DEGREE PROJECT, IN COMPUTER SCIENCE , FIRST LEVEL STOCKHOLM, SWEDEN 2015
Scheduling modern elevators
A COMPARISON OF THE TWO ALGORITHMS FSO AND FS4
JENNY HANSDOTTER AND KATJA RÖÖS
KTH ROYAL INSTITUTE OF TECHNOLOGY
Scheduling Modern Elevators
A comparison of the two algorithms FS4 and FSO
Katja Röös, katjaro@kth.se Jenny Hansdotter, hansdo@kth.se
Course: Degree Project in Computer Science Course number: DD143X
University: Royal Institute of Tehnology Institution: Computer Science Supervisor: Michael Schliephake
Examinator: Örjan Ekeberg
Abstract
Two of the most common elevator algorithms, FS4 and FSO, are discussed in this thesis. Their pros and cons regarding passenger wait- ing time and energy consumption are compared to find which of the algorithms perform best and what factors affect this. These topics are of interest for owners of modern building. By developing a simulation program the behavior of elevators controlled by these algorithms were simulated. Passenger pattern in the simulation was meant to emulate the pattern that occurs in office buildings at lunch hour. The conclusion is that due to differences in sector usage and specific rules for each algo-
Referat
I den här rapporten diskuteras två av de vanligaste algoritmerna för att kontrollera hissar, FS4 och FSO. Algoritmernas för och nackdelar gällande väntetid för passagerare och energiförbrukning jämförs för att finna vilken av algoritmerna som presterar bäst samt finna fakorer som påverkar detta. Dessa två områden är av intresse för ägare av mod- erna byggnader. Genom att utveckla ett simulationsprogram simuler- ades hissarnas prestation då de kontrollerades av de två algoritmerna.
Passagerarmönstret i simulationen gjordes att efterlikna mönstret som uppstår i en kontorsbyggnad vid lunch. Slutsatsen är att skillnaden i hur algoritmerna nyttjar sektorer och vilka regler de följer gör att de har
Contents
1 Introduction 1
2 Background 3
2.1 Previous research . . . 3
2.2 History of the elevator algorithms . . . 3
2.3 Demands on elevators . . . 5
2.3.1 Passenger experience and time demands . . . 5
2.3.2 Energy consumption . . . 5
3 Algorithms 7 3.1 About algorithms . . . 7
3.2 FS4 - fixed sectoring, priority timed unidirectional sectors . . . . 7
3.3 FSO - fixed sectoring, bidirectional sector . . . 9
4 Method and theory 11 4.1 Environment specification . . . 11
4.2 Definition . . . 11
4.3 Equations . . . 11
4.4 Ways of simulating . . . 12
4.5 Simulation program development . . . 12
5 Results 15 5.1 Waiting times for chosen algorithms . . . 15
5.2 Distances of travel for algorithms . . . 17
6 Discussion 21 6.1 Results . . . 21
6.2 Algorithms . . . 22
6.2.1 FS4 . . . 22
6.2.2 FSO . . . 23
6.3 Literature . . . 23
6.4 Method . . . 23
6.4.1 The time definition . . . 23
6.4.2 The equations . . . 24
6.4.3 Simulation program . . . 24
6.5 Continued studies . . . 24
7 Conclusion 27
8 References 28
1 Introduction
Elevators are a means of transport for moving people and goods in buildings.
Both the construction and function are complicated, requiring many advanced problems to be solved in order to produce a well-functioning elevator. Fields such as mechanics, mathematics, statistics, physics and psychology must all be taken into consideration to make them functional. Elevator cars need to move fast but, if the speed is too high or the stops too abrupt, there is a risk that passengers will be affected negatively. These factors need to be respected when constructing the mechanics of the elevator and the algorithms controlling the elevators.
The amount of electricity that is used to run elevators should be minimized and the capacity maximized. By changing the order in which the passenger calls are responded to it is possible to affect the passenger-time-energy consumption relationship. This order is controlled by algorithms that have different strate- gies of how they operate. This makes different algorithms suited for different locations and/or different traffic flows.
The manufacturer of the elevator decides which algorithm or algorithms are best suited for the location of the elevator. The key attributes that affect this decision are the size of the building, number of people in it and their pattern of movement. For office buildings where there are distinct up peak in the mornings and down peak in the afternoon it is important to implement an algorithm that handles that in the best way. An elevator algorithm in an apartment house does not need to handle as many simultaneous requests, and people there are often more patient when waiting for an elevator to answer their call [3, p.4].
Therefore these elevator algorithms can prioritize energy consumption more.
Another example of an environment is hospitals where the algorithms have to be able to prioritize emergency calls without disrupting the flow more than necessary.
