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2008

Henri Hakonen & Marja-Liisa Siikonen

PUBLICATION

ELEVATOR TRAFFIC SIMULATION PROCEDURE

Henri Hakonen

E-mail: henri.hakonen@kone.com

Marja-Liisa Siikonen

E-mail: marja-liisa.siikonen@kone.com

This paper was presented at THESSALONIKI 2008, the International Congress on Vertical

Transportation Technologies and first published in IAEE book "Elevator Technology 17", edited by A. Lustig.

It is a reprint with permission from The International Association of Elevator Engineers [website

www.elevcon.com].

2008

Henri Hakonen & Marja-Liisa Siikonen

2

ABSTRACT

Passenger service level in an elevator system depends on the group

control and cannot be calculated directly. With conventional control,

waiting times and interval have a correlation in up-peak. With a destination

control system (DC), interval and waiting times do not have a similar

correlation as with conventional full collective control. Therefore, simulation

has become important in determining passenger waiting times with DC.

Passenger arrivals follow a Poisson distribution, and simulation results

vary depending on the random seed number of the simulation. In this

article, different simulation procedures and consistency of the simulation

results are studied.

Keywords: Destination control, elevator, planning, simulation, traffic

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Henri Hakonen & Marja-Liisa Siikonen

3

1 INTRODUCTION

Two of the most used performance criteria in elevator planning are up-

peak handling capacity (HC) and up-peak interval. HC is an important

performance measure that shows how well the system can handle up-peak

traffic. HC is calculated from well known formulas (Barney 1987). The

formulas assume full collective control, where passengers can enter the

first arriving elevator. Destination Control (DC) is different in that sense that

the control system arranges passengers in the most appropriate cars using

the destination information. This approach reduces the number of stops

per round trip, travel per round trip and the round trip time, which, on the

other hand, increases HC. Also passenger Time To Destination (TTD)

becomes shorter. Equations for the round trip time and HC using DC were

first introduced by Schröder (1990), and later by Sorsa et al. (2006).

Interval is up-peak round trip time divided by the number of lifts in the

group. Conventionally, passenger Waiting Times (WT) are much shorter

than Interval when the arrival rate is below the HC. This happens when

passengers can enter any car that leaves from the lobby. With DC,

passenger waiting times can be longer than Interval. To be able to

compare the performance of full collective control and DC, one should

rather look at the passenger Waiting Times and Times to Destination than

Interval. Interval is just an intermediate result to find out waiting times, but

with simulations waiting times can be analyzed without Interval. WT and

TTD definitions were given by Barney (2005).

Simulations can be used to find out HC, i.e. the highest acceptable arrival

rate with 80 % car load, or to study elevator performance with realistic

building traffic patterns. Simulation practices were discussed in the CIBSE

meeting in 2007 (Peters 2007a). DC has increased the need of simulation

in elevator planning since conventional planning criteria cannot be applied

with it. There are commercial elevator traffic simulators on the market as

well as simulators of elevator companies and consultants. Each of them

has their own procedures and ways to show the results. The aim of the

meeting was find consensus or an industrial standard for how the

simulation results should be utilized in elevator planning. Many questions

were addressed but open questions still remain. This article seeks answers

to some of those questions.

2 SIMULATION OF HANDLING CAPACITY

2.1 Determining of handling capacity

The traditional HC formula is based on a theoretical traffic situation where

all arriving passengers travel from the lobby to upper floors. HC is defined

as the number passengers or percentage of people that can be

transported in an up-peak situation with 80 % car load. According to

Western practice, HC should be higher than passenger arrival rate in daily

traffic situations. Pure up-peak situations are rare in buildings although

2008

Henri Hakonen & Marja-Liisa Siikonen

4

sometimes they may happen, e.g. after an evacuation when the

emergency is over and all passengers return to the building. This is,

however, an abnormal situation where all passengers enter the lobby at

once, and waiting times become long.

Simulation can be used for determining the HC. Simulations and

calculation formulas should give about the same HC with 80 % load factor.

