The Efficiency of Double-Decked Elevators

Transcription

1 DEGREE PROJECT, IN COMPUTER SCIENCE, FIRST LEVEL STOCKHOLM, SWEDEN 2015 The Efficiency of Double-Decked Elevators A COMPARISON BETWEEN SINGLE-DECKED AND DOUBLE-DECKED ELEVATORS IN A SKYSCRAPER ENVIRONMENT WILLIAM SCHRÖDER AND JACK SHABO KTH ROYAL INSTITUTE OF TECHNOLOGY CSC SCHOOL

2 The Efficiency of Double-Decked Elevators A comparison between single-decked and double-decked elevators in a skyscraper environment Jack Shabo, William Schröder Degree Project in Computer Science, First Cycle - DD143X School of computer science and communications Royal Institute of Technology Supervisor: Vahid Mosavat Examinator: Örjan Ekeberg

3 Abstract The purpose of this study was to investigate the efficiency of double-decked elevators in a skyscraper environment. This was done by simulating elevator activity using different elevator types and elevator control algorithms. The results gained from the simulation suggested that double-decked elevators always provide better performance over using regular single-decked elevators. Some control algorithms proved to have up to ten times better efficiency compared to others using double-decked elevators.

4 Sammanfattning Syftet med denna rapport var att undersöka hur effektiva dubbeldäckade hissar är i skyskrapsmiljö. Detta gjordes med att genomföra en simulation över olika hisstyper och kontrollalgoritmer. Resultatet från simulationen indikerar att dubbeldäckade hissar alltid ger bättre prestanda jämfört med vanliga enkeldäckade hissar. Vissa kontrollalgoritmer visade sig vara upp till 10 gånger så effektivare än andra med dubbeldäckade hissar.

5 Contents 1 Introduction 1 2 Terminology 2 3 Background Environments, Elevators and Efficiency Low to High Rise Buildings Skyscrapers Measuring Elevator Efficiency Passenger Traffic and Time Classical Control Algorithms Single Automatic Control Collective Control Zone Control Advanced Control Algorithms Search Control Destination Dispatch Double-decked Control Problem Definition Problem Statement Purpose Method Traffic Generator Interfloor Traffic Up-peak Traffic Down-peak Traffic Lunch time Traffic Elevator Implementations Simulating the Control Algorithms Local Elevators Shuttle Elevators System Specifications Simplifications Assumptions Validity through Testing Results Single Automatic Single Automatic Zone Single Automatic Search Selective Collective Selective Collective Zone Selective Collective Search Diagrams Discussion Interpretations Error Sources Applications Conclusion 31 References 32

6 1 Introduction Effective elevator control is far more sophisticated than serving one passenger at a time. Instead, programmers face the challenge of assigning multiple passengers to elevators within certain time constraints. In fact, when assigning n passengers to elevators in the general case, there are n! potential pick-up orders. Furthermore, if all possible pick-up orders are allowed and considered by a scheduler, the corresponding problem of planning an optimal route has proven to be NP hard[1]. In order to cope with this problem, there are multiple heuristic and approximate elevator control strategies each performing differently according to a variety of parameters. Using the most efficient strategies, or more precisely control algorithms, is vital to impressive buildings. One such example would be the tallest building in the world: Burj Khalifa [2] which has 57 elevators, 167 floors and hundreds of thousands of visitors per year[3]. However, not only the control algorithms constitute a varying factor in the problem of time optimization; an elevator consisting of several elevator cars stacked upon each other serve as an alternative to the single-decked version. The skyscraper Burj Khalifa [2], as well as other buildings of the same scale, use such varying elevators. Thus with respect to the plethora of control algorithms the issue is raised of whether or not more complex elevator types provide better time efficiency for buildings of high altitude. 1

7 2 Terminology Pick-up Drop-off The state in which a passenger embarks on an elevator. The state in which a passenger disembarks from an elevator. Control algorithm An algorithm allocating elevators in response to passenger calls, including the order in which pick-up and drop-off occur. Elevator car A metallic box in which passengers ride the elevator. An elevator consist of one or more of these boxes. Single-decked Double-decked other. An elevator consisting of one elevator car. An elevator consisting of two elevator cars stacked upon each Sky lobby A secondary lobby higher up in a building. Shuttle elevator sky lobbies. An elevator which only travel between lobbies, including Local elevator An elevator that travel between a certain amount of floors, including only one lobby/sky lobby. Waiting time elevator. The time a passenger remains within an elevator before disem- Travel time barking. The time a passenger has to wait before embarking on an 2