This thesis will focus on two elevator control algorithms, their strengths and weaknesses regarding time and energy consumption. In the beginning of the the- sis the problem being researched and the purpose are presented. This is followed by background presenting the evolution of algorithms, and the demands they have to handle. In section three the chosen algorithms will be presented. In the fourth section the equations and method being used are described. In the fifth section the results of the simulation are presented. The sixth section contains discussion about the results, the algorithms, the literature, the method used, the simulation and possible continued studies. The seventh section presents a conclusion.
Problem statement
The passengers waiting time and energy consumption are two main factors to consider when constructing algorithms for elevators. The elevators in an office building consume 11% of the total energy consumption in the building according to the elevator company Schindler’s investigation into Hong Kong buildings [4].
Therefore it is of interest for building owners to reduce the energy consumption
of the elevator system. At the same time elevator service consists of serving passengers whose needs and expectations it has to fulfil. The waiting time affects the passengers’ appreciation of the total service even if the service of transportation is effective [5].
The problem that will be handled in this thesis is to find out which of two algorithms is best suited to handle the lunch hour traffic in an office building.
The two algorithms to be compared are fixed sectoring, priority timed unidi- rectional sectors (FS4) and fixed sectoring, bidirectional sector (FSO). As the names indicate both algorithms are using fixed sectors when scheduling passen- ger collections. The way of using sectors differs between them making these algorithms suitable for comparison.
The research question is: Which algorithm is the most effective considering the waiting time of passengers and energy consumption? What are the key factors that contribute to this effectiveness?
Purpose
This thesis compares two classic elevator algorithms to determine which of them is most suited for using on lunch hour in an office building. The waiting time and energy consumption are taken into consideration. Low energy consumption is good for the environment and reduces the electricity costs for building owners.
A shorter waiting time will keep the passengers in a good mood. The big number of office buildings all over the world makes even a small reduction of energy consumption notable for the environment. At the same time the building owners have to consider the waiting time to give the best service. Therefore both aspects need to be considered when choosing the elevator algorithms.
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2 Background
The first part in this section presents literature read on the subject. The second part describes the evolution of elevator algorithms. The third part presents the demands an elevator algorithm must be able to handle.
2.1 Previous research
There are several books and reports about this topic. A selection of them will be described shortly in this section.
Books
The books presents the elevator theory. In these books requirements on the physical elevator as well as classical control algorithms are thoroughly investi- gated [1][2][3].
Reports
Most reports have dealt with narrow subjects concerning elevator algorithms.
The writers have simulated elevators in different environments to investigate ser- vice quality or energy consumption. The energy consumption is often estimated through the use of simulation programs. In the simulation programs differ- ent technologies and optimizations are tested to see the effects on the energy consumption [6], [7]. Studies about service quality improvement often involve optimizations of existing algorithms or technological enhancements. The opti- mizations can be done by letting the control system access traffic information and utilize it to improve performance [8]. Technological enhancements that have been investigated are motion traction in corridors to detect passengers. That could improve the efficiency of the elevator service [9].
2.2 History of the elevator algorithms
Elevator control systems have evolved during its lifetime. Early elevators had no automatic system to control the elevator cars. From the middle of the 19th- century to about 1890, elevators were controlled with a rope by the person travelling or who wanted the elevator to arrive at their floor. When electrical elevators were invented the movement was regulated by a lift attendant con- trolling a handspike to make the elevator ascend, descend or stop. The use of algorithms to control the elevator’s travels came in the next generation of elevators in the 1950s [2, ch. 10.1ff].
With the electrical elevators serving parallel shafts followed a problem of elevators clustering and moving as a group during hectic traffic conditions. Due to this inefficiency the algorithms of the computer controlled elevators were at first written to schedule a continuous movement for the elevators. This was a bad way of handling the problems because the elevators made unnecessary trips without performing any services for passengers. Therefore systems responding to landing calls were developed [2, ch. 10.1.2f].
One of the algorithms used in systems is the single call automatic control, also called noncollective or automatic pushbutton (APB) control. The elevator is operated by car buttons and single call buttons. The calls made from within the car have priority over floor calls, which are only answered if the elevator is free. This makes the algorithm suited for buildings with up to four floors [2, ch.
10.2.1].
The most common algorithm used is the collective control. There are three versions of this algorithm given by G.Barney [2, ch. 10.2.2]:
• Non-directional collective, where the elevator answers all calls that are made when not in use or when passing floors.
• Down collective, where the elevator answers calls if it is empty or going down. Ignoring floor calls that the elevator is passing when going up to leave a passenger.
• Full collective is used when the call buttons are supplied with an UP and DOWN alternative of travelling direction. The elevator stops for calls that match the direction it is travelling in.
When several elevators are active in parallel shafts it is not effective or profitable to send more than one elevator to collect the same passenger. To avoid this grouping the elevators should be equipped with a collective call button. The group traffic control system recives the calls and decides which elevator should answer a call to give the passengers a better service [2, ch. 10.3.1].
