditions. As for the results validation this was based on comparing real field traffic volumes with the volumes estimated by the simulation platform. Because of the fact that in this research we deal with a meso-scopic simulation model which included an extremely large number of roads and intersections, the comparison procedure for the result validation was limited to internal intersections of the major corridors of the network. The validation procedure was based on using the test method which requires that the factor which is produced from the comparison of the actual field volumes and the model calculated volumes to be between 0.9 and 1.0 in order the model to be valid. After the calibration and the validation of the model, the analysis of the traffic characteristics of the case study area followed. The model s simulation mainly focused on P.M. peak period from 4:00 to 6:00 p.m. In order to accurately identify the various characteristics of the selected case study transportation network, the simulation analysis defined the major Measures of Effectiveness (MOEs) of the related system. However, in this case, the simulation analysis focused on different Measures of Effectiveness (MOEs) than the usual ones, such as the fuel consumptions or the emissions. Some of the Measures of Effectiveness (MOEs) that were calculated were: fuel consumption, pollution emissions (Co, NOx, HC), travel time, delay time, speed, etc. 30

42 3.4 Optimization Procedure The various modes of transportation have different characteristics which can affect the total systems performance. This research although it considers how the different modes affect the traffic conditions in an urban area, it focuses on the public transportation modes and especially buses. Different parameters such as the vehicle routing, the fleet assignment, or the people demand are crucial for the efficiency of a bus system in total. In this research there was a focus on the bus routing problem and how a potential optimization of a selected set of bus lines can improve the total networks performance. The optimization analysis was based on the development of a least cost related model. The minimization of the cost that corresponds to the use of a specific bus line route, by optimizing different factors which include the fleet size or the number of stops per line and affect this cost, revealed the optimal route for one selected bus line or for the system of bus lines under analysis. After applying the cost related optimization technique which defined the optimal routes from the least cost point of view, the application of the new routes to the traffic network and its consequences was tested. The network performance and as a result the optimization procedure was testified by comparing the systems measures of effectiveness (MOEs) before and after applying the new routes. 3.5 Mathematical Model For the mathematical model development a combination of the existing literature review conclusions such as Chien et al., 2001 or Chien, 2005, etc. on the cost model 31

43 development area with some modifications in order additional parameters to be considered (bus dwell time, intersection delay, etc.), was applied. The cost that corresponds to the use of a specific bus line route has many components that have to be analyzed. In this study a non-linear mathematical model that minimizes the total cost of the bus system operations was developed. The different cost variables that were used in this study are summarized in the following table: Table 1: Cost Variables Parameter Definition Units Total cost $ Supplier cost $ User cost $ Operating cost $ Intersection delay cost $ Dwell time delay cost $ Access time cost $ Waiting time cost $ In vehicle time cost $ 32

44 The objective function of our study referred to the minimization of the total cost of bus operations. The objective function is described in formulation (1) as follows: M m ze (1) Where: is the total cost = 1 2 j = 1 2 m The above objective function in equation (1) minimizes the total cost when a system of different bus lines operates simultaneously in a transportation network. Parameter corresponds to the set of the different bus lines ( is the maximum number of bus lines and is equal to 6 in this case study) that was applied to the optimization analysis whereas parameter jcorresponds to the available alternative routes for each different bus line (m is the maximum number of alternative routes and is equal to 4 in this case study). The total cost of the bus system consists of two major components which are the supplier cost and user cost (Chien, 2005): Where: = (2) : Corresponds to the total system s cost 33

45 : Corresponds to the supplier s cost : Corresponds to the user s cost Equation (2) above describes the fact that the total cost of a bus system is equal to the sum of the supplier s and user s cost Supplier Cost The supplier cost refers to the cost of the bus system operators where different parameters can affect its values. The major parameters that can affect the supplier s or operator s cost are summarized on equation (3) below: Where: Corresponds to the supplier s cost Corresponds to the operating cost Corresponds to the intersection delay cost Corresponds to the dwell time delay cost The above equation (3) describes the fact that the supplier s cost is affected by three different parameters which are the bus line operating cost, the intersection delay cost and also the bus dwell time cost. Especially, it is stated that the supplier s cost is equal to the sum of the bus line operating cost (cost of fuel, cost of driver, etc.) plus the 34