8 3 Background This section will go over the necessary background information needed to understand the remaining parts of the report. First, there will be an introduction of different buildings and the elevator systems used in these. Thereafter, different control algorithms for different types of buildings will be introduced. Finally, the control algorithms used in double-decked elevators will be presented. 3.1 Environments, Elevators and Efficiency Different buildings require different types of elevator systems. A regular suburb residential building of a few floors (typically no more than 20) tend to be served by one or in some cases two elevators. At the same time there are buildings such as Burj Khalifa which have over 50 operating elevators. Obviously, these vastly different buildings require some sort of categorization in consideration to the elevator systems involved Low to High Rise Buildings To begin with, consider regular buildings having less than 20 floors, a category which represents the majority of buildings. The buildings of this category tends to be referred to as low-, medium and high rise buildings depending on the amount of floors involved. Generally, they have a need for an elevator but tends not to have more than one or two shafts. Due to the simplicity of these systems they do not present a particularly challenging problem to operate [4] Skyscrapers In contrast, when buildings reach extreme heights problems with time constraints arise due to the long travel distance of the elevators. This category of buildings, named more commonly as very tall buildings or skyscrapers [4], calls for a more efficient solution. While more shafts and efficient control algorithms could improve the situation, only a certain amount of space in the buildings can be assigned to elevator shafts. For this reason, there are solutions that improve the efficiency of each shaft by allowing multiple elevators to operate in each shaft. The obvious problem with this would be that the elevators are in the way of each other. Today there are two different solutions to prevent this from occurring. To begin with, there are double-decked elevators which solves the issue by simply attaching two elevator cars together so that two floors, one directly above the other, can be served simultaneously [6], see Image 3.1. This strategy can clearly increase performance since one shaft can serve two calls at the same time. Consider for example two different groups of people making calls on two adjacent lower floors. A double-decked elevator would allow both these groups to embark on the two different elevator cars before traveling towards their destination floors. While it is true that passengers of one of the elevator cars might have to wait for passengers boarding the other elevator car, such 3

9 delay is negligible compared to the time it takes for a regular elevator to ascend with one group of passengers and descend back again to pick up the next. Image 3.1: Double-decked elevators [7] Although double-decked elevators can as much as double the elevator performance, passengers traveling to high numbered floors are still likely to have to stop on a number of intermediate floors to let other passengers on and off. To truly deal with this problem, having sky lobbies allow passengers to travel with shuttle elevators directly to special floors, the sky lobbies, from which passengers then switch elevator and use a local elevator to get to their respective final destination floor [10]. As an example, Image 3.2 shows a schematic figure of a sky lobby implementation. In this, each sky lobby serve all floors from the sky lobby floor up to the floor below the next sky lobby using local elevators. Consequently, the local elevators for the different sky lobbies can share shafts since each sky lobby as well as the main lobby only serve a separate range of floors. Each such interval can be treated as a separate sub-building which can be operated as its own high-rise building. Therefore it can be concluded that as the number of floors grows the amount of local elevator shafts does not need to be increased, although extra shafts for shuttle elevators provides extra service to the different sky lobbies. 4

10 Image 3.2: A schematic overview of the sky lobbies in the old World Trade Center buildings [9] Moreover, there is nothing that prevents double-decked elevators from being used in conjunction with sky lobbies. One solution [11] involves using doubledecked elevators both as shuttle and local elevators. This means that each lobby includes two floors, one for boarding each elevator car in the doubledecked elevators. Equally plausible is to have double-decked shuttle elevators that takes the passengers to sky lobbies from where the local elevators are singledecked [4] Measuring Elevator Efficiency Elevator systems efficiency is measured on the performance of several parameters, with the average waiting time(awt) of passenger pick-up being the most common one to optimize [1]. The waiting time of a passenger is defined as the time it takes for a passenger to make an elevator call and then board a given elevator. With a set of passengers over a certain range of time, one can compute the waiting time of each of these passengers and then calculate an AWT. This number provide a rough measurement of how well an elevator system performs, in which low AWT is considered efficient while high AWT often is a sign of bad scheduling [1]. In order to detect variances of passengers waiting times, which could be secluded when averaging, one can use average squared waiting time(aswt) as an alternative performance parameter[1]. Much like AWT, the ASWT is calculated by measuring the waiting time (w) of passengers and then squaring the results according to the following formula: ASW T = w1 2 + w w2 n 5

