Public Railway Disruption Recovery Planning: A New Recovery Strategy for Metro Train Melbourne

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1 Public Railway Disruption Recovery Planning: A New Recovery Strategy for Metro Melbourne Tim Darmanin 1 and Calvin Lim 2 Department of Mathematics and Statistics, University of Melbourne Parkville, VIC 3010, Australia t.darmanin@pgrad.unimelb.edu.au 1 calim@trinity.unimelb.edu.au 2 Heng-Soon Gan Department of Mathematics and Statistics, University of Melbourne Parkville, VIC 3010, Australia hsg@unimelb.edu.au Abstract We examine the consequences of disruptions on the Metro Melbourne in this paper. The current recovery plan employed by the Metro Melbourne is compared with a new proposal based on existing route buses. A mathematical model, where the objective is to minimize commuter discomfort, has been developed accounting for a number of operational constraints. We implemented our model on the Epping line and results indicate significant improvement in servicing stranded commuters. We note that the new proposal is able to transport more stranded commuters to their designated destinations at any point in time, as compared to the current strategy. Keywords: passenger railway transportation, disruption handling, recovery. 1. INTRODUCTION Metro s Melbourne (MTM) operates 150 trains on over 830 kilometres of track all around Victoria, Australia. This extensive rail network, one of the largest in the world, serves as the backbone of the public transport system in Metropolitan Melbourne. The train fleet services more than 200 million customer journeys through over 12,000 weekly services. Every day the rail network services close to around 680,000 commuters. Of this figure, 400,000 commuters use the train system as their primary means of transport. As such, delays and inefficiencies in the rail networks pose a significant threat to the efficiency and productivity of the overall transport system. One such issue that arises is when a fault or blockage on a section of track occurs. In this instance, train operations on the entire train line are immediately stopped. As a result, thousands of commuters are stranded at the train stations until the faults or blockages are cleared. This problem is further magnified during peak hours, when commuters travel to and from their homes to their workplaces as the number of stranded commuters significantly increases. There is an emergency contingency plan followed by MTM when such an event occurs. As soon as line operators detect a fault, they immediately report this to management. Here, MTM immediately notifies the relevant local authorities to further examine and resolve the issue. This could entail contacting the police, the fire brigade, or dispatching their engineering team to resolve the issue. Second, MTM tries to attend to stranded commuters as well. Management contacts the bus depots serving or in close proximity to the relevant train lines to hire idle charter buses to transport stranded train commuters to their destination. Finally, MTM also advises the public of the current issue. This is done through the use of various forms of media that includes updating their website, texting commuters, or via the news on radio or TV. Several issues arise with regards to the current contingency plan used during a breakdown. The first key deficiency is the slow response time and deployment of charter buses to the affected train stations. Another deficiency with the plan is its inability to cope with the sheer volume of commuters especially during peak hours. Countless commuters are stranded at train stations, unable to reach their destination on time. : Corresponding Author

2 The response and deployment time of buses are usually quite long. One reason behind this is that there are only a few idle buses at a bus depot as it is not financially viable for bus depots to keep spare buses available. As such, in order to service stranded commuters, the bus depot deploys current charter buses hired out for excursions, school runs, etc., that can be used. According to the Operations Manager for Reservoir Bus Company, the deployment of buses usually takes around 15 to 30 minutes. This is highly dependent on the location and time of day, as sometimes there are no charter buses available for use in a lengthy time period. This is most usually the case during peak hours where all the charter buses are servicing students. In this scenario, buses first become available only after school runs are completed. Consequently, the deployments of buses take even longer. Likewise, the number of buses used to transport stranded commuters is often inadequate to deal with the sheer volume of stranded commuters. A single six-carriage train can carry up to 1,200 commuters, while a bus can only carry up to 60 commuters. Even if several buses are deployed, this still leaves a lot of commuters stranded at train stations. The uncertainty around the response time and the number of buses deployed results in an unreliable and uncertain system that causes discomfort and inconvenience to a great deal of commuters. We propose an alternative to the current MTM contingency plan in this paper. 