In a modern control system there are various algorithms controlling the dis- tribution of elevators. Depending on the intensity of passenger flow the system is programmed to use a special algorithm. The complexity degree of a control system depends on the number of elevators being controlled, the number of different algorithms the system has at its disposal and the complexity of the algorithms [2, ch. 10.3.1].
There are several methods to assign elevators to calls. To make elevators answer the calls in the best way the control system needs to obtain all the calls made and assign an elevator to answer each call. There are different methods to assign elevators to calls. The simplest is to send the closest elevator. Another way to assign calls is to divide the building in sectors, assign elevators to the sectors and park inactive elevators in sectors without an elevator assigned to it.
If a new call is made the elevator assigned to the call’s sector will handle that call. The main ways to divide a building in sectors is with static and dynamic sectors [2, ch. 10.3.2]. The static sectors can be divided by subsequent floors or in directional sectors; the sectors are made up by a series of down-calls and other sectors of a series of up-calls. If an elevator is not in its own sector or busy handling other calls a reassignment will be done to make another elevator take care of this call [2, ch. 10.3.2.1].
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2.3 Demands on elevators
Elevator scheduling has several different efficiency demands to meet from pas- sengers and the building owners.
2.3.1 Passenger experience and time demands
Passengers demand efficiency, functionality and comfort. The acceleration and the deceleration of the elevator need to be adapted to what the human body perceives as comfortable. The acceleration/deceleration should therefore not exceed 1.5m/s2 and the change of acceleration should not exceed 2m/s2 [3, p.3]. Transportation by elevator should not take too long and there should not be too many stops on the way. The waiting time for an elevator to arrive can not be too long either. Studies have shown that a passenger will become impatient if they have to wait for too long. In office buildings the waiting time can not surpass 30 seconds and in apartment buildings 60 seconds [1, p.64].
Demands are also put on the time of travel. This means there are demands on the round trip time (RTT) of an elevator. The RTT is the time it takes for an elevator to go on one trip around the building, opening doors at the bottom floor and returning there again. These trips should not take more than 2-3 minutes, with exceptions for tall buildings. This is because passengers who are going to the top of a building will have a big part of the RTT as their time of travel [3, p.13]. Other studies have shown that there is a limit of 100 seconds of travel time before passengers will become impatient if the elevator stops multiple times. This travel time can be prolonged due to the circumstances of the passenger, for example if they are in company with others or if many other passengers are collected/dropped-off at each stop [1, p.64].
Measuring time is problematic. A passenger perceives time depending on his/her destination and goal with the elevator trip. It is for example more acceptable if a trip in the morning to the floor where the passenger works takes longer than a trip down to the entry floor on the way home [3, p.2ff].
2.3.2 Energy consumption
A running elevator motor consumes energy. To have an algorithm that is effec- tive in how the passengers are picked up and planning the travel should lead to less energy being consumed. This saves the building owners money and lowers the wear of the motor and wires, making the technical components last longer.
In this thesis the energy consumption will be evaluated by measuring the dis- tances that the different algorithms make the elevator travel. Longer distances travelled will be assessed as consuming more energy.
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3 Algorithms
This section will shortly present algorithms for elevator systems and the reg- ulations they need to follow. Then the two algorithms to be compared are presented.
3.1 About algorithms
Most of the modern elevator systems are using algorithms based on some of the classical elevator control algorithms such as NC(nearest car), FSO(fixed sec- toring, bidirectional sector), FS4 (fixed sectoring, priority timed unidirectional sectors) and DS(dynamic sectoring) [2, ch. 11.2.3]. These algorithms can be manipulated, combined and made to learn what is best suited for the environ- ment it is operating in. The designer of elevator control system may also write a completely new algorithm to serve an environment. There are two basic rules that all algorithms must follow.
• Elevators must always give the highest priority to calls made from inside the car.
• Elevators can not change travel direction as long as there are passengers in the car.
The algorithms compared in this thesis are FS4 and FSO.
3.2 FS4 - fixed sectoring, priority timed unidirectional sectors
This algorithm divides the building in dynamic up and down sectors, where every sector has a priority level. Each sector consists of a few floors, where the number of floors depends on the height of the building. When a call comes from a sector the whole sector is registered. This sector receives a priority level. The priority level will be one at the start if no special conditions are applied and increase up to priority six as waiting time increases for a passenger. The waiting time is measured in periods and the number of seconds needed to reach the next priority level can vary for different sectors. It is common to have six priority levels, time periods for reaching them is 10,15,20,30,40,60 seconds for a standard priority sector and 30,50,70,90,105,120 seconds for a low priority sector.