11 3.1.4 Passenger Traffic and Time The amount of passengers can vary from building to building depending on the building s layout and size. For example, consider the case where there is only a handful of people in a building compared to where the building is almost full. In the first case there would be little or non-apparent practice of the elevators while in the latter they would most likely be occupied without rest. As such, one could categorize elevator traffic, based on passenger density, into low, medium or heavy traffic. These different markers of intensity are of interest when designing as well as selecting control algorithms. Most control algorithms have a goal to minimize AWT, although other control algorithms could aspire for minimizing average traveling time(att), the average time a passenger spend riding an elevator [14]. The first goal builds upon how elevators are dispatched and controlled by the system to answer calls, while the latter depends more on how the elevator behaves in the traffic. In an environment with heavy traffic, elevators could get quite full and thus, in the average case, require more stops effectively increasing the ATT. Not only does elevator traffic depend on the amount of passengers, but also the type of traffic. Passenger traffic can be divided into four different situations: uppeak traffic, lunchtime traffic, downpeak traffic and interfloor traffic [14]. Uppeak traffic represents the arrival of passengers to the very first floor, the lobby, while on the contrary in downpeak traffic passengers travel from various floors down to the lobby. As one could guess, lunchtime traffic represents the habit of passengers traveling down to the lobby and then up again in a very short time. Finally, passengers traveling between floors is the definition for interfloor traffic. [14] 3.2 Classical Control Algorithms Elevator control began at a very primitive stage with human elevator operators controlling levers and ropes. However, as the years progressed, so did the approach for an automatic control system. Hence did the world s early control algorithms see the light of day. Even though these were invented in the early stage of automatic elevator control, they are still widely used in modern elevators either in full or indirectly as enhanced versions. [12] Single Automatic Control One of the earliest developments of an automatic electrical control system was the Single Automatic operation strategy which was used for single-decked elevators [12]. This elevator system consisted of single call buttons at each floor, and buttons on the operating panel inside the elevator car which represented each floor destination. The elevator could be called from each floor but once in use, it would not respond to calls from other floors until it had reached the given destination floor. Due to this limitation, this strategy is more fit for exclusive use of elevators [12] such as for vehicle transportation in garages or sky lobby shuttle elevators having only one other floor as a destination. 6

12 3.2.2 Collective Control In order to have a system which provides elevator service to multiple stops in one ride, thereby not providing exclusive use and effectively reducing the waiting time of passengers, one can use the collective operation strategy. Generally, this strategy makes use of two landing call buttons for either upwards or downwards travel instead of the aforementioned single button. By having passengers specify their desired direction on these landing call buttons, they would then be assigned to an elevator going in the specified direction. After a passenger embark on such an elevator, any intermediate calls in the same direction results in the elevator stopping and collecting the additional calls, thus serving calls along the way. When an elevator have answered all calls in one direction, it will reverse and answer any upcoming calls in the opposite direction. Although this is the general approach for elevators using the collective strategy, most elevators used derived versions. [12] The Selective Collective operation is the most common version [13] which behaves as specified before with the addition that the elevator remembers calls in the opposite direction and attempts to answer to them after a reversal. Should there be no calls in the opposite direction, the elevator would by default park at the last-served floor Zone Control In order to cope with heavier passenger traffic as well as attempt to reduce the average passenger waiting time, the concept of zone control provides a simple, yet powerful approach. Zone control can be used as an extension for most multielevator algorithms and is all about distributing the labor in an elevator system by dividing the given building into particular zones. Each elevator is assigned a particular zone and answers calls primarily within it and, if sought, secondarily outside the zone. A building can be zoned into stacked or interleaved zones [4]. Stacked zones consists of subsequent floors, meaning that (tall) buildings are divided into horizontal layers. This is the recommended practice for office and institutional buildings [4](pg. 2) and thus of interest in the study. An interleaved zone division is defined as having elevators either serving odd or even floor, but since interleaved zoning is common practice in public housing[4] such zoning will not be further considered. 3.3 Advanced Control Algorithms Modern elevators require better performance, in the form of better AWT and ATT, than the classical control algorithms have to offer. As such, one can use some more advanced control algorithms in which some take use of mathematical models or computational concepts. These algorithms generally provide a better distribution of elevators responding to calls, and hereby give better timeresults[1]. While these advanced algorithms often provide optimized results, 7

13 they require much more computational time. Such is the case of the Search control algorithm Search Control Control algorithms which utilize the concept of searching through the system and then deciding the best possible elevator assignments, by optimizing some criteria such as AWT [15], could be an option as well in addition to classical algorithms. There are two different types of search-based strategies, greedy or non-greedy algorithms. A greedy search-based algorithm does not usually perform extensive search but rather assign hall calls to elevators when they are first registered to the system [15] and then do not reconsider their choice. However while it requires little computational time, it does result in a lack in performance [15]. A non-greedy search control algorithm require a lot of computational time since it searches through all available allocations for a new passenger call to any elevator. Although this approach does indeed give the most optimal assignment, it is not feasible for larger systems due to the computational requirement [15]. However, if one were to use it on a smaller system such as a building divided by sky lobbies, preferably in an low-medium traffic environment, it could certainly be worth the calculation time Destination Dispatch In order for the elevator control algorithms to have as much information as possible available when assigning elevators, it would have to know the destination floors for the passengers when they call for the elevators. This type of system is known as destination dispatch. The idea is that each floor has a panel of floor buttons, corresponding to the different available floors from the elevator system. Passengers then call for elevators by selecting their destination floor. Finally, the control algorithm then decides which elevator should be assigned to serve the request, and informs the user which elevator to use [17], see Image