2. LITERATURE REVIEW Timetable readjustment, and rolling stock and crew rescheduling are central to the work in disruption management in the area of passenger railway transportation. Jesperson-Groth et al. (2009) presented an overview of these problems, and noted the practical and technical challenges involved. We refer interested readers to articles listed in this review (Jesperson-Groth et al. 2009) for further details. Readjustment and rescheduling aim to restore feasibility and move stranded commuters as fast as possible through the system using the same mode of transport. However, on complete failure the system e.g. complete track closure, commuters will be left stranded over the duration of the downtime, causing serious congestions at affected stops. This will adversely affect commuters view on the quality of service of the transport provider. Therefore keeping commuters on-the-move is critical, even more so for long downtime durations. We have not yet spotted published work on addressing the problem of keeping train commuters on-the-move during disruption of the original system by utilizing other modes of transport within close proximity. The closest we have come to is that of the work by Zhang and Hansen (2008). Zhang and Hansen (2008) considered intermodal transport substitution for airlines with the aim to mitigate airport congestion and to recover the perturbed schedules. A mathematical program was formulated here to decide how to delay, cancel flights or substitute flights with buses. Our paper considers a simpler, yet interesting problem for the public railway transportation, with the aim to quantify the improvements that could be gained by utilizing an intermodal transport within close proximity. 3. THE PROPOSED RECOVERY PLAN There are currently 332 bus routes around Metropolitan Melbourne that are being operated by a number of private companies subcontracted by the state government. Almost all of the routes serve as local feeders to train stations as buses stop at a train station to facilitate the transport of commuters. Consequently, several bus routes stop at each train station. Also, each route is serviced by between 3 to 5 buses. We consider a disruption where there are no other planned modes of public transport connecting the stations involved. We propose the use of existing route buses as an alternative to deploying charter buses during a disruption. The close proximity to stations and the sheer number of route buses operating around train stations make it ideal for contingency planning, where quick response time and reliability are vital. We plan to divert the existing route buses so that they cycle between the two stations adjacent to the affected track a number of times, before returning to their normal routes.this will result in an almost immediate response time, whilst also eliminating uncertainty with respect to the number of buses we can use. The disruption recovery strategy is illustrated in Figure 1, showing existing route buses A and B with their respective recovery service routes. Station 1 Route A using bus on Route B using bus on Route A Route B Station 2 Figure 1: The proposed disruption recovery strategy using existing bus routes A and B.

3 A drawback to the proposed recovery plan is that of the uncertainty that will be created in the existing bus transport system. To dampen the effect of this uncertainty we have weighted the bus commuters to be more important than the train commuters. We have also limited the number of loops that the diverted buses can make between the affected stations. 4. PROBLEM FORMULATION We will only outline the mixed integer linear program (MILP) for the recovery strategy here for the sake of brevity. Interested readers are welcomed to contact the corresponding author for further details. The MILP aims to minimize commuter discomfort by decide when each existing route buses should run recovery services. Commuter discomfort is measured as the total waiting times at disrupted train stations and bus stops over a fixed planning horizon. The planning horizon is chosen to be 120 minutes with discrete one-minute time intervals. The 120-minute planning horizon, in most cases, is ample for the disruption to be resolved and for trains to resume to normal services. All stops on an existing bus route, except for the stop within proximity of a train station, will be aggregated (see Figure 2). Waiting times for bus commuters will be measured at both train stations, whereas waiting times for bus commuters will be measured at the node representing aggregated bus stops. It is assumed that buses will take half of its roundtrip time to transit between a train station and the node representing the aggregated bus stops. Node representing aggregated bus stops commuter arrivals Bus commuter arrivals Station 1 Route A using bus on Route B using bus on Route A Route B Station 2 Figure 2: Diagram showing aggregated bus stops with commuter arrivals. Several other assumptions have been for the MILP. These are outlined below. First, the model assumes that there is at least one train operating on either side of the