The problem is how to arrange 80 % car loads in simulation since elevators

do not leave at even intervals as assumed in the up-peak calculation. One

approach is to limit the maximum load to 80 %, to use a very intense arrival

rate and to measure the throughput. Another, and better, approach is to

limit the maximum load to 100 % and to find an arrival rate where the

average car load is 80 %.

If we want more realism in up-peak simulations, a good rationale is the

conflict between the rated load and the car floor areas. Fewer people may

fit in a car than the number of passengers obtained from the rated load. If

we for this reason limit the maximum number of people fitting in a car to

80%, and simulate random passenger arrivals, this would be the same as if

we used a smaller rated load. With smaller load HC will be smaller and the

results do not correspond to the calculated HC.

If in an up-peak simulation we allow cars to load up to 100% also an

estimate of passenger waiting times is found. The random arrivals

sometimes cause loads close to 100 % and on some round trips the load is

below 80 %. The average car load factor becomes 80% at an arrival rate

equal to HC, and passenger waiting times start to increase with arrival

rates higher than HC.

In simulations the average car load factor will be 80% at the passenger

arrival rate of calculated handling capacity if cars are allowed to fill up to

100%. Or conversely, handling capacity can be found from the passenger

arrival rate where average load factor is 80%. Even though HC is defined

for the up-peak situation only, there is no reason why HC could not be

generalized to cover other traffic situations as well. Then a few new

definitions are needed:

• Round Trip Time: Time from moment car starts up to the next time it starts up after

two reversals

• Handling Capacity (HC): the number of passengers or percentage of population an

elevator group can transport in five minutes on average with 80 % car load factor

• Car Load Factor (CLF): The maximum load during the round trip of elevator

2.2 Effect of initial transient

In the beginning of simulation the system has no passengers and the

elevators are vacant. In the first minutes of simulation, the number of

passengers in the system increases and also WT and TTD increase. When

a constant traffic flow goes through the system during the simulation the

system will eventually reach a steady state. Since the passenger arrivals

2008

Henri Hakonen & Marja-Liisa Siikonen

5

follow a Poisson distribution, the state is steady only in a statistical sense,

which means that the distributions of results do not change in time. In the

beginning of simulation there is a transient or warm-up period that causes

bias in the results. The effect of bias is small, when the simulation time is

long, but the accuracy is better, if the initial part is removed from the

results. The same applies to the transient at the end of the simulation after

the last passenger has arrived.

Table 1. Test case

Entrance floor 0 Acceleration [m/s2] 0.8

Populated floors 1-16, 18 Jerk [m/s3] 1.2

Travel height [m] 72 Door closing [s] 3.1

Population 850 Door opening [s] 1.4

Number of elevators 5 Transfer time [s] in+out 2

Rated load [persons] 21 Start delay [s] 0.7

Rated speed [m/s] 3 Photocell delay [s] 0.9

The effect of initial transient was tested with the Building Traffic Simulator,

BTS (Siikonen et al., 2001) in an up-peak traffic situation. The test case is

shown in Table 1. A series of 1 000 simulations for 20 minutes were made

using different seed numbers in passenger generation and one-minute

averages were calculated. The result in Figure 1a shows that waiting time

is short in the first few minutes of simulation. After 5 minutes, the results

approach the steady state, and after 10 minutes no difference from steady

state can be distinguished. Based on this case, it is justified to remove the

first 5 minutes, or if high accuracy is necessary, the first 10 minutes can be

removed.

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Henri Hakonen & Marja-Liisa Siikonen

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(a) (b)

Figure 1. Effect of initial transient (a) and effect of the length of the

simulation time (b)

2.3 Effect of simulation time

Simulation time must be longer than the initial transient. In addition, there

should be enough data, such that the calculated averages do not have too

much deviation. Figure 1b shows average waiting times of single 5-minute,

30-minute, 2-hour and 6-hour simulations. The number of iterations (also

called replications) is 100 in each histogram. The initial transient is not

removed from the distributions in order to see the effect of the transient.

Therefore, the distribution for 5-minute simulations is clearly biased. Its

average WT is below 3 s while the others have average WT close to 8 s.