14 Image 3.3: A call panel for a destination dispatch system. The letter on the top shows which elevator to use (A) in order to reach floor 50 which has just been requested by the user. [17] Double-decked Control Since most elevator rides takes place to or from a lobby it is clear that lobbies have to be constructed over two floors in order for double-decked elevators to be effective. This way, passengers can board both the elevator cars of the elevator simultaneously which in turn could at most double the amount of passengers carried in every ride. This is usually done by installing an escalator between the two lobby floors (this include sky lobbies) and then direct passengers to use the upper or lower deck depending if they are headed to an odd or even floor. Indeed this is the solution all current elevator manufacturers use [20]. Of course, passengers boarding at any intermediate floor cannot choose between floors and will thus enter either the upper or lower elevator car depending on where the elevator stops. Clearly any call system can be used for a double-decked elevator, i.e. simple call, up/down call or destination dispatch. However, the most important factor when optimizing control of double-decked elevators is of course that both elevator cars are served simultaneously as much as possible. For this reason, destination dispatch is well equipped to handle double-decked elevator control since it provides information about the destination floor of passengers at the time the call is made. This allows the control algorithm to group passengers going to adjacent floors by assigning them to different cars of the same elevator, meaning both elevator cars can drop off the passengers simultaneously. As an example, two passengers boarding at the lobby with destination floor 7 and 8 respectively could be assigned to the same elevator, the passenger going to floor 8 on the upper car and the passenger going to floor 7 on the lower car. Using these assignments, the passengers could board and disembark simultaneously and there would be no idle waiting time for one elevator car while only the other car is being served. Due to these reasons, destination dispatch is commonly used in modern double-deck elevator systems, just as those developed by Schindler [11] and Otis [21], in conjunction with advanced control algorithms such as the following. 9

15 The ETD (Estimated Time to Destination) algorithm used by ThyssenKrupp utilizes a type of search algorithm to determine which of the elevators can most efficiently serve a call [19]. This is done by calculating the amount of extra waiting- as well as traveling time that would be generated for each of the available elevators to serve this new call. For example: Assume there is a call for an elevator on floor 3 with destination floor 8. Elevator A is just leaving floor 1 for floor 5 with two passengers. The total delay for elevator A can now be calculated. The stop at floor 3 to pick up the new passenger delays the elevator on its trip to floor 5 by some time, say 10 seconds. Since there are two people in the elevator they both have to wait these 10 seconds so the total delay time is so far 20 seconds. Now the passenger on floor 3 gets on and the elevators next stop is on floor 5. However, the passenger boarding on floor 3 is going to floor 8 so the stop on floor 5 delays him 10 seconds as well. Therefore the total cost for elevator A to respond to this call is 30 seconds. This cost is calculated for all available elevators and the one with the least total cost will be chosen to respond to the call [19]. This assumes of course that the amount of passengers in each elevator is known. This is difficult to know exactly, but the elevators could have a scale inside to determine the total weight which gives an idea of how many people are inside the elevator. It is however clear that destination dispatch is used by the algorithm to perform a more accurate search estimation that a regular up/down elevator system could do. Another solution, developed by Otis Compass Plus [18], utilizes a variation of the zone control algorithm rather than the search control algorithm. This is done in an effort to avoid different elevators going to the same floor. Moreover, it is done by allocating each elevator to a group of adjacent floors, including the lobby floor. For example, if there are four elevators and nine floors, including the lobby, then each elevator could serve two floors each. Each elevator call is further responded to by the elevator assigned to the zone having either the passengers destination floor or origin floor, whereby the amount of zones are 4 in this example.[18] 10

16 4 Problem Definition This study investigates how efficient double-decked solutions are compared to single-decked variants, or combinations of these. It is done by finding an answer to a hypothetical scenario; to plan the construction of an elevator system for a new skyscraper. Its goal is to be the first 400 meter high skyscraper with 100 floors, including a sky lobby, in northern Europe. With respect to the ground area available, the owners have agreed to an elevator system of 40 shafts with elevator cars having a carrying capacity of 15 people. However, the owners are concerned that the passengers elevator rides will be too slow, with respect to waiting time as well as travel time. They therefore consider if they have to use double-decked elevators in order to reduce passenger waiting time. These special elevators would certainly cost more than regular single-decked variants. To help with the trade-off, and at the same investigate if the use of doubledecked elevators increase performance, this study aims to provide an answer to how well different elevator types perform in the setting above, using different control algorithms. 4.1 Problem Statement Can something be said about whether single-decked or double-decked elevators are to be preferred in a skyscraper environment? Which control algorithms are more time efficient in a skyscraper using single-decked and/or double-decked elevators? 4.2 Purpose Today, multiple different combinations of double-decked and single-decked elevators are used as shuttle and local elevators in different buildings [4]. This raises the question of why multiple different solutions are used. By answering the problem statement, this study draws conclusions on the efficiency of double-decked elevators using different control algorithms. 11