46 cost that is created because of the delay that buses face on the different network s intersections plus the cost because of the time that busses spend for the passengers boarding / un-boarding at the bus stops. The set of parameters that was involved in the identification of the supplier cost and its components is presented in table 2 that follows. Furthermore, the variables that correspond to each one of the different parameters that were used in the cost model are defined in the same table. Table 2: Parameters Variables - Units for Supplier Cost Parameter Definition Operating cost factor Route length Number of seat capacity I vehicles Number of seat capacity II vehicles Vehicle speed Intersection delay cost factor Intersection delay Number of intersections Dwell time cost factor Dwell time of seat capacity I vehicles Dwell time of seat capacity II vehicles Number of stops 35

47 Focusing on the bus line operating cost, the different variables that are related to this specific type of cost are shown on equation (4) below: (4) Where: : Stands for the operating cost Stands for the cost factor related to the operating cost Stands for each bus route length Stands for the fleet size of vehicles of seat capacity Stands for the fleet size of vehicles of seat capacity Stands for the bus vehicles speed Equation (4) defines the relationship between the operating cost and all the different variables that can affect its value. Especially, it is stated that the operating cost of one bus line is equal to the specific cost factor related to the operating cost multiplied by the length of each specific bus line route, multiplied by the fleet size of the different seat capacity buses that are used in a specific line and all these divided by the operating speed of the bus vehicles. A new parameter regarding the intersection delay was added to the formulation. This can let us the delay that is caused to the bus lines operations from the background traffic (private cars, trucks, etc.) of the network to be considered in the total supplier s 36

48 cost. The variables that influence the value of the intersection delay cost are presented in equation (5): Where: Stands for the intersection delay cost Stands for the cost factor related to the intersection delay cost Stands for the average intersection delay at each bus line route Stands for the number of intersections at each bus line route Stands for the fleet size of vehicles of seat capacity Stands for the fleet size of vehicles of seat capacity Equation (5) focuses on the relationship between the intersection delay cost and how different variables can affect its value. This specific equation describes the fact that the intersection delay cost of one bus line route is equal to the specific cost factor related to the intersection delay cost multiplied by the average intersection delay that vehicles face at this specific route, multiplied by total number of intersections at the specific route and lastly multiplied by the fleet size of the different seat capacity buses that are used in this line. The last main factor that is closely related to the supplier s cost is the cost that is caused by the dwell time of buses or else the time that buses are immobilized at the bus 37

49 stops for the passenger serving. The parameters that influence the dwell time related cost are: Where: Stands for the dwell time delay cost Stands for the cost factor related to the dwell time cost Stands for the number of stops per each bus line route Stands for the mean dwell time of buses of seat capacity : Stands for the mean dwell time of buses of seat capacity : Stands for the fleet size of vehicles of seat capacity : Stands for the fleet size of vehicles of seat capacity From the above equation (6) it is obvious how different variables affect the value of the intersection delay cost. Especially, it is stated that the dwell time related cost is equal to the specific cost factor related to the dwell time cost multiplied by the number of stops at each specific bus line route, multiplied by the average dwell time per different seat capacity vehicle, multiplied by the number of vehicles of each different seat capacity that are assigned at a specific bus line route. 38

50 3.5.2 User Cost The user cost refers to the cost of the bus system users or else the passengers who are transit and especially bus dependent for their trips. The basic parameters that were involved in the user s cost identification are presented in the following equation (Chien et al., 2001): Where: Corresponds to the user s cost Corresponds to the access time cost Corresponds to the waiting time cost Corresponds to in vehicle time cost Equation (7) describes how different parameters such as the access time at bus stops, the waiting time of people at bus stops and the time that passengers spend riding the bus affect the users cost in total. In addition, in equation (7) is stated that the user s cost is equal to the sum of the passenger access time cost plus the passenger waiting time cost plus the in vehicle time cost. How these three previously described components of the user s cost are influenced from some additional factors each one separately, is something that is explained later in this section. The set of parameters that were used to define the user cost is presented in table 3. The variables that correspond to the different parameters are also included at the same table below: 39

51 Table 3: Parameters Variables - Units for User Cost Parameter Definition Access distance Vw Walking speed Number of stops Number of passengers Walking distance cost factor Waiting time Number of seat capacity I vehicles Number of seat capacity II vehicles Waiting time cost factor In-vehicle cost factor Route length V Vehicle speed The passenger access time cost is an important factor for the user cost identification. The factors that are related with the final value of the access time cost are described in equation (8): (8) Where: 40