The deviation of waiting time decreases as the simulation time becomes

longer.

2.4 Serial simulation

Passenger traffic in simulations can be generated using the arrival rate and

three traffic components: incoming, outgoing and inter-floor. Arrival rate is

usually given as percentage of population in five minutes and the three

components are percentages of total traffic. Passenger arrival rate can be

constant, it can be increased continuously (ramp profile) or stepwise as

shown in Figure 2, or it can follow a typical daily traffic pattern. Greater

accuracy is achieved by using a larger number of simulations or longer

simulation time. According to Law and Kelton (2000), the deviance of

results is inversely proportional to the square root of iterations

(replications); thus we get an accuracy of one more decimal by making 100

times more iterations. Computation time sets limits to the simulation time

and to the number of iterations.

2008

Henri Hakonen & Marja-Liisa Siikonen

7

Step and Ramp Profiles

0

2

4

6

8

10

12

14

16

18

12345678 9101112

Step

Arrival Rate [%]

0:00

0:30

1:00

1:30

2:00

2:30

3:00

3:30

4:00

4:30

5:00

5:30

6:00

Simulation Time

Step

Ramp

Figure 2. Ramp and stepwise arrival rate profiles

2.4.1 Stepwise profile

In the stepwise profile, the system is usually empty in the beginning of the

simulation. There is a transient in the beginning of the simulation before

the results are stabilized. A defined time, e.g. 30 minutes, is simulated with

a fixed, constant passenger arrival rate. All arrived passengers are served

first before a new simulation with higher arrival rate starts. A series of

simulations can be made starting from a certain arrival rate and stepwise

increasing the arrival rate ending at an arrival rate close to the HC.

2.4.2 Ramp profile

Ramp profile is not a constant traffic situation but the arrival rate increases

slowly. If the increment is too fast, the effect of initial transient is visible in

the simulation results. If the arrival rate changes slowly enough, the results

are essentially the same as with a constant arrival rate. More accuracy is

achieved by making several iterations and calculating the average of all

simulations.

2.5 Comparison of ramp and stepwise methods

Different simulation procedures in the ramp and stepwise methods may

cause differences in the results. Comparing individual passengers in

simulations is not meaningful. For this reason we calculate average values

to get one to one correspondence between the results. The initial transient

period is removed before averaging. The results of ramp stepwise methods

are compared by making two kinds of simulation tests for pure incoming

traffic

• 30-minute stepwise simulations for 13 arrival rates: 4, 5, …, 16 % of population in five

minutes

• 6-hour ramp simulation where the first arrival rate is 4 % and the last is 16 %. Half-

hour averages are taken from the results

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Henri Hakonen & Marja-Liisa Siikonen

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(a) (b) (c)

Figure 3. Waiting times with stepwise method without (Step 1) and

with (Step 2) transient and ramp method (a), and waiting time

deviations of step (b) and ramp (c) methods

The process was iterated four times to get standard deviations. Figure 3a

shows waiting times with three methods: using the step method with and

without initial transients and using the ramp method. The results are

averages of four simulations. The difference between the methods is quite

small. The step method without initial transient gives longest waiting times,

0.2 s longer than the ramp method and 0.4 s longer than the step method

with initial transient. Figures 3b and 3c show averages and 90%

confidence intervals for average waiting time for a single simulation. The

confidence interval is about the same in both stepwise method (without

transient) and ramp method. This is quite natural, since simulation time per

data point is 30 minutes in both cases. The confidence interval gets quite

large, when the arrival rate is close to the HC where it is necessary to

simulate a longer time than 30 minutes or more than just one simulation to

get good accuracy.