17 5 Method The defined problem consists of many parameters: a variety of control algorithms, elevator types and different intensities of traffic. Hence, an answer for this problem is sought using a simulation of elevator activity. This simulation is written in Java and should be sufficient to provide answers, or at least hints, on which elevator setting provides better time efficiency. The simulation has such capability due to the fact that it attempts to imitate real-life behavior of passengers moving from one point to another via a system of elevators, under real-life conditions. To perform a simulation imitating real-life behavior, one would first need a collection of passengers representing a type of traffic. This collection is generated by a traffic generator given a traffic type, such as up-peak traffic, and a number representing how many different passengers one would wish to have in the selected traffic type. The output of the traffic generator is a number of elevator calls that have an origin, a destination and a time stamp telling at which time in the simulation the call will be made. The generated traffic is then sent as input to the current elevator system, consisting of a set of elevators, which mimics the elevators natural behavior (movement and opening/closing of doors) using the current control algorithm. The chosen control algorithm processes the given data by assigning incoming calls to elevators. In order to measure the waiting- and travel time of passengers, each elevator dynamically calculates the time allocated passengers have to wait for, and ride with, the elevator before reaching its destination. After each simulation, results are given in form of the AWT and ATT of the entire system. Furthermore, one will also be given the ASWT, defined in Section 3.1.1, as well as the average squared travel time(astt) of the system in order to highlight passengers variances not only in passenger waiting time, but in travel time as well. The following sections specify the different parameters and settings of the simulation. 5.1 Traffic Generator The responsibilities of the traffic generator is to generate realistic passenger data according to the different hours of a normal working day. These are interpreted to be the following: 7-9: Up-peak traffic where the vast majority of passengers are traveling from the lobby to their destination floor. 9-11: Interfloor traffic 11-13: Lunch time traffic where most passengers travel either to or from the lobby floor : Interfloor traffic 12

18 15-17: Down-peak traffic where the vast majority of passengers are traveling to the lobby. The subsections below cover the different traffic-types which together form a day of simulation, a simulation day. Chosen numbers for the different periods, as well as the choice for having the periods themselves, are based upon the theory in Section Note that the sky lobby floors can never be the final destination of any travel, and that unfinished calls from each period overlap onto the next period. Should there be any remaining calls in the system after the last period, the simulation extend the day by keeping the simulation running with the same settings, without having any new additional calls added to the system. Each simulation day consist of a certain number of time units, in which one time unit is represented as one "loop through the system", where one loop is simulated as one second of activity; each loop update elevator movement, elevator boarding, call allocations in the current control algorithm as well as the update of waiting and travel time. Each random operation mentioned in the following traffic states, as well as the exact time of which a call is made, is used with Javas pseudo-random linear distribution class Interfloor Traffic There is interfloor traffic both in the morning between up-peak traffic and lunchtraffic as well as between lunch-traffic and down-peak traffic. Such traffic is simulated by having 33% of the total amount of passengers per period do an interfloor elevator ride from a random floor to a random destination floor Up-peak Traffic The up-peak traffic is generated by having 100% of the given amount of passengers take an elevator ride from the lobby floor at some point during the period. The destination floor of these is chosen at random Down-peak Traffic During down-peak traffic, 100% of the given passenger amount travel from a random originating floor down to the lobby sometime within the period. When double-decked elevators are used, the floor above the lobby floor is also one possible destination. Consequently, this floor is not a valid floor to originate from Lunch time Traffic In lunch-time traffic, 50% of the given passenger amount does at some point travel down to the lobby from a random origin. After 30 simulation time units, these passengers travel back up again. 13

19 5.2 Elevator Implementations This section lists the different elevator implementations that are used in the simulation. When a double-decked shuttle elevator is used, the lobby and sky lobby consist of two floors, instead of just having one floor, namely the original lobby/sky lobby floor as well as the floor directly above it. The simulation run with the following elevator structures: Double-decked locals with double-decked shuttles Single-decked locals with double-decked shuttles Single-decked locals with single-decked shuttles The structure of Double-decked locals with single-decked shuttles is not used in the simulation. This is due to the fact that the double-decked locals would then only be able to have its lower half in the lobby/sky lobby floor, since there is a single-decked shuttle elevator between these floors. Thus this structure is interpreted as surrealistic according to the description of sky lobbies in Section Simulating the Control Algorithms Local Elevators All local elevators, regardless of whether they are single-decked or doubledecked, will be simulated with the following control algorithms: Single Automatic with logical elevator assignments Single Automatic with a zone implementation Single Automatic with a search implementation Selective Collective with logical elevator assignments Selective Collective with a zone implementation Selective Collective with a search implementation Logical elevator assignments are used on both Single Automatic and Selective Collective in order to investigate if a logical, but yet simple, allocation of elevator can prove to be useful. Each such logical elevator are chosen in the following order: 1. The chosen elevator is the one having the least workload (amount of assigned calls) 2. The chosen elevator is the one closest to the call 14