52 Stands for the access time cost Stands for the cost factor related to the access time cost Stands for the average passenger walking distance Stands for the number of stops at each bus line route Stands for the passenger demand per bus stop : Stands for the average passenger walking speed In the above equation it is described how different parameters affect the passengers access time cost. It is shown that the access time cost is equal to the cost factor related to the access time cost multiplied by the average passenger walking distance in each line, multiplied by the number of stops at each different route, multiplied by the passenger demand per bus stop and all these divided by the average passenger walking speed. As for the waiting time cost because of the waiting time of passengers at the bus stops, different parameters that can affect its value are summarized in equation (9) below: (9) Where: : Stands for the waiting time cost : Stands for the cost factor related to the waiting time cost Stands for the number of stops at each bus line route 41

53 : Stands for the passenger demand per bus stop : Stands for the fleet size of vehicles of seat capacity Stands for the fleet size of vehicles of seat capacity In equation (9) it is presented how the different parameters influence the waiting time cost. Especially, it is stated that the waiting time cost is equal to the cost factor related to the waiting time cost multiplied by the number of stops at each different route, multiplied by the passenger demand per bus stop and all these divided by two times of the fleet size of the different seat capacity buses that are used in this line. The last factor that is related to the user cost is the passenger in vehicle time cost. The in vehicle time cost is related with different parameters which are: (10) Where: : Stands for the in vehicle time cost : Stands for cost factor related to the in-vehicle travel time : Stands for the number of stops at each bus line route : Stands for the passenger demand per bus stop : Stands for the fleet size of vehicles of seat capacity : Stands for the fleet size of vehicles of seat capacity : Stands for the average bus vehicle speed 42

54 : Stands for the bus route length In equation (10) is described how different parameters affect the in-vehicle travel time cost. It is stated that the in-vehicle travel time cost is equal to the cost factor related to the in-vehicle travel time multiplied with the route length, multiplied with the number of bus stops at each route, multiplied with the passenger demand per bus stop, multiplied with the buses fleet size and all these divided by the average bus speed Model Constraints The suggested constrains will identify the range of the parameter values in order to reach the best possible solution. The constraints can vary in different levels but are here to ensure the feasibility and the optimality of the recommended solutions. The major constraints of the formulation were as they follow: Variables Non Negativity:, (1) The application of constraint (1) ensures the non-negativity of the values for the set of the different variables of the formulation 43

55 Fleet Size: (2) Where: : Stands for the seat capacity of bus vehicle type I : Stands for the seat capacity of bus vehicle type II : Stands for the fleet size of vehicles of seat capacity : Stands for the fleet size of vehicles of seat capacity : Stands for the number of stops at each bus line route : Stands for the passenger demand per bus stop per line Constraint (2) ensures that the fleet size of the bus vehicles that is assigned in each bus line and as a result to the system in total, can serve the passenger demand so as the uncovered demand to be the minimum possible. Passenger Waiting Time: (3) Where: : Stands for the fleet size of vehicles of seat capacity : Stands for the fleet size of vehicles of seat capacity Stands for the maximum allowable waiting time at bus stops 44

56 The application of constraint (3) in the formulation ensures that the passengers waiting time at a specific bus stop of the system will not exceed the maximum allowable passenger waiting time at a bus stop. Number of Bus Stops: minls maxls (4) Where: : Stands for the number of stops at each bus line route : Stands for the minimum number of bus stops per route : Stands for the maximum number of bus stops per route The above constraint (4) states that the assigned number of bus stops per each bus line route must not be less than the minimum allowable number of bus stops and also must not exceed the maximum allowable number of bus stops per bus line route. Variables Integrality:,, (5) Constraint 5 ensures that integer variables in the model are applied. 45