Several aspects are considered when deciding if/when an elevator will be assigned to a calling sector. One aspect is the number of free elevators, if there is a free elevator it will be assigned to a sector with the highest priority level.
If several elevators are free at the same time it will be the elevator that is nearest located to that sector that will get assigned. When an elevator gets the assignment it will move to that sector without any stops. If there is space left in the elevator after picking up all calls in the assigned sector the elevator will pick up calls going in the same direction as it is moving.
Exceptions are made for the bottom floor which is a whole sector by itself and when an elevator is assigned to its call it only picks up people in sectors with priority five or higher on the way down. If there is more than one elevator free and a call occurs, the elevator that stands on bottom floor is always the last one to get that assignment.
Calls from sectors with priority level six receive full attention. Next available elevator moves there without any stops on the way. If the car gets full before the whole sector is served next available car will be sent to the sector.
This algorithm is best suitable for light to heavy balanced interfloor traffic [2, ch. 10.4.4].
Example:
The building has 8 floors and 3 elevators with capacity of 4 passengers. See figure 1.
• Elevator 1 is on floor 2 and ascending to its next stop which is floor 3.
• Elevator 2 is on floor 4 and ascending to stop at floor 5 and then 6.
• Elevator 3 is on floor 2 and descending to its next stop on the bottom floor.
There are 6 calls at the moment.
• The bottom floor call is being handled by elevator 3. This elevator will not pick up the call on floor 1 because of the rule that says than an elevator does not pick up any calls with priority lower than 5 when it is scheduled to handle a call from the bottom floor.
• The floor 1 call is still placed in the queue.
• The floor 3 call is handled by elevator 1.
• The floor 5 and floor 6 call is handled by elevator 2, even though the call at floor 5 came in later than the call at floor 6.
• The floor 4 call is placed in the queue.
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Figure 1: Example of a fixed sectoring scheme for FS4.
3.3 FSO - fixed sectoring, bidirectional sector
FSO divides a building in static sectors, where every sector gets an elevator assigned to it. The number of sectors depends on the number of elevator cars and the sectors consist of consecutive floors, covering both up and down calls.
An elevator is assigned to a sector if it is in the sector, the sector is empty and both elevator and sector are unassigned. The elevator can lose the assignment to its sector if it receives a call that forces it to move outside its own sector.
When the elevator is travelling to its next stop it will answer the calls on its way matching its moving direction. Another way of losing the assignment to a sector is if the elevator becomes full. The elevator assigned to a sector answers floor calls in its own sector and in empty adjacent sectors above [3, p. 129f].
Free elevators are parked in different sectors to provide fast service for pas- sengers.An elevator car that is assigned to a sector where no calls are made parks itself at the current position. An elevator car that is unassigned moves to the nearest vacant sector and parks in it. To have an elevator parked at the bottom floor is preferred over having elevators parked in other sectors. This means that if the elevator stationed at the bottom floor leaves the closest parked elevator car will go to the bottom floor to park instead [3, p.130].
The algorithm is suited to handle balanced interfloor traffic, but can handle unbalanced interfloor traffic and up-peak traffic [3, p.131].
Example:
The building has 6 floors, including the bottom floor, and two elevators with capacity of 4 passengers. See figure 2.
• Elevator 1 is stationed at the bottom floor and assigned to sector 1.
• Elevator 2 is assigned to sector 2 and has just arrived at the top floor to answer a down-call. On the way down elevator 2 picks up two passengers at floor 4 and one passenger at floor 3 both wishing to travel down. Elevator 2 is now full and it loses its assignment to sector 2.
• A new passenger arrives at floor 3 shortly after and a new call is registered.
Elevator 1 leaves its sector to answer the call. Sector 1 becomes vacant and sector 2 gets elevator 1 assigned to it.
• Elevator 2 drops of the passengers at their floors and gets assigned to sector 1 which is vacant. Since no calls are made in the sector it parks there.
• Elevator 1 picks up the passenger at floor 3 and begins to travel down to drop of the passenger at the bottom floor.
• A call is made at floor 1, this passenger is picked up by elevator 1 which picks up calls on the way it travels.
• Elevator 1 now lost the assignment to sector 2 since it left the sector. But no calls are made in it so it stays vacant.
• When dropping of the passengers at the bottom floor elevator 1 gets as- signed to the vacant sector 2 and returns to park in it to wait for new calls.
Figure 2: Example of a fixed sectoring scheme for FSO.
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4 Method and theory
The first part of this section will describe the office building which the algorithms will be tested in. The second part contains a definition of time used in the project. The third part presents equations used. The fourth part presents ways of simulating. The last part presents the simulation program developed for the project.
4.1 Environment specification
The elevators will be called by passengers pressing an UP or DOWN button at the floor they are on, indicating their required direction of travel. The number of elevators in service will vary, two to four elevators will be used in the simulation.
