Final Project
Rensselaer Hartford’s Elevator System Simulation Study with Promodel.
DES 6620
Fall 2002
William L. Allan
12/5/02
Table of Contents
1.0 Introduction
2.0 Objective of the Study
3.0 Description and Location of Elevators
4.0 Starwell Travel
5.0 Results
6.0 Summary and Conclusions
7.0 Recommendation for Improvements
2
2
3
15
16
20
21
1
Introduction
The elevators at Rensselaer Hartford are rumored to be the slowest and most inefficient
elevators in the world. Students and faculty waste considerable time waiting for elevators
and occasionally going in the wrong directions. The main bottleneck is all classes start
at the same time and the students tend to arrive at the same time.
Rensselaer Hartford provides graduate education and other service, primarily in the
evening four days a week. The building is a 7 story building serviced by 3 elevators and
2 stairwells. Student and faculty primarily arrive at one of two floors and are transported
to their classes either by one of three elevators or one of two stairwells. The wait time at
these elevators is judged to be excessive, relative to elevators at other buildings. At times
the direction of elevator travel is mistaken by the elevator users, and they enter an
elevator traveling in the opposite direction.
2.0 Objective of Study
The objectives of this simulation are as follows:
1) Assuming nothing can be done to change the elevator operation, determine the
best individual strategy to arrive at class in the shortest (on average) time.
Possible strategies are follows: Take the stairs, always go to the south elevator,
take the south elevator. It is imagined that the optimum individual strategy may
be different, depending on the number of levels that need to be traveled. This
study focus on arrivals at floor 2 and classes at floor 6.
2) Assuming the elevator can be programmed to wait at one floor, determine if there
is a significant improvement by having elevators wait at floors 2 or 3.
3.0 Description and Location of Elevators and the Model
The elevator and floor layout is shown in Figure 1. The layout is similar on floors 2 and
3, the primary entry floors.
South
Entrance
South
Stairwell
South
Elevator
East
Entrance
North
Elevator
1
North
Stairwell
North
Elevator
2
2
Figure 1 – Show Arrangement of Floors 1 and 2
3.1 Student Arrival data
Students arrival data was collected on two different floors. Data was collected for one
floor on a Monday and aTuesday for the other floor. It was immediately clear from these
observations that the east entrance in the primary entrance and the south elevator is not
significantly utilized. Hence the simulation need only consider the primary entrance and
the two north elevators. In addition, there is no waiting required to uses the stairwell and
there is no need to model the stairwells.
Originally it was planned to collect not only the arrival of students at each floor, but also
to keep track of which elevator they used and/or what floors they went too. However,
there were too many students to keep track of, and it was decided to collect only the
arrival data (students waiting for elevators, not students passing through and going to
classes on the entry floor).
The number of students who arrived who waited for the elevators was counted in two
minute intervals. Students who arrived and did not wait, because there class was on the
arrival floor, were not counted. The data is tabulated in Table 1.
3
Table 1 Elevator Data Collection Hartford Graduate Center
Floor3
Floor2
Start time
5:14 PM 5:14 PM
date:
11/4/02 10/29/2002
Day
Monday Tuesday
Floor3
Floor2
Floor3
Floor2
Additional time from
Start (min)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
Number of Number of
Arrivals
Arrivals
Floor 3 in Floor2 in
time
time
Inter Arrival Inter Arrival
interval
intervals
time(min)
Time (min)
7
7
0.286
0.286
8
17
0.250
0.118
8
6
0.250
0.333
6
13
0.333
0.154
10
15
0.200
0.133
9
13
0.222
0.154
17
15
0.118
0.133
16
17
0.125
0.118
11
10
0.182
0.200
10
10
0.200
0.200
10
6
0.200
0.333
4
6
0.500
0.333
10
7
0.200
0.286
3
3
0.667
0.667
3
0.667
3
0.667
2
1.000
1
2.000
1
2.000
3.2 Analysis of Arrival Data – Floor 3
Stat:Fit was used to determine the best distribution to represent the arrival times. The
results of the Auto:Fit function are shown in Table 2 for floor 3. A scatter plot is shown
in Figure 3 indicating the data is not correlated. Several possible distributions are shown
in Figures 4 to 6.