57 3.6 Solution Approach Result Analysis The mathematical model was solved using LINGO 13.0 optimization software. LINGO software is a qualified tool which was developed for building and solving Linear, Nonlinear, Quadratic, Stochastic, Integer and other optimization models. LINGO can provide a set of tools such as program language optimization models, a full featured environment for problem edition, and a large number of optimization problem solvers. As far as this research is concerned, by adjusting different parameters and options, the software became able to be used for solving transportation related optimization problems. The solution technique that was applied for solving the mathematical non linear cost model through the optimization software was based on the Steepest Edge Algorithm. Steepest Edge Algorithm was developed for identifying the searching direction for finding the optimal solution in non-linear problems when iterative solution methods are used. After applying the optimization procedure in LINGO software, the non linear solver identified the optimal solution which minimizes the total system s cost after checking all the different solution combinations. The major outputs of the optimization procedure were: minimum total cost of the system, optimal bus routes for each different bus line, optimal number of bus vehicles per line and optimal number of stops per bus line. The efficiency of the optimization procedure that was followed in this research and its results were tested in two different levels. The first one included the comparison of the cost values (total cost, supplier cost and user cost) if the current conditions of the traffic network are considered (current bus routes, fleet size, number of stops, demand) 46

58 with the case when the optimized characteristics of the bus system, after the optimization procedure, are applied. The second strategy for the procedures testing included the comparison of the Measures of Effectiveness (MOEs) of the simulation model. Especially, the (MOEs) of the simulation model which were produced from the current traffic conditions (current bus routes, fleet size, number of stops, demand) were compared with the (MOEs) of the simulation model after applying the suggested changes (updated routes, new fleet size, etc.) from the optimization analysis. 3.7 Future Demand and Cost After identifying the optimal solution to the problem by applying the previously described optimization procedure and testing the optimality of the suggested results, an additional analysis followed. This analysis concentrated on identifying how a potential future increase in the passengers bus demand will affect the various parameters that are related to the bus system s cost identification. In order to identify the future relationship between cost and demand, different demand increase scenarios were applied to the optimization cost model and the updated optimal solutions for each different scenario cases were pointed out. 3.8 Evacuation Analysis The mathematical model was applied until this point in cases were public transportation operate under normal traffic conditions. At this point, research focuses on cases of emergency where the need for evacuation of a specified area occurs something which affect all the network s characteristics in total. 47

59 After an emergency event where a no notice evacuation is required, the time limitations are extended, something which causes great troubles at the evacuation operations regarding especially the transit dependent people. In this study it was testified if it is possible to overcome the time issues and generally reduce the evacuation time by using the regular bus line routes for the evacuation of the transit dependent people instead of spending additional time in order the existing evacuation routes to be assigned to the evacuation bus vehicles. The first step of the evacuation analysis included the development of a case study emergency scenario and the identification of its characteristics (nature of the danger, location and time, evacuation demand etc.). An important factor that had to be clearly identified was the increased demand at the network because of the evacuation. Especially, the demand was identified in two different levels. The first one refers to the bus trips in the network that were created because of the evacuation of the transit dependent people while the second refers to the increased evacuation trips which were carried out with private cars. All the evacuation trips in this research were estimated based on the census data of the area under evacuation. The location of the pickup points and the safe zones had to be identified as well. As for the pickup points for the transit dependent citizens, the closest bus stops in a safe distance from the emergency event were assigned for the bus demand collection. As far as the safe zones are concerned, their location was identified in a region out of a one mile radius area from the center point of the emergency event. 48

60 An important issue regarding the involvement of public transportation in emergency evacuation is the selection of the bus lines that are used in the evacuation operations. The criteria for selecting these bus lines was based on their proximity to the evacuated area, the location of their bus stops which could be used as pickup points and also their regular routes. In this research only the optimized bus lines that were used for the optimization procedure under normal conditions of operation were candidates for use to the evacuation operations. The identification of the existing evacuation plans and mainly the existing evacuation routes followed so as to be able to compare the use of the regular bus routes with the use of the existing evacuation routes to the evacuation operations. The last part of the analysis included the simulation of the evacuation operations so as compare the Measures of Effectiveness (MOEs) of the use of the regular bus lines in evacuation in contrast with the use of the specified evacuation routes. The analysis focused on the comparison of the bus evacuation operations clearance time for different strategies (signal timings adjustments, lane blockage, etc.). Bus System clearance time is the total time needed for the evacuation of all transit dependent citizens. In this research, clearance time was defined from the departure time of the last bus plus its dwell time at the origin and the destination point plus the travel time of this vehicle between the pickup point and the safe zone. 49