affected rail. This is, in fact, not unreasonable in reality as there is always at least one train in any train depot, where train depots are located at both ends of any train lines. Second, several buses serve a route and are evenly spaced out along their respective routes. The model considers these buses inactive until they return to the station on their normal route. This is representative of the current industry practice. Third, the model assumes that the buses must make a full loop - to and from a train station that belongs to its route. Finally, commuter boarding and alighting times are ignored. Key input parameters to the MILP are passenger arrival numbers, bus transit times, bus capacity and maximum number of recovery services that could be carried out by each existing route bus. Important decision variables in the MILP include: x ijkt = 1 if bus k of Route 1 connects train stations i and j in time period t, 0 otherwise; y ijkt = 1 if bus k of Route 2 connects train stations i and j in time period t, 0 otherwise; n it the number of commuters stranded at train station i, at the end of time period t; b rt the number of commuters waiting for Route r bus, at the end of time period t; o it the number of commuters getting onto a bus service at bus stop/train station i, in time period t. The MILP aims to minimize 2 T 2 T B n it C i 1 t 1 r 1 t 1 where T is the last time period of the time horizon and C B is the weight assigned to the total waiting times of bus commuters. The MILP accounts for the following constraints: commuter balance constraints, bus route definition, maximum number of times a bus runs recovery services within the planning horizon, and bus capacity constraints 5. RESULTS AND DISCUSSIONS The proposed recovery strategy is tested on one of MTM s train line the Epping line. The Epping line has two zones, namely Zone 1 and Zone 2 with Zone 1 being the zone closer to Melbourne Central Business District. Experiments are carried for both zones. Traffic conditions and commuter volumes at different time periods of each b rt 1

4 zone are considered in the experiment. Table 1 and Table 2 outlines the parameters used for different periods in Zone 1 and Zone 2 respectively. We refer the reader to Figure 2 for an illustration of the parameters used in these tables. Data in Table 1 and Table 2 are approximated for experimentation purposes, which are based on actual data. Transit times were obtained from Google Maps, bus and train arrival frequency are based on current schedules (Metlink 2010). Commuter arrival rates are modeled using Poisson distributions based on census data (Australian Bureau of Statistics 2006). Table 1: Zone 1 experimental settings. ZONE 1 Peak (7:00-9:30am, 3:30-5:00pm) Non-peak (9:30-3:30pm, 5pm-12am) arrival frequency (minutes) /Bus Commuter arrival rate (pax per minute) One-way transit time 7 5 between Stations 1 and 2 for each bus (minutes) Round Trip time for Route A (minutes) Round Trip time for Route B (minutes) Number of buses on each route 4 4 Table 2: Zone 2 experimental settings. ZONE 2 Peak (7:00-9:30am, 3:30-5:00pm) Non-peak (9:30-3:30pm, 5pm-12am) arrival frequency (minutes) /Bus Commuter arrival rate (pax per minute) One-way transit time 5 4 between Stations 1 and 2 for each bus (minutes) Round Trip time for Route A (minutes) Round Trip time for Route B (minutes) Number of buses on each route 4 4 We assume buses can carry up to 60 passengers, and the trains on the Epping line can carry up to 1,200 passengers at any given time. The MILP is implemented using Xpress-Mosel and solved using Xpress-MP Optimiser version at default settings. We set C B = 10, and limit the number of recovery services for each bus to five. 5.1 Zone 1: Peak hours Peak hours in Zone 1 represent the largest commuter arrival to train stations and traffic conditions are the worst. During peak hours very few charter buses (or none) are available for use as most will be transporting school students. The result is a fast build-up of commuters if disruption were to occur during these hours. Figure 3: Total number of stranded commuters over time during Zone 1 peak hours. Figure 3 shows a plot of the number the number of stranded commuters over time for both current (top) and proposed (bottom) recovery strategies. The number of stranded commuters for the current recovery strategy is the number commuters stranded at station only (since existing route buses are not used here), whereas the numbers for the proposed strategy is the sum of all stranded train and bus commuters. The area under each graph represents the total waiting time. Despite the large number of stranded commuters, it is evident that the proposed system is a superior response to disruption, almost reducing the number of stranded commuters by 40% at the end of the planning horizon. 5.2 Zone 1: Non-peak hours Commuter traffic into train stations at non-peak hours are generally less than that of during peak hours, and more charter buses are also available for use during non-peak hours. Road traffic conditions are also better during these hours, allowing for faster travel times. This results in a slower build-up of commuters, as compared to the build-up