Ramp: Deviation of

Average Waiting Time

0

5

10

15

20

25

4 6 8 10121416

Arrival Rate [%]

[s]

Step: Deviation of

Average Waiting Time

0

5

10

15

20

25

4 6 8 10 12 14 16

Arrival Rate [%]

[s]

Average Waiting Time

0

2

4

6

8

10

12

14

16

46810121416

Arrival Rate [%]

[s]

Step 1

Ramp

Step 2

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Henri Hakonen & Marja-Liisa Siikonen

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3 SIMULATION OF TYPICAL TRAFFIC PATTERNS

3.1 Up-peak simulation

0

5

10

15

08:15 08:30 08:45 09:00 09:15

Arri val Rate [% / 5 minutes]

Barney Up-peak Template

Outgoing

Inte r fl oo r

Incom i ng

0

5

10

15

20

25

08:15 08:30 08:45 09:00 09:15

Arri va Rate [% / 5 mi nutes]

Consta nt Up-pe ak Template

Outgoing

Inte r flo o r

Inc om i ng

(a) (b)

Figure 4. Peaked (a) and constant (b) passenger arrival profiles in up-

peak

Morning up-peak traffic is a critical traffic situation in office buildings. For

this reason performance requirements are often specified for an up-peak

situation and elevator configurations are compared in an up-peak situation.

Simulations make it possible to assess more performance measures than

calculations and enable comparison of different control systems.

Pure incoming traffic at a constant arrival rate, e.g. 15% of the population

in five minutes, is a basic simulation case (Figure 4b). The system will

reach a steady-state unless HC is exceeded. It is advisable to remove

initial and end transients, as with the step profile.

Non-constant up-peak arrival profiles can be simulated as well. Figure 4a

shows a one-hour up-peak template by Barney (Peters 2007b), which is

scaled so that the highest peak is the required up-peak HC. The hourly

average arrival rate is only about a quarter of the peak arrival rate.

Therefore, if the peak arrival rate in Barney’s profile is the same as the

arrival rate in the constant profile, the results are better with Barney’s

profile.

Full collective control with up and down call buttons, and DC control were

simulated for constant and Barney profiles for one hour (Figure 4). DC

allocates a passenger call immediately to an elevator which, during light

incoming traffic, can produce longer passenger Waiting Times than

conventional control with continuous call allocation. On the other hand,

passenger Transit Times (TT) and Times to Destination will be shorter with

DC (see Figure 5a). In Figure 5b passenger waiting time distribution and

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Henri Hakonen & Marja-Liisa Siikonen

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cumulative waiting times (axis on the right) are shown for conventional and

DC systems.

Time to Destination (TTD)

WT

WT

WT

WT

TT

TT

TT

TT

0,0 20,0 40,0 60,0 80,0 100,0 120,0

Barney DC

(λ=3,8%/5 mi n)

Barney

Conventional

(λ=3,8%/5 mi n)

Co nstant D C

(λ=15%/5 mi n)

Co nstant

Conventional

(λ=15%/5 mi n)

0

10

20

30

40

50

60

%

Time [s]

0

20

40

60

80

100

120

Cumulative %

Waiting Time Distribution with Constant

Demand Pattern (15%/ 5 minutes)

Constant DC

Constant Conventional

Constant DC

Constant Conventional

15 30 45 60 75 90 105 120 135 150 165 180 195 210

(a) (b)

Figure 5. Average TTD for Barney and constant profiles with full

collective control and DC (a) and waiting time distribution with

constant profile using full collective control and DC (b)

3.2 Lunch hour traffic simulations

During mixed lunch-hour period, traffic is often heaviest in office buildings.

In the beginning of the lunch hour, outgoing traffic is dominant and the

percentage of incoming traffic increases towards the end of the lunch hour.

Inter-floor traffic is heavier in a single-tenant than in a multi-tenant office

building. Working times of the companies, culture, habits of employees,

and locations of restaurants cause differences in lunch-hour traffic in every

country and building. Lunch-hour traffic patterns have been suggested by

Powell and by Barney (Barney 2003). In the following, three traffic profiles

are compared:

• two-hour lunch-time profile by Powell (Peters 2007b)

• lunch-time of one-day multi-tenant office profile by Siikonen

• lunch-time of one-day single-tenant office profile by Siikonen

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Henri Hakonen & Marja-Liisa Siikonen