61 4. CASE STUDY 4.1 General The case study area of this research concentrated on the greater area of Washington, the District of Columbia. Washington D.C. is the capital of the United States since 1790 so it is not part of any U.S. state. In figure 3 that follows, through a Google map image is depicted the District of Columbia which is identified in the related shape in black: Figure 3: District of Columbia (Google Earth) 50

62 The specific district is located at the east part of the U.S and is surrounded by the states of Maryland and Virginia. The whole area is characterized by the existence of Potomac River which is a physical border between the specific district and the other states. The district in total covers an area of 68.3 square miles which are translated into 61.4 square miles of land and 6.9 square miles covered with water. As for the demographics, the estimated population by the end of 2011 was 617,966 people. However, the population number raise up to 1,000,000 people for an average day due to the commuters from the close areas of Maryland and Virginia. Another important parameter that strongly affects the demographics of the Washington D.C is the everyday tourist population which is attracted from the various historical and government buildings (U.S. Census Bureau, 2010). The selected case study area for this research is a part of the Washington D.C which is located in the downtown area and consists of approximately 2.8 square miles. The corridors borders which identify the specific area are: P Street at the north part, Constitution Avenue at the south part, 23 rd Street at the west part and North Capitol Street at the east part. 51

63 23 rd Street P Street North Capitol Street Constitution Avenue Figure 4: Case Study Area (Google Earth) The specific area is characterized by the complexity of the transportation network in general. The large number of signalized intersections, the great involvement of public transportation and the increased congestion are some of the major network s characteristics. It was selected as case study for various reasons. Washington D.C. is highly populated and with great tourist demand, so the transit dependent people number is significant. Furthermore, downtown Washington D.C area is served by an extended bus system, something which can assist us in analyzing the bus system operations and characteristics in general. What is more, the specific area includes the existence of a large number of historical monuments and government buildings which can be target for potential terrorist attack. Also, the proximity of the area with the current evacuation 52

64 routes of the related district is a key factor for this research analysis and that s one of the major reasons why this area was identified as the case study one. 4.2 Simulation Model Development A major step for the simulation model development was the road and intersection geometry construction. The construction was based on the use of a combination of Google Earth images maps and ArcGIS files. In general, the network s characteristics include a model of 1.2 miles x 2.6 miles dimensions and 512 major intersections (signalized, non signalized, etc.). Then the import of additional information such as link name, type, speed and capacity or intersection name, type and turning movements was executed using the provided data files from the Washington Metropolitan Area Transit Authority (WMATA). The signal timings adjustment to real life conditions is crucial for the accuracy of the analysis that will be carried out. The import of the signal timings was based on the use of the provided SYNCHRO files (SYNCHRO is specialized software for traffic signal analysis) from the Washington Metropolitan Area Transit Authority (WMATA). The data that were provided included information of the signal timings for three different time periods which were: A.M. peak period from 7:00 to 9:00 a.m., off peak period from 10:00 to 12:00 a.m. and P.M. peak period from 4:00 to 6:00 p.m. The additional parameters that had to be specified regarding the signals configuration included the identification of the Yellow time which was set to 4 seconds and the red time which was set to 50% of the related green time. As for the interphase 53

65 time and the offset, these parameters were adjusted based on the information that was included at the related SYNCHRO files. Regarding the import of the traffic volumes to the network, this phase is one of the most crucial ones for the accurate demand modeling of a simulation model. For the import of the traffic volumes to the model, the use of the external intersections of the system for the volume import and the internal intersections for the model calibration and validation were used. The external intersections and the related links were the vehicles entry points at the system (links at the boundaries of the case study area, points such as close to buildings of significant demand generation created new entry points at the system, etc.). The real volumes data for the external intersection of the simulation model was provided through demand matrix files from the Washington Metropolitan Area Transit Authority (WMATA). Approximately 101 intersections were identified as external ones and the related flow of vehicles (veh./hour) were inserted to the system. Additionally, the initial route choices of vehicles inside the network were identified through the turning percentages of vehicles at each intersection that were provided from WMATA. The volumes data included two different types of vehicles and especially focused on the volumes of the private car and heavy vehicles of the case study network. The volumes of the public transportation systems were introduced in the model through the headway parameter of the related bus lines. 54