The building the elevators are placed in is an office building with at least 8 and at most 20 floors. Office buildings have a characteristic movement of passengers. The passenger pressure is higher in the morning, during the lunch hour and in the afternoon. The research in this thesis will be concentrated on the lunch traffic.
The hypothesis is that 30 employees will be stationed at each floor, 70% of the people are assumed to potentially leave the building. The elevators capacity is 10 people per elevator.
4.2 Definition
tu = time unit, the time it takes for an elevator to transport between two stops or to make a stop at a floor.
This definition of time is chosen because of the ease it provides when com- paring the algorithms. It does not matter if we handle seconds or time units when comparing the two algorithms because they move according to the same timeline.
4.3 Equations
Poisson distribution:
pr(n) = (λT )n!n ∗ e−λT [3, p.46]
λ = numberof calls/f loor/tu[3, p.216]
n = number of calls
T = time interval for calls to happen
The Poisson distribution is used to modulate a certain number of events hap- pening during a certain time span [3, p.46].
This equation is used to decide the passenger flow of each floor. It is chosen because it is the equation used in the literature and motivated to be the one that is generally accepted for the purpose of simulate passenger flow [3, p.46].
Calculation to decide total amount of passengers:
total amount of passengers = f * x
x = the amount of calls with the highest probability in the Poisson calculation f = number of floors
This equation together with the Poisson equation are used to estimate the num- ber of people that will move from and within the building during the lunch hour.
Calculation of elevator travel distance:
distance = f ∗ 3.5 f = number of floors
3.5 = height between two floors.
This is used to calculate the total distance that an elevator travels. In this case the height of a floor is 3,5 meters.
4.4 Ways of simulating
Time-driven simulation contains a time variable which is keeping track of the current time. The variable is incremented and after each increment all objects are updated, if an event occurs at that second it is taken care of . If the variable increases with a fixed value it is a fixed-time driven simulation. The simulation ends when the time variable reaches a certain value or the simulation reaches a certain state [10].
Event-driven simulation ”jumps” between occurring events, updating all ob- jects to the current state and handling the event. Event-driven simulation method is more advanced in its implementation, but is suited for simulations with a long time period and big number of objects to be updated. The sim- ulation ends when the time in the simulation reaches a certain value or the simulation reaches a certain state [11].
The time period investigated in this project is short and the number of objects in the simulation is of manageable size. This means the objects can be iterated over without significantly affecting the runtime of the simulation program. Therefore the time-driven simulation will be used.
4.5 Simulation program development
A simulation program makes it possible to test the algorithms performance over several days. In an office building the flow of passengers on the different floors will vary from day to day. Because of the simplicity to run the simulation big amounts of test data can be generated. This allows studies of the overall performance of the algorithms. Testing the algorithms for several days will make the results more applicable on a real environment.
The simulation program is constructed in Java. Java is an object oriented language and the simulated environment consists of objects that interact with each other. This makes Java suitable for this project.
An analytical evaluation of the algorithms could be another way to investi- gate the problem. However it is not preferred in this case since the aim is to investigate the algorithms during lunch in an office building. To do this several lunches need to be observed and different flows of passengers would occur. In a
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building of at least 8 stories and 30 people per floor the amount of passengers travelling is too big to be able to test this analytically.
Factors that affect the comparison
When testing the algorithms’ performance the physical aspects of the elevators are not taken into account. The reason is that the elevators in the simulation are identical for both algorithms, so factors such as speed, deceleration and acceleration do not affect the comparison.
Every time an elevator stops it affects the waiting time. The number of stops depend on how the scheduling is done by the algorithms. Since the algorithms operate differently there is a probability that the number of stops will differ between them. In the simulation a time unit passes every time an elevator makes a stop. This way the number of stops made by the elevators will affect the result.
Time constraint from passengers will not be taken into consideration. Time units will be used for the comparison and the real time a passenger has been waiting is not included in our research.
Description of the simulation program
The simulation program has three main parts consisting of one class that creates a list of passenger call events (that will be called distribution class in the rest of this section) and two classes with the implementation of each algorithm (these will be called algorithm classes in the rest of the section).
In the beginning of the simulation data about the building is required. Num- ber of elevators, number of floors, passengers per floor and the time that the simulation will run is handed by the user. This data is passed into the distribu- tion class and the different algorithm classes.
The distribution class creates passenger call events. The movement of the passengers leaving is distributed in the beginning and end of the simulation time. The passengers that did not leave the building are distributed over the entire time for simulation. The class calculates the number of calls that will occur in the two groups of passengers by using Poisson distribution. The list of call events are passed to the algorithm classes.
The two algorithm classes divide the building into sectors depending on the building information.