4
Table 2 – Third Floor Arrival Distributions
THIRD.SFP
Auto::Fit Distributions
distribution
rank
Pearson 6(0, 0.0122, 105, 5.81) 98.1
Log-Logistic(0, 4.05, 0.229)
97.6
Pearson 5(0, 5.55, 1.21)
97.1
Lognormal(0, -1.43, 0.453)
79.7
Inverse Gaussian(0, 1.17, 0.267)74.6
Beta(0, 0.667, 3.97, 7.08)
65.4
Gamma(0, 4.59, 0.0581)
48
Erlang(0, 5, 0.0533)
42.8
Weibull(0, 2, 0.303)
36.2
Triangular(0, 0.736, 0.158)
5.17
Exponential(0, 0.267)
1.4
Uniform(0, 0.667)
0.288
Pareto
no fit
acceptance
accept
accept
accept
accept
accept
accept
accept
accept
accept
accept
reject
reject
reject
5
Figure 3 Scatter Plot – Floor 3 Arrivals
Figure 4 Floor 3 Inverse Gaussian
6
Figure 5 Floor 3 Exponetial Distribution
Figure 6 Pearson Distribution Floor 3
3.2.1 Discussion Floor 3 – Arrival Data
This is the arrival of student at floor3 waiting for the elevator to go to other floors.
These arrivals have to be broken up or scaled to represent student going to different
floors.
This data represents the inter arrival time at floor 3(Model Floor 2). The best fitting data
is the pearson6 distribution (rank 98). The inverse gaussian has a rank of 74, but has a
very similar shape as the better fitting pearson6. The exponential distribution has a rank
of low rank of 1.4 and its shape is not like the data. Normally exponential distributions
are used for arrival times, but in this case is does not appear to be reasonable distribution.
7
Since the inverse gaussian and the pearson6 distributions have similar shapes and the
inverse guasian distribution is easily scaled or broken up to represent arrivals for different
floors, the inverse gaussian distribution is selected.
3.3 Analysis of Arrival Data – Floor 2
Possible arrival distributions are shown in Table 4. A scatter plot is shown in Figure 7.
Several candidate distributions are shown in Figures 8 to 10.
Table 4 – Floor 2’s Arrival Distributions
SECOND.SFP
Auto::Fit Distributions
distribution
rank
Pearson 5(0, 1.78, 0.437)
100
Pearson 6(0, 0.000886, 497, 1.79)99.8
Log-Logistic(0, 1.95, 0.306)
89.9
Lognormal(0, -1.1, 0.879)
53.5
Inverse Gaussian(0, 0.468, 0.515)50.5
Exponential(0, 0.515)
32.6
Erlang(0, 1, 0.515)
32.6
Weibull(0, 1.07, 0.53)
21
Beta(0, 2, 1.84, 8.81)
14.7
Gamma(0, 1.29, 0.4)
13.1
Triangular(0, 2.24, 0.118)
0.000355
Uniform(0, 2)
0
Pareto
no fit
acceptance
accept
accept
accept
accept
accept
accept
accept
accept
accept
accept
reject
reject
reject
8
Figure 7 Scatter plot of Floor 2 Data
Comment on scatter plot
The scatter plot suggest some correlation between data or the data is
not completely independent.
Figure 8 Floor 2 Distribution – Pearson5
9
Figure 9 Floor 2 Distribution – Inverse Gaussian
Figure 10 Floor 2 Distribution – Exponential
10
3.3.1 Discussion Floor 2 – Arrival Data
This is the arrival of student at floor2 waiting for the elevator to go to other floors.
These arrivals have to be broken up or scaled to represent student going to different
floors.