20 3. If there should be multiple elevators with the same workload and proximity, one of these would be picked at random using Javas own linear, pseudo-random distribution An algorithm implemented with zone control is given a list of elevators in which each elevator are assigned to a zone, consisting of the lobby/sky lobby as well as two or three consecutive floors. Each passenger s call is then handled by an elevator having the passenger s origin floor within their zone. Thus, the algorithm using zone is given a subset of the available elevators, rather than all of them, when performing their respective queue allocations. Algorithms using search control are based on ETD and use a greedy search control variant which, as mentioned in Section 3.3.3, does not consider different queue allocations. Instead, such algorithms calculate the performance of placing new calls into each possible elevator. When all possibilities are accounted for, the algorithm then allocates the new call to the elevator taking the least amount of waiting time and travel time Shuttle Elevators Shuttle elevators run with the Single Automatic algorithm with logical elevator assignments, regardless of whether double-decked elevators are used or not. This is due to that shuttle elevators only travel in between two floors (or set of floors) and thus does not require advanced elevator assignments. 5.4 System Specifications The building layout consist of a single lobby floor with multiple destination floors including exactly one sky lobby. Garage floors and other entrance floors are not considered present. The following list describe the fixed or alternative parameters to the simulation and represent a simplification of the One World Trade Center building and elevator specifications. Floors: 100 Building Height: 400 m Distance between floor: 4 m Daily amount of people riding elevators: 2500 / 6000 / 7200 (low traffic/medium traffic/heavy traffic) Shafts: 40 Amount of shuttle elevators: 16 Amount of local elevators: 24 in each part of the building (top and bottom) Elevator car capacity: 15 passengers Average elevator speed: 20 m/s 15

21 Sky lobby floor: 66 Floor delay time (time spent embarking/disembarking passengers): 10 seconds Number of simulation days: 14 Time per period: 7200 seconds (two hours per period) Extended time after each simulation day: unlimited 5.5 Simplifications To simplify the simulation, elevator acceleration and deceleration are not considered. Instead, the average speed of the elevator are used for elevator movement. Furthermore, the elevators keep track of the amount of passengers currently inside them at all times in order to check whether they are full or not. If such is the case, elevators will at first drop-off a passenger before picking up another regardless of the current queue. Additionally, elevators are only open for embarking/disembarking for a fixed period of time (see above) and are not delayed further. Moreover, a passenger cannot be allocated with another elevator once the call has been processed by the control algorithm. Some of the consequences of this simplification is that passengers cannot ride with another elevator, should one arrive at the same floor, or be reassigned to another elevator if the allocated elevator happens to be full. Finally, algorithms using search based elevator allocations use a simplified version of the real ETD, whereas algorithms using zone control use a derived version of Compass. 5.6 Assumptions The simulation is based on a number of assumptions, namely the following: Destination dispatch is assumed to be used on all floors regardless of elevator setting. This has the consequence that the simulated elevator control system is able to perform elevator allocations with the destination floors of passengers taken into account as soon as a call for an elevator is made. Passengers know their whole route, including lobby interchange (if any) and position in lobby floor should double-decked shuttle elevators be used. Eventual movement between the ground lobby floors or sky lobby floors in a double-decked shuttle elevator scenario is assumed to take zero seconds. Such is the case when a passenger ride from the lobby/sky lobby and has to embark on the upper or lower elevator car of the double-decked elevator in order to reach their respective destination. 16

22 5.7 Validity through Testing In order to ensure that the given results are creditable, the program was run with a number of test classes. More specifically, the expected behavior of the following parts of the program was validated: Elevator movement and embarkment/disembarkment Passenger movement and tracking The selective collective algorithm Passenger traffic generation Other parts of the program was validated through debugging and error printing along with multiple runs of the program. 17

23 6 Results The following subsections display the simulation results for each control algorithm. In these, there are tables for each respective algorithm variant for 14 simulation-days of simulation in low, medium and heavy traffic passenger amounts. At the end of section, one can find diagrams that graphically present differences in waiting time and squared waiting time for the different traffics and algorithms. There are no such diagrams for travel time or squared travel time due to it having few significant differences. Furthermore, computational time is not an issue in the simulation and is thus not investigated upon. AWT = Average Waiting Time ASWT = Average Squared Waiting Time ATT = Average Traveling Time ASTT = Average Squared Traveling Time 6.1 Single Automatic Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 12,55 15,04 17,77 18,36 Double/Single 12,59 15,07 17,81 18,39 Double/Double 12,48 15,00 17,77 18,36 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 14,91 18,47 17,76 18,36 Double/Single 14,83 18,42 17,82 18,42 Double/Double 14,64 18,17 17,76 18,36 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 42,97 75,87 17,77 18,36 Double/Single 42,06 73,89 17,82 18,42 Double/Double 39,75 68,30 17,76 18,36 18