At each time step the algorithms check if any call is made and if it can be handled by any of the elevators. If that is not the case, the call is placed in a queue and will be handled later. This queue will be handled before new calls in the following time steps. The distances of the elevator and the waiting time of every passenger are increased in every time step.
The structure of the program is to have classes for all interacting objects such as elevators, sectors and passengers. These objects are overlooked by the control algorithm which receives and handles the calls made by passengers.
This structure makes each object hold its own information, so that the control
algorithm can get the information needed from the objects to evaluate the next step.
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5 Results
This section presents the results of both algorithms handling passengers in build- ings of different heights and with different number of elevators at its disposal.
The results have been generated through a simulation program. In the tests the number of floors and number of elevators have been varied. The number of passengers per floor was 30 and the runtime for the simulation was set to 4500 tu. The simulation was run 10 times per number of floors and mean values were calculated from the results given by the simulation. The results are presented in graphs.
5.1 Waiting times for chosen algorithms
This section presents the graphs for the results of waiting time. The x-axis shows numbers of floors and the y-axis the mean value of the mean waiting time for passengers.
The first graph is for two elevators, the second for three elevators and the third for four elevators.
Graph 1: Mean waiting time for two elevators.
Graph 1 shows the mean waiting time of passengers for two elevators and the number of floors were varied from 8 to 20.
Both algorithms algorithms increase similarly, but FS4 is for the most parts a bit lower in the waiting times than the FSO. After 10 floors the waiting time
increase much and after 12 floors even more. After 14 floors the waiting times are increasing more slowly again.
Graph 2: Mean waiting time for three elevators
Graph 2 shows the mean value of waiting time of passengers for three eleva- tors and the number of floors were varied from 8 to 20.
Both FS4 and FSO develop in the same pattern. For all numbers of floors the FS4 has lower waiting times. From 14 stories the waiting time increases more than in previous numbers of floors, and after 16 stories it increases even more but then the increment is stabilised.
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Graph 3: Average waiting time four elevators
Graph 3 shows the mean waiting time of passengers for four elevators and the number of floors were varied from 8 to 20.
The FS4 and FSO develop in a similar way, but the FS4 has lower waiting times than FSO. From 16 floors the waiting time start to increase more than for lower buildings.
5.2 Distances of travel for algorithms
This section presents the graphs for the results of energy consumption. The x- axis shows numbers of floors and the y-axis the mean value of the total distance the elevators travelled during the simulation time.
The distance the elevators has travelled is used to estimate the energy con- sumption. Longer distances travelled for the elevators are presumed to consume more energy.
The first graph is for two elevators, the second for three elevators and the third for four elevators.
Graph 4: Energy consumption for two elevators
Graph 4 shows the mean energy consumption of passengers for two elevators and the number of floors were varied from 8 to 20.
For buildings up to 12 floors the energy consumption is almost equal for both algorithms. When the building is more than 12 floors the FSO is more energy efficient.
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Graph 5: Energy consumption for three elevators
Graph 5 shows the mean energy consumption of passengers for three eleva- tors and the number of floors were varied from 8 to 20.
For buildings up to 12 floors the algorithms are equal. For 14 to 16 stories the FS4 has a lower energy consumption. The FSO is more energy efficient when the building is over 18 floors.
Graph 6: Energy consumption for four elevators
Graph 6 shows the mean energy consumption of passengers for four elevators and the numbers of floors were varied from 8 to 20.
Both algorithms have an equal development of energy consumption up to 12 floors, but the FS4 is more energy efficient. For buildings of 14 to 16 storiess the FS4 is more efficient than the FSO, but for buildings over 16 stories the FSO is more energy efficient.
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6 Discussion
The first part of this section presents a discussion about the results. The second part focuses on the algorithms that have been compared. The third part presents a discussion of the literature. The last part presents discussion of the method.
6.1 Results
Waiting time
The graphs show that the waiting time for both algorithms increase at almost the same rate. When the building has two elevators the algorithm can handle passengers from 8 to 10 floors for both algorithms. (By handle we mean that the waiting time increases steadily as the number of floors increases). The two algorithms have almost the same waiting time for 10 storey buildings (see Graph 1 and appendix 1, table 1). For more than 10 floors the waiting time increases significantly. When there are three elevators handling 10 floors the waiting time for FS4 is improved, but not for FSO. Three elevators are able to handle passengers up to 14 floors in both algorithms. For a bigger number of floors the waiting time increased (see Graph 2 and appendix 1, table 2). For four elevators in the building, up to 16 floors can be handled before the waiting time increases significantly (see Graph 3 and appendix 1, table 3). Over all FSO has higher waiting times than FS4 (see appendix 3 Graph 7).
There were no significant differences between the mean waiting time for the algorithms. The cause for these similarities in the results could be due to the high passenger flow at the beginning and end of the lunch. These cause queuing and mean that FSO elevators will be less influenced by what sector they belongs to. The algorithm will assign the first passenger of the queue and other passengers on the way, with the same direction of travel, to an appropriate elevator. This will make the two algorithms work similarly.