66 4.2.1 Transportation Bus System As for the modes of public transportation, downtown Washington D.C has a significantly developed transit network. The Washington Metropolitan Area Transit Authority (WMATA) which was founded on 1967 is a government agency that is responsible for organizing and providing transit services in the Washington D.C. metropolitan area. The basic components of the WMATA transit system are the Metrorail, the Metrobus and the MetroAccess. Metrobus services are provided in an extended area of 1,500 square miles in Washington D.C., Maryland and Virginia. A fleet size of 1,480 vehicles is serving approximately 300 bus routes with around 12,000 bus stops. During the fiscal year million trips were carried out through Metrobus services with an average of around 400,000 trips per typical weekday (WMATA, 2011). As far as this research is concerned, it focused on the operations of the Metrobus system and a total of 33 different bus lines are identified in the case study area. The bus line routes and their schedule were identified using the related maps that were provided from the Washington Metropolitan Area Transit Authority (WMATA). A sample of these maps is provided in figure 5 below: Figure 5: Bus Line 37 55

67 Based on the schedule of each bus line and their corresponding headways, the bus vehicle volumes were calculated and inserted to the simulation model. Additionally, using the related bus lines maps, the number and the location of the bus stops of each bus line were identified Calibration Validation The calibration process in this research focused on adjusting different default parameters of the simulation platform in order the real life traffic conditions to be more accurately presented. This research focuses on calibrating the Car Following Model parameter and the Lane Changing parameter, as they strongly affect the traffic assignment in the simulation model. As for the Car Following Model, the three available options (Leader Deceleration, Average of Follower & Leader Deceleration, and Sensitivity Factor) were analytically tested out. As far as the Lane Changing Model, the Percentage Overtake factor (percentage of the desired speed of a vehicle below which the vehicle may decide to overtake) and the Percent Recover factor (percentage of the desired speed of a vehicle above which a vehicle may decide to back into the slower lane) were analyzed and adjusted. After the model calibration and validation, in order to identify the Measures of Effectiveness (MOEs) of the system, various simulation runs took place which focused on the P.M. peak period from 4:00 to 6:00 p.m. 56

68 4.3 Mathematical Model Optimization Procedure In this research, the optimization procedure concentrated on optimizing the characteristics and mainly the vehicle routes of 6 randomly selected Metrobus lines. Form the literature it was found that until now research focused on the characteristics of one bus line, so in order this analysis to match more with real life traffic conditions 6 bus lines were considered in the optimization analysis. For each bus line, 4 alternative routes were identified and were applied in the optimization analysis (4 alternative routes for each bus lines were selected in order to limit the size of the problem in 4096 different combinations of bus lines and routes). One of the major parameters of this research was the fact that the 6 different lines should operate simultaneously. So, in order to reach the optimal solution for the system, 4096 different combinations of bus line routes had to be checked and evaluated Parameters Values Some of the major components of the developed least cost model were the different cost factors that had to be considered to the analysis. After thoroughly examining the related literature and based on related research such as Chien et al., 2001, Chien, 2005 or Parry and Small, 2009, etc. the values of the various cost factors are summarized in the following table: 57

69 Table 4: Cost Factor Values Parameter Definition Value ($) Operating Cost 50 Intersection Delay Cost 15 Dwell Time Cost 10 Walking Distance Cost 10 Waiting Time Cost 12 In-Vehicle Time Cost 8 As for the additional parameter values that were used in the optimization analysis, a major variable that had to be identified was the passenger demand at bus stops. This was done using the average weekday ridership data that was provided from the Washington Metropolitan Area Transit Authority (WMATA). Also, the bus delay at each intersection was identified from WMATA data. The length of each different bus line was calculated by using the related Google images and specialized software. The major tool that was used was Gmaps Pedometer which allows the accurate identification of a path route and its length. Other parameter values that had to be specified included the average bus vehicle speed which was set to 25 miles/hour or the average walking speed which was set to 3 miles/hour. Additionally, it was concluded that two bus vehicle classes operate at the case study area, so in order these conditions to be represented, bus vehicles of 42 seats capacity and bus vehicles of 60 seats capacity with average dwell times of 0.5 minutes and 0.58 minutes respectively were considered. Regarding the constraints configuration, the maximum passenger waiting time at bus stops was set to 20 minutes, 58