24 6.2 Single Automatic Zone Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 17,69 23,61 17,76 18,36 Double/Single 16,31 20,28 17,80 18,39 Double/Double 15,93 20,13 17,76 18,36 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 71,49 185,75 17,77 18,36 Double/Single 70,62 192,78 17,83 18,42 Double/Double 63,62 174,44 17,76 18,36 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 184,38 429,61 17,77 18,36 Double/Single 174,51 434,97 17,83 18,32 Double/Double 165,92 419,50 17,76 18,36 19

25 6.3 Single Automatic Search Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 12,77 526,06 17,77 546,81 Double/Single 12,83 527,25 17,82 548,77 Double/Double 12,60 524,66 17,76 545,45 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 14,12 771,83 17,78 780,96 Double/Single 14,04 767,62 17,82 782,86 Double/Double 13,81 759,82 17,75 774,67 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 27, ,22 17, ,65 Double/Single 25, ,57 17, ,85 Double/Double 24, ,28 17, ,14 20

26 6.4 Selective Collective Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 12,52 15,04 17,77 18,36 Double/Single 12,59 15,07 17,83 18,42 Double/Double 12,52 15,04 17,77 18,36 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 13,95 17,55 17,88 18,53 Double/Single 13,78 17,27 17,93 18,58 Double/Double 13,69 17,21 17,84 18,50 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 26,84 54,54 18,09 18,85 Double/Single 24,65 46,10 18,16 18,90 Double/Double 22,95 41,87 18,03 18,77 21

27 6.5 Selective Collective Zone Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 13,59 16,16 18,26 19,03 Double/Single 13,59 16,10 18,26 18,95 Double/Double 13,03 15,72 17,93 18,61 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 15,01 19,06 18,92 19,88 Double/Single 14,98 18,93 19,00 19,90 Double/Double 14,01 18,12 18,15 18,98 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 30,10 59,63 19,13 20,15 Double/Single 26,59 49,27 19,28 20,28 Double/Double 23,85 43,93 18,25 19,11 22

28 6.6 Selective Collective Search Low Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 8,75 433,20 18,65 565,35 Double/Single 8,77 434,30 18,33 568,50 Double/Double 8,50 430,82 18,49 561,50 Medium Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 8,09 484,15 18,70 800,24 Double/Single 8,10 485,97 18,97 804,90 Double/Double 7,70 478,24 18,35 777,07 Heavy Traffic Elevator Type AWT ASWT ATT ASTT Single/Single 7,98 501,88 18,70 883,11 Double/Single 7,96 503,30 18,79 889,41 Double/Double 7,54 492,93 18,28 848,97 23

29 6.7 Diagrams Diagram 6.1: AWT for low traffic Diagram 6.2: AWT for medium traffic 24

30 Diagram 6.3:AWT for heavy traffic Diagram 6.4: ASWT for low traffic 25

31 Diagram 6.5: ASWT for medium traffic Diagram 6.6: ASWT for heavy traffic 26

32 7 Discussion 7.1 Interpretations To maintain elevator traffic in the extreme environment of a skyscraper is hard, yet again NP-hard in general when a scheduler consider all possible pick-up orders. This has however not been the case in this study, due to the usage of the heuristics Single Automatic and Selective Collective. These has proven to give different, but feasible results in accordance to their respective theoretical aspect. Single Automatic has proven to be on par with Selective Collective in a number of different traffics and alternative structures in terms of AWT as well as for ASWT, although only in the low and medium traffics. A certain equality seem to arise in Diagram 6.4 and Diagram 6.5 as well. Nevertheless, the differences become majorly apparent in heavy traffic with Selective Collective having better waiting time with results being from 20 up to hundreds of seconds better than the algorithms utilizing Single Automatic. Indeed, utilizing the concept of collection provides better overall results even with the simple logical elevator allocation. Even though the waiting times seem to differ between the algorithms, there are no real significant change in travel time. In the majority of the results, ATT seem to be a (rounded) constant value of 18 seconds while ASTT seem to be constant to approximately 20 seconds. Thus, it would seem that the chosen algorithm or state of traffic has negligible effect on how long a passenger has to ride in order to get to its destination. The only particular changes in travel time occur in the squared travel time of section 6.3 and section 6.6 which provide the result for the two algorithms respective search variant. Indeed, the difference between Single Automatic and Selective Collective as a control algorithm does not appear to be diversified by the core algorithm type but rather around the different variants of these. There is a clear difference between the performance of the logical, zone and search based algorithms from the diagrams. The observation that first meets the eye is that the search based algorithms performs very well in terms of waiting time compared to the other algorithms, such as in Diagram 6.3. In fact, it performs best in terms of waiting time compared to all the other algorithm/trafficintensity combinations. The probable explanation for this would be that search based actually finds the best suited elevator for each call by analyzing the running time for each possible allocation. While this is true, one has to keep in mind that new passengers arriving between the time of allocation and the time of arrival of the first passenger could affect which elevator would perform the best in terms of waiting time. Yet, passengers can not be allocated to a new elevator once they have been assigned to one in the first place since destination dispatch is used. For this reason, one could argue that search based algorithms performs the best in terms of waiting time from the given information. This is not necessarily true though, since it could be possible for the algorithm to guess the flow of incoming traffic and thus allocate passengers in a more efficient way to begin with. 27