The difference that appeared, where FS4 has a shorter waiting time then FSO, may be an effect of FS4 priority rules. When FS4 decides to attend to a sector with the highest priority and it takes care of all the passengers in that sector. This makes FS4 more efficient, considering waiting time. FSO always starts the trip by attending to the call that has been waiting longest, but it also takes care of every possible call on the way to next the destination. This will increase the waiting time of other passengers, where some of them already have been waiting for a long time.
The results also showed that FS4, for some cases, did not service all passen- gers during the test time. For two elevators there are people waiting when there are 12 floors in the building. For three elevators people are waiting when there are 18 floors, and four elevators 20 floors. The reason for this is probably the same as mentioned before, that the FSO picks up the people with high waiting time and others on the way but FS4 only takes care of people in high priority sectors. FS4 also passes by passengers that have a low priority as soon as calls come in from the bottom floor. This means these people have to keep standing in the queue until their priority is five or six before they are answered during
the end rush of people coming back.
In our comparison of the waiting time the mean values was used. These values could have been affected by extreme values generated by a few passengers.
Because of this the median value would have been of interest to investigate.
Energy consumption
Energy consumption, for the two algorithms, increases with the height of the building and the number of elevators.
In test case with two elevators and buildings with up to 12 floors the energy consumption is almost the same for both algorithms. The FSO is consistently more energy efficient than FS4 for buildings up to 20 storeys, except for 12 storeys buildings. The 12 storeys deviation is probably due to the circum- stances for the test. For buildings with up to 12 floors the difference in energy consumption is small and that could mean that the algorithm which uses more energy could switch. For these floors extra tests were done and that showed FSO and FS4 varied in being the most energy efficient. For buildings higher than 12 floors the difference in energy consumption becomes more remarkable.
With three and four elevators the FS4 is more energy efficient between 8 and 16 stories, after which its energy consumption significantly increases (see Graph 4-6 and appendix 2). FSO then becomes the leading algorithm when it comes to energy efficiency.
The FSO algorithm has a lower energy consumption for buildings higher than 16 floors and when there are two elevators. The reason is that the algorithm assigns an elevator to answer as many calls as possible on its way and assigns a moving elevator, if it is possible, before assigning a free elevator to answer calls.
This is the same quality that made the waiting time longer for FSO and might also contribute to make the graph curve linear (see Graph 4-6).
The most striking result is that the FS4 has a sudden increase of energy con- sumption(see appendix 3 Graph 8). This is probably caused by how the sectors are made in FS4. The sectors are of static size but vary in number, so high buildings are divided in many sectors. This and the priority rule, that makes the elevator pass calls, create an increased movement. Another reason might be that when assigning a new call the algorithm first looks for free elevators, instead of an elevator that will pass by this floor.
FS4 has a better logic to serve passengers in a sector than FSO. This could be the reason for its advantage for buildings with three or four elevators and 8 to 16 stories.
6.2 Algorithms
6.2.1 FS4
There are positive and negative aspects of the algorithm. The positive aspects are that FS4 keeps the waiting times down by concentrating on answering the calls that have been waiting longest and that the bottom floor calls are priori- tized.
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A situation leading to passengers getting a negative experience could occur in the FS4. This happens when the elevator is leaving its last passenger on a floor that does not belong to a highly prioritized sector. Because of the highly prioritized calls this elevator will not give service to the people waiting here even if they enter this car and try to make it go to their destination.To encourage passengers on that floor not to enter usual strategies are to turn down the lights in the elevator car or having a sign that lights up encouraging them not to enter [2, ch. 10.4.3].
6.2.2 FSO
As mentioned earlier in this section, this algorithm answers all the calls effi- ciently. If the traffic is low, the free elevators park in different sectors to provide fast service [3, p.130]. This logic enables this algorithm to make maximum use the elevators size in most cases.
The FSO algorithm also has the situation where the elevator drops off its last passenger and someone on that floor who is not first in the queue tries to use it. The elevator will not give service to this passenger.
6.3 Literature
The books deals with almost everything needed regarding algorithms, physical requirements, passenger requirements and mathematical calculations to con- struct an elevator simulation program. Therefore these books have been of most use for this project. The fact that the authors consists of Ph.D.s, M.Sc.s and experts in the field of elevators makes these books a reliable resource of information.
The reports we have read have been used as inspiration to the possibilities of simulations of elevator performance. We decided to compare classical forms of algorithms, which made the modified algorithms handled in the most reports unsuited for our research. Numbers regarding energy consumption that are mentioned in this report were confirmed by other reports and their sources.