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Table 2. Portions of Incoming (In), Outgoing (Out) and Inter-floor (Int) traffic

components and arrival rate (Arr) in single and multi-tenant lunch-hour profile

Siikonen multi-tenant (6b) Siikonen single-tenant (6c)

Time In Out Inter Arr Time In Out Inter Arr

12:00 20 59 21 9.6 12:00 14 56 30 9.6

12:15 22 61 17 9.9 12:15 11 58 31 14.2

12:30 20 70 10 9.3 12:30 11 43 46 12.5

12:45 36 57 7 10.9 12:45 13 44 43 12.6

13:00 57 31 12 8.5 13:00 16 34 50 11.1

13:15 59 28 13 9 13:15 23 29 48 11.5

13:30 65 15 20 9.4 13:30 35 22 43 11.4

13:45 68 13 19 10.3 13:45 33 19 48 11

0

2

4

6

8

10

12

12:00 12:30 13:00 13:30 14:00

Intensity [% / 5 minutes]

Lunch Hour De mand P atter n

Powell

Outgoing

Interfloor

Inco m i ng

0

1

2

3

4

5

6

7

8

9

10

11

12:30 13:00 13:30 14:00

Intensity [% / 5 minutes]

Lunch Ho ur Dema nd Patt ern

Multi tenant Office B uilding

Outgoing

Interfloor

Inco m i ng

(a) (b)

Figure 6. Lunch Hour demand patterns (a) Powell (b) Siikonen multi-tenant (BTS)

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Henri Hakonen & Marja-Liisa Siikonen

12

The case in Table 1 is used in the simulations. A series of simulations is

performed for each profile to determine the accuracy of the simulation.

Passenger arrival profiles are defined in Table 2 and Figure 6. Table 3

shows the average service times and their standard deviations for the two-

hour simulations. Average WT and TTD are the shortest for the Powell

profile where the average passenger arrival rate is the lowest. When we

compare the averages of traffic profiles, we notice that the differences in

average WT and TTD values are much bigger than the standard

deviations. This means that the chosen traffic pattern has much more

impact on the simulated WT and TTD than the simulation method.

Table 3. Averages of lunch hour traffic simulations

Profile Powell 6a Multi-tenant 6b Single-tenant 6c

Average arrival

rate [%/5min]

7.7 % 9.6 % 11.7 %

Performance

measure

Average Std. Dev. Average Std. Dev. Average Std. Dev.

Waiting time [s] 12 0.5 16 0.6 28 1.0

Time to

destination [s]

48 0.9 58 1.0 78 1.4

Load factor [%] 14 0.3 19 0.4 27 0.6

3.3 Daily traffic simulations

Daily traffic profiles are based on real daily traffic in office buildings. The

pattern of Figure 7a was measured from an office building in Paris

(Siikonen et al. 1991). The daily traffic pattern is simulated to determine the

service level and to find out how the elevator group can handle traffic

peaks during the day. Usually WT and TTD are studied, but also other

features such as passenger queuing in the lobby (Figure 7b). Also the

number of round trips, number of starts, and energy consumption during

the day and year are interesting figures.

2008

Henri Hakonen & Marja-Liisa Siikonen

13

0

10

20

30

40

50

60

70

80

09:00 12:00 15:00 18:00

s

Simulation time

0.0

1.0

2.0

3.0

N

Simulated Daily Traffic

Waiting Time

Time to Destination

Lobby Queue Length

(a) (b)

Figure 7. Typical daily traffic profile for a single-tenant office building (a) and

the simulation results for full collective control (b)

4 PERFORMANCE CRITERIA

The performance measures are related either to elevator performance or

passenger service level. WT and TTD are good criteria for passenger

service level. To be able to judge how good the service level of the

elevator group is, there should be criteria for it. In an elevator group with

an efficient control system waiting time distribution roughly follows

exponential distribution

Ft = exp(-t/Tav) (1)

where Tav is the average waiting time and Ft shows the fraction of waiting

times that exceed time t. Waiting time recommendations are shown in

Table 4. Time to destination follows Gamma distribution, and the limits in

Table 5 were specified according to it. These recommendations are valid in

all types of buildings for the daily traffic, and also for one peak hour and a

15-minute peak period. In practice, service level parameters can be

checked from the BMS or elevator monitoring systems.