70 the minimum number of bus stops was set to 3 per mile and the maximum number of stops was set to 5 per bus route mile. These were the values of all the major parameters that were included to the least cost model that was developed for the optimization analysis of this research. 4.4 Emergency Conditions Evacuation All the previous analysis described the case when the transit systems operate under normal conditions. However what will happen when an emergency occurs which will create the need for an affected area evacuation. This research focused on cases of no notice evacuation events where great time limitations exist. Especially it was identified if time could be saved by using the everyday bus line routes for transit dependent people evacuation instead of spending time in order to assign the existing evacuation routes plans to the evacuating bus vehicles Existing Evacuation Plans The current evacuation plans are mainly developed by the District Department of Transportation and refer to the greater Washington metropolitan area. The evacuation plans that are included in the previous plan identify all the major and secondary corridors that should be used during the evacuation operation. In general 19 major routes are assigned for the emergency evacuation and all of them extend toward the Capital Beltway (I-495) (DDOT, 2012). The major routes that are assigned for the district evacuation involve: Canal and Benning Road, Constitution Avenue, Wisconsin Avenue, Connecticut Avenue, Georgia 59

71 Avenue, Rhode Island Avenue, New York Avenue, Kenilworth Avenue, Pennsylvania Avenue, 16th Street NW, Interstates 295 and 395 and lastly Key Bridge. The previously listed routes are summarized in the following figure: Evacuation Routes Figure 6: Evacuation Routes (dc.gov/dc/) The additional evacuation plans include the involvement of police officers in critical intersections or the adjustment of the signal timings on the main streets so as to provide more green times to the evacuating vehicles. Additionally, Pennsylvania Avenue NW, will serve as the dividing line for the emergency plan. Evacuees above Pennsylvania Avenue will be directed to take north, east and westbound evacuation route, while evacuees below Pennsylvania Avenue will be directed toward south, east and westbound evacuation routes (DDOT, 2012). 60

72 4.4.2 Evacuation Case Study Scenario As for the case study scenario, this included a terrorist attack at George Washington University which is located in the Downtown Washington D.C. area. Figure 7: George Washington University (Google Earth) The no notice terrorist attack took place at 3:45 p.m. at a center building of the university, something which created a need for an extended area evacuation. In similar cases, it is suggested that a total area of a half a mile radius from the attack point should be evacuated. As far as this case study is concerned, after applying this half a mile radius area, it creates the need for evacuation of the whole area that is covered from the university facilities. 61

73 4.4.3 Simulation Model Adjustments In order to start the simulation analysis regarding the evacuation operations, the next task that had to be accomplished was the identification of the different safe zones location. According to the official evacuation plans, the safe zones should be located out of a one mile radius area from the location of the emergency event. In order to follow this constraint, three safe zones location were identified at Stead Playground area, at D.C Convention center and lastly Gallery Place Chinatown area. After analyzing the various routes of the different bus lines which were identified in the Downtown Washington D.C area, it was found that bus line 80, bus line 42 and bus line S1 could assist in the population evacuation. Regarding the pick-up points, the closest bus stops can be the optimal pick-up locations. In this case three different bus stops were assigned as pick up locations, one for each of the three different bus lines that will be used for the evacuation operations. The selected pick up points and safe zone locations are shown in the next figure where P1 corresponds to bus line 80 pickup point, P2 is related to the pickup point of bus line 42, P3 refers to the bus line s1 pickup point, S1 corresponds to Stead Playground area, S2 refers to D.C. Convention Center, S3 is related to Gallery Place Chinatown and the location of the terrorist attack is described with a symbol in red: 62

74 Figure 8: Pickup Points - Safe Zones In the previous chapters the existing evacuation plans and the specified major evacuation routes were reviewed as they were provided from District Department of Transportation. As far as the greater area of the George Washington University is concerned, the closest evacuation routes include: Georgia Avenue (NW 7 th Street), NW Pennsylvania Avenue, Rhode Island Avenue, New York Avenue, 16 th Street, Constitution Avenue and Connecticut Avenue. Another important parameter that had to be specified regarding the evacuation model development was the identification of the evacuation demand. After reviewing the data which were available for the George Washington University and considering that the 60% of the university population is transit dependent and that the average private car ridership is 1.3 people, we developed the evacuation demand. According to the previous 63