5 rate during peak hours, and hence allows for more opportunity to ease the disruption. This is clearly shown in Figure 4, where peaks and troughs of the number of stranded commuters are more obvious. At the end of the planning horizon, we observe an approximately 60% reduction in number of stranded commuters when the proposed recovery strategy is implemented. Figure 6: Total number of stranded commuters over time during Zone 2 non-peak hours. 6. CONCLUSION Figure 4: Total number of stranded commuters over time during Zone 1 non-peak hours. 5.3 Zone 2 Commuter traffic into train stations in Zone 2 are less than Zone 1 stations, due to higher population density closer to the Melbourne Central Business District. Road traffic conditions in Zone 2 are also better, thus improving travel times. Figure 5 and Figure 6, again illustrates the effectiveness of the proposed recovery strategy in responding to railway disruptions. Note that whilst the improvements introduced in Zone 2 is smaller than in Zone 1, this observation is expected as conditions in Zone 2 are relatively less hectic. This paper proposes a novel disruption recovery strategy which utilizes existing route buses as an alternative strategy to charter buses, which is currently adopted by Metro s Melbourne. The proposed strategy involves using existing route buses to connect stranded commuters between stations affected by the disruption. Initial experiments strongly advocate the ability of the proposed strategy to respond to public railway disruptions, even for peak hours of the day. It is clear that the MILP model for the proposed strategy requires further refinement, in order to gauge the relative improvements more accurately. Extensions to the MILP may include actual representation (instead of an aggregated view) of existing bus routes, recovery using more than two existing bus routes, recovery services that combine charter buses and existing route buses, and the possibility of including other modes of public transports within close proximity. Furthermore, the MILP should also be extended to consider the case where more than one track segments fail at the same time. The MILP-based recovery plan is constructed based on deterministic knowledge of commuter arrivals and travel times. A more robust recovery plan must be built based stochastic counterparts of this information. The implementation of the above-mentioned extensions is currently in progress. REFERENCES Figure 5: Total number of stranded commuters over time during Zone 2 peak hours. Australian Bureau of Statistics, 2006 Census data. Access date: May 2010.

6 Google Maps, Access date: May Jespersen-Groth, J., Potthoff, D., Clausen, J., Huisman, D., Kroon, L., Maroti, G., and Nielsen, M.N. (2009) Disruption management in passenger railway transportation, Lecture Notes in Computer Science, 5868/2009, Metlink. Access date: May Zhang, Y., and Hansen, M. (2008) Real-time intermodal substitution: strategy for airline recovery from schedule perturbation and for mitigation of airport congestion, Transportation Research Record: Journal of the Transportation Research Board, 2052/2008, ACKNOWLEDGMENT We wish to thank Edgar Tellis, Station Manager at Melbourne Central Station who briefed us extensively about the inadequacy of current contingency plans in place for the public rail network. We would also like to thank Steve Cooper, Operations Manager at Reservoir Bus Company who briefed us on their role in the public rail backup systems. AUTHOR BIOGRAPHIES Tim Darmanin is a Master of Operations Research and Management Science student at the Faculty of Science, University of Melbourne, Australia. He received a Bachelor of Science degree from the Department of Mathematics and Statistics, University of Melbourne in He has keen interest in industrial applications of Operations Research techniques. He has experience applying Operations Research techniques to logistics problems for an Australian not-for-profit organization. He can be reached at <t.darmanin@pgrad.unimelb.edu.au> Calvin Lim is pursuing his Honours degree at the Department of Mathematics and Statistics, Faculty of Science, University of Melbourne, Australia. He received a Bachelor of Science degree from the same department in His Honours thesis entitled, Stochastic Programming Models for a Portfolio Optimization Problem investigates performances of heuristics and decomposition methods for a multi-period stochastic portfolio optimization problem. He can be reached at <calim@trinity.unimelb.edu.au> Heng-Soon Gan is a Lecturer and the Director of Melbourne Operations Research at the Department of Mathematics and Statistics, Faculty of Science, University of Melbourne, Australia. He received a Doctoral Degree from the Department of Mechanical and Manufacturing Engineering, University of Melbourne in 2004, for which his doctoral thesis was awarded the MH de Fina prize for best thesis. His teaching and research interests include mixed integer program, heuristics and hybrid optimization techniques with applications to scheduling, logistics and transportation problems. He can be reached at <hsg@unimelb.edu.au>