This data represents the inter arrival time at floor 2(Model Floor 1). The best fitting data
is the pearson5 distribution (rank 100). The inverse gaussian has a rank of 50, but has a
very similar shape as the better fitting pearson5. The exponential distribution has a rank
of 32. Normally exponential distributions are used for arrival times, and at this floor it is
more representative than at floor 3.
Since the inverse gaussian and the pearson5 distributions have similar shapes and the
inverse gaussian distribution is easily scaled or broken up to represent arrivals for
different floors, the inverse gaussian distribution is selected. The inverse gaussian
distribution is a reasonable representation of both floors 2 and 3.
3.4 Destination Distribution – Number of Student on Each Floor
The Registar of Rensselaer Hartford provide class size and most room assignments for
each day of the week. Review of this data and walk through inspections indicates that
floors 2, 3, 4 and 6 are the primary class room floors. Floor 1 (the basement) was only
sparely filled during the data collection period. Floor 5 is the library with very few
students and they probably do not all arrive at the same time. The seventh floor has no
classrooms.
As will be discussed later, promodel student edition has limitations on the number of
entities. To facilitate this limitation, only 4 floors will be modeled. The classes on floor
1 will be lumped with floor2, and the fifth floor (Library) and seventh floor will be
ignored. In addition, limitation, required modeling only one of the 2 north elevators, and
the number of arrivals and the arrival frequency needs to be adjusted.
Table 5 Floor 2 Arrival Data
Class Floor
Arrival Floor
3 (ProModel2)
4 (Promodel 3)
6 (Promodel 4)
2 (ProModel 1)
2 (ProModel 1)
2 (ProModel 1)
Total
Number of
students
43
33
6
81
Ratio
0.53
0.40
0.07
1.00
Inverse Gaussian Coef
Shape Value
Scale Value
(min)
1.78
1.96
2.32
2.56
13.10
14.42
The arrival distributions used are shown in Tables 5 and 6.
11
Table 6 Floor 3Arrival Data
Class Floor
2(Promodel 1)
4(Promodel 3)
6(Promodel 4)
Arrival Floor
Number
of
students
3(ProModel 2)
26
3(ProModel 2)
27
3(ProModel 2)
5
Total
58
Ratio
Shape Value
Scale Value
(min)
0.45
0.47
0.08
1
5.25
4.97
28.02
1.20
1.13
6.39
3.5 Locations
The Promodel Location are shown in Figure 11.
Floor 4
Floor 3
Exit
Que for Floor 2
Floor 2
Que for Floor 1
Floor 1
Figure 11 Locations
3.6 Network Path
A Network path for the elevator is established between Floor1, Floor2, Floor3 and Floor
4. During the data collection the travel times for the elevator between floors was very
consistent. The variability in the elevator performance is judged insignificant relative to
the demand variability.
The elevator travel times between floor, excluding door opening time and accelerations
was effectively measure and is shown in Table 7.
12
Table 7 Elevator(Network Path travel Times)
From to floor
1 to 2
2 to 3
3 to 4
Travel Time (sec)
1.4
1.4
2.8
The acceleration and door opening time was calculated to be 10 seconds and is included
in the processing time, and not included in the network path travel times.
3.8 Entities
3.8.1 Students
Four different student entities were selected. One student entity was used to represent the
floor of destination of the student. This was the original selection and it has significant
impact on the process logic. It was not easy to change after this selection. Since this the
model was limited by entities, in hindsight, it would have been better to have a single
entity and assign attributes to indicate which floor it came from and where it was going.
3.8.2 Pallets
A pallet is a necessary entity to load passengers on. A Promodel resource can only pick
up only one entity at a time, so an extra entity is required. This entity is move around by
the elevator.
3.9 Resources
An resource, named “elevator”, is used to move the pallet from floor to floor. The speed,
acceleration, and home are not used. (The pallet never releases the elevator).
3.10 Attributes
Five attributes (Promodel’s Student version