75 information and considering the number of pedestrian evacuees and the fact that for a regular day a specific percentage of the university faculty and students will be present at the university facilities the time of the incident, the evacuation demand was approximately as follows: 5000 transit dependent citizens and 2500 private cars generated trips. For assigning the car demand to the simulation model, three different volume entry points were created, whereas for transit dependent citizens, a fleet size of 84 bus vehicles of 60 seats capacity were assigned. In order to analyze the bus system evacuation operations, various assumptions were developed. First of all, the metro stations of the close area were closed for passengers service. As for the time factor, the terrorist attack took place at 3:45 p.m., the event was notified by the authorities by 4:00 p.m. and the bus system evacuation operations started at 4:30 p.m. as a time period of 30 minutes is necessary for the fleet size availability ensuring and the operations programming and coordination. According to the formulation of Levinson et al. (1973) and considering the transit people demand, in this case study the evacuation bus dwell times were set to 3 minutes with a standard deviation of 2 minutes. Lastly, 2 different evacuation strategies were tested and evaluated: Lane Blockage (Blockage of the major roads that are related to the evacuation routes) and Signal timings adjustment (Priority to evacuation vehicles by adjusting the green time at the intersections which are included to the evacuation routes to 240 seconds according to the official evacuation plans). 64

76 5. RESULTS ANALYSIS This chapter includes the results that were obtained after the analysis that took place in accordance with the previously described research methodology. The results are fully described through four different categories. The first includes the results of the optimization procedure that was applied to the 6 randomly selected bus lines and then the model calibration and validation results then will follow. The third compares the systems measures of effectiveness before and after the application of the optimized bus line routes under normal traffic conditions of operation. The last category focuses on the application of the updated bus routes in evacuation operations and compares the results of such a decision in contrast with the use of the specified evacuation routes. 5.1 Optimization Procedure Cost Results After applying the optimization procedure for minimizing the total cost of operations for the system of the 6 selected bus lines, the optimal solution was reached by testing 4096 different combinations of bus line routes. The minimum average cost per line was specified to ($). 65

77 In order to reach the minimum cost of the system, the various parameters of each bus line that influence the cost should be optimized. Regarding the characteristics of each case study bus line separately, for bus line G8 alternative route G8-3 was identified as the optimal one. Additionally, 4 bus stops should be assigned to this specific route and as for the fleet size 3 buses of 42 seat capacity should be included. The updated route of bus line G-8 is presented in the following figure: Figure 9: Line G-8 Updated Route As for bus line 37, the optimization analysis assigned 4 vehicles of 42 seats and 7 bus stops. Alternative route 37-4 was identified as the optimal one. 66

78 Figure 10: Line 37 Updated Route The next case study line that was under analysis was bus line 42. Due to the high demand that was identified to this specific bus line, it was necessary an extended fleet size to be assigned. Especially, the cost model required 1 bus of 42 seat capacity and 4 buses of 60 seat capacity in order the related demand passengers demand to be covered. Also 5 bus stops must be used. As far as the optimal route of bus line 42 is concerned, alternative route 42-1 is the best own as it is stated in figure 11: 67

79 Figure 11: Line 42 Updated Route As for bus line S1, 6 bus stops should be assigned to the new route which is alternative route 3. Due to the fact that the people demand was low, only 3 bus vehicles of 42 seat capacity must be used. The optimal route is alternative route S1-3 and is depicted in the following figure: 68

80 Figure 12: Line S1 Updated Route In order to reach the system s optimal solution, bus line 80 should have 9 bus stops. The specific line is one of the highest passengers demand, so in order all this demand to be served the fleet size should include 1 vehicle of 42 seat capacity and 5 bus vehicles of 60 seats capacity. The optimal route as it is shown in the following figure is alternative route 80-3: 69

81 Figure 13: Line 80 Updated Route The last line under analysis was bus line N2. For this line the application of the non-linear cost model showed that 8 bus stops should be used and as for the fleet size 2 buses of 42 seats capacity and 1 bus of 60 seats capacity should be assigned in order to cover the related passengers demand. The optimal route was proved out to be alternative route N2-2, something which is shown in figure 14: 70

82 Figure 14: Line N2 Updated Route All the previously described results are summarized in the following table: Table 5: Optimization Procedure Results Bus Line Optimal Route Busses 42-Seat Busses 60-Seat Bus Stops Minimum Cost ($) Line G8 Alternative Line 37 Alternative System Cost Line 42 Alternative , Line S1 Alternative Average Line Cost Line 80 Alternative , Line N2 Alternative