0

5

10

15

12:00 18:00

Intensity [% / 5 minutes]

Daily Traffic

Single Tenant Office Building

Outgoing

Interfloor

Inc o min g

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Henri Hakonen & Marja-Liisa Siikonen

14

Table 4. Passenger waiting time recommendation where walking time

is not included

Average waiting time % of passengers served

within

Service level

(s) 30 s 60 s 90 s

Excellent < 20 75% 95% 99%

Good 20 – 30 65% 85% 95%

Satisfactory 30 – 40 50% 75% 90%

Acceptable 40 – 60 40% 60% 75%

Table 5. Passenger time to destination recommendation where

walking time is not included

Average time to

destination % of passengers served

within

Service level

(s) 90 s 120 s 150 s

Excellent < 80 70% 85% 95%

Good 80 – 100 40% 75% 90%

Satisfactory 100 – 120 15% 50% 80%

Acceptable 120 - 150 5% 20% 55%

5 CONCLUSION

In this article, simulation procedures and their accuracy were compared. In

determining Handling Capacity, the choice of whether to use the ramp or

stepwise method does not have much effect on the results as long as the

simulation time is long enough. The initial transient decreases the average

value of waiting time, especially in short simulations. If about 5 – 10

minutes are removed from the beginning of the simulation, the results

become quite stable. If the simulation is run until all passengers are

served, also the transient after the last passenger arrival should be

removed. The accuracy of waiting time improves, if the simulation time is

made longer or the number of iterations is increased. If only one iteration is

performed, the simulation time should be at least 30 minutes long. If the

2008

Henri Hakonen & Marja-Liisa Siikonen

15

arrival rate is close to Handling Capacity, a longer simulation time or more

iterations are needed.

A general way to compare the efficiency of alternative elevator

arrangements is to show average passenger waiting times and times to

destination at a desired arrival rate. Constant or typical traffic profiles can

be simulated to make the comparison. The same demand pattern should

then be used for all alternatives with a proper arrival rate.

REFERENCES

Barney, G.C. (2003), Elevator Traffic Handbook: Theory and Practice,

Spon Press, London and NewYork, ISBN 0-415-27476-1, 438 p.

Barney, G.(2005) Towards agreed traffic design definitions. Elevator World, February

2005, pp. 108.

Law, A. M. and Kelton W. D. (2000). Simulation Modeling and Analysis,

3rd. edition, McGraw-Hill, NY.

Peters, R..(2007a) CIBSE LIFTS GROUP: Traffic Analysis & Simulation

Open Forum. Elevator World, December 2007, pp. 128-131.

Peters R. (2007b). Getting Started with Elevate Version 7. Peters Research Ltd, 2007.

Schröder, J. (1990). Elevator Calculation – Probable Stops and Reversal Floor “M-10”,

Elevator World, No. 3, pp. 40-46.

Siikonen M-L., Susi T., Hakonen H. (2001). Passenger Traffic Flow Simulation in Tall

Buildings, Elevator World, August 2001, pp. 117-123.

Sorsa J., Hakonen H., Siikonen M-L, (2006). Elevator Selection with Destination Control

System, Elevator World, January 2006, pp. 148-155

BIOGRAPHICAL DETAILS

Henri Hakonen currently works as Traffic Calculation Specialist in the

Major Projects unit of the KONE Corporation. He received an M.Sc. degree

in applied mathematics from Helsinki University of Technology in 1996 and

Licentiate of Technology degree in 2003.

Dr. Marja-Liisa Siikonen works as Director – People Flow in the Major

Projects unit of the KONE Corporation, She has an M.Sc. degree in

technical physics from Helsinki University of Technology. In 1989 she

obtained the degree of Licentiate of Technology, and in 1997 the degree of

Doctor of Technology in applied mathematics from Helsinki University of

Technology. Both authors work in KONE Corporate Offices, Keilasatama,

Espoo, Finland.