6.4 Method
6.4.1 The time definition
By using time units it was easy to compare algorithms to each other. We could simulate the behaviour of lunch hour passengers.
However, we were unable to see which of the start conditions for the building met the demand of waiting times of 30 seconds. If we had decided on a certain type of algorithm and adjusted its movements to the physical constraints of the elevator mechanics and passengers, this could have been found.
6.4.2 The equations
The Poisson distribution was used to estimate the number of people most likely to leave the office during lunch. We had to estimate the total number of people leaving the building for lunch by counting the probability of the number of passengers per floor leaving, instead of the probability of the total number of people in the building. This was because Java could not handle the big numbers that resulted in the Poisson formula, for calculating the probability for the whole population of the building. We thought restricting the numbers to the population per floor was the best way to estimate the total number of passengers during lunch.
The equation for calculating the distance of travel for the elevators has an estimated floor height. This height can vary between different buildings. But the comparison would not be affected by it since the relation between the algorithm and movement would still exist.
6.4.3 Simulation program
There exists more elements that affect an elevators travel route that are not taken into consideration in this simulation. For example, what if a particular floor is more popular, maybe a cafeteria? What if someone moves furniture and holds an elevator for a longer time on the same floor?
It is possible to know how close this simulation is to the reality by making more studies on this subject. Elements as those mentioned earlier could be added to the simulation.
The simulation shows differences and similarities in the algorithms, but it is not possible to see if these algorithms are actually able to handle the traffic because of the time unit that is used.
The way the FS4 algorithm divides the building into sectors is through a static size for up- and down-sectors. This probably affected the results. To get a fairer comparison the size and number of sectors in FS4 should have been dynamically calculated, as in FSO, where it depends on the number of elevators and floors.
The size of this problem made it possible to use a time-step simulation.
This type of simulation made it easy to get an overlook of the program and to test parts of the program during its construction. If the duration time of the simulation had been longer this would not have been efficient. For longer times, event-based simulation would have been more suited.
For the purpose of this thesis, however, the simulation fulfilled its role.
6.5 Continued studies
Continued studies on this could be done by testing the algorithms performance on the three main parts of the lunch. These constitute of the beginning when people are leaving, the middle part with interfloor traffic and the end when people return to the office.
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To investigate the median could give us better indication the occurrence of extreme values.
Real data from a buildings passenger flow could be gathered to make the simulation more suited for the buildings of interest.
A interesting aspect to investigate would be the real waiting time. By adding an elevator speed variable, acceleration, deceleration, door opening and closing, the time unit could be transformed to seconds in this simulation.
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7 Conclusion
The main factors that affect the waiting time and energy consumption when using these algorithms are:
• way of using sectors
• priority rules
• elevator parking
The way FS4 uses its sectors and its priority rule for handling calls from the bottom floor makes this algorithm superior in the context of waiting time.
The elevator always collects passengers from a sector where the waiting time is longest. The bottom floor has a special priority in the FS4 algorithm [3, p.128], which probably depends on the algorithm expecting more calls from this floor than any other floor in the building.
Concerning the energy consumption FSO performed better overall. The FSO maximizes the number of passengers collected every time it answers calls, leading to fewer passengers needing to be collected later.
Looking at both the waiting time and energy consumption the conclusion is that the FS4 algorithm is the better choice, in most cases, for building owners.
8 References
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Appendix 1
Table 1 (Average waiting time 2 elevators)
Table 2 (Average waiting time 3 elevators)
Floors 8 10 12 14 16 18 20
FS4 16 30 156 346 377 421 437
FSO 26 31 168 355 390 440 456
Floors 8 10 12 14 16 18 20
FS4 15 19 42 40 110 301 355
FSO 30 36 62 54 128 316 380
8 10 12 14 16 18 20
FS4 11 19 30 33 39 148 342
FSO 28 44 44 51 55 185 369
Appendix 2
Table 4 (Average energy consumption 2 elevators)
Table 5 (Average energy consumption 3 elevators)
Table 6 (Average energy consumption 4 elevators)
8 10 12 14 16 18 20
FS4 6321 8517 9150 12390 12990 14292 15159
FSO 6222 8382 9339 10434 11358 13020 14094
8 10 12 14 16 18 20
FS4 7251 10236 12624 13380 14574 20481 21966
FSO 7662 10674 12741 14235 15327 17427 18897
8 10 12 14 16 18 20
FS4 8097 11310 14880 16752 17748 27174 27903
FSO 8664 11934 15456 18408 19716 22266 24138
Appendix 3
Graph 7 (Waiting time difference
) FSO-FS4
Distance
−5000m
−3750m
−2500m
−1250m 0m 1250m 2500m
Floors
8 10 12 14 16 18 20
2 e 3 e 4 e
Time
0 10 20 30 40
Floors
8 10 12 14 16 18 20
2 e 3 e 4 e
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