33 Upon further inspection of the results in the diagrams it is also clear that the search based algorithms performs much worse compared to other algorithms in terms of squared waiting time. This would indicate that the waiting time distribution between the different passengers is unevenly distributed which in turn suggest search based algorithms makes some passengers wait longer in order for more passengers to be served with less waiting time. One might express it as sacrificing the few for the greater good. The reason for this is difficult to analyze since search based algorithms operates on nothing but runtime specific calculations. A possible analysis would be that new calls originating from distant locations would be allocated to empty but not necessarily nearby elevators. This would save time since an elevator that might be close, but contains several passengers, would cause an increase in the total delay time. On the other hand, the passenger who is making the new call might have to wait for a longer time since the chosen elevator could be further away which would affect the squared waiting time negatively. Another algorithm with surprising results is the zone algorithm, which performed worse in terms of waiting time than the logical version in all scenarios in the diagrams. It can also be seen from the same diagrams that while the singledecked version of zoned algorithms performs considerably worse than the logical versions, double-decked implementations seems to be a somewhat closer race. This would indicate that zone control algorithms works well with double-decked implementation, even if still slightly slower than the logical versions in terms of waiting time. This property seems to be unique for zone control; neither logical nor search based algorithms have a performance increase with double-decked. While logical algorithms seems to have about half the improvement compared to zone algorithms, search based practically reach the same waiting time using both single- and double-decked systems. This could be explained by the fact that double-decked zone control in the implementation for this simulation consisted of two adjacent floors in conjunction with the relevant lobby floor. This would mean a double-decked elevator achieves grouping with passengers traveling to the upper of the two adjacent floors boarding the upper elevator car and similar for the lower elevator car, meaning these passengers make efficient use of the fact that these elevator cars travel together. The question remains as to why the zone algorithm performed worse the logical algorithm in all cases. This result indicate that the logical algorithm s way of choosing elevator is superior to the zone version, which is worth investigating since the very reason zone algorithms exist are to improve performance. There are two factors to consider, they way the logical algorithm choose an elevator and the exact way the zone control is set up in the simulation. Firstly, the logical algorithm select elevator by finding the closest non-empty elevator. While this might appear as a very effective algorithm at first glance it has the issue of bunching up a lot of people from possibly different floors, meaning the first passengers to enter the elevator might have to wait a very long time. These issues are illustrated by the way the search algorithm performs the elevator allocation much more efficiently in terms of AWT. Secondly, the zone control of the elevators was implemented in such a manner that as few elevators as possible 28

34 were to serve each zone. This means that in a system of 40 elevators and 64 floors, the first 32 elevators serve two floors each and the remaining 8 help serve the top 16 floors. This type of distribution have the consequence that there are only some elevators serving some of the zones and thus passengers calling from the floors within a particular zone might have to wait a very long time if the elevator already have left the zone. It is possible zone control would have performed better if there were more elevators in each zone, but this was not investigated. Another aspect worth considering is that while rides to or from the lobby floors work well with zone control, interfloor traffic is more difficult to handle. The reason for this is that the origin and destination are unlikely to be in the same zone and thus zone control is not really achieved. 7.2 Error Sources The perhaps most obvious flaw with the performed simulation was that the elevator speed was set to an average value at all times. This speed was also the same for local and shuttle elevators, something that is far from true in real systems. The effects of these simplifications is that elevators traveling shorter distances are faster than they should be while elevators traveling long distances are slower than they should be. This means the simulated systems favors shorter elevator rides and thus also that multiple stops on close floors are conducted faster than should be possible. This flaw could also have been a factor of the slow efficiency of the zone algorithms, since these depend on traveling long distances with passengers between the lobby and the designated zoned floors. Another simplification made for the simulation is that each elevator knows the exact numbers of passengers currently inside at all times. While this is not entirely incorrect (there have been attempts with scales in elevators as described in the background) it in unlikely the elevator knows its current passenger amount with such precision, which thus makes the simulated elevators more efficient since they allow more passengers to board even though the elevator is almost full. While this different might provide different results, the simulated elevators still behaves just as real ones do by traveling to the next drop-off destination, ignoring pick-ups, when the elevator is considered full. It is worth to consider how elevators behaves when they stop at a floor to either let passengers embark or disembark. The time this process takes is set to ten seconds in the simulation. Yet, in real systems it is clear this number varies heavily depending on the situation. While ten seconds might be a reasonable average value it could possibly be more realistically represented by a stochastic variable ranging from 5-30 seconds with the highest probability being around 5-15 seconds. This type of change would let the system be affected by the occasional passenger that requires extra time boarding and disembarking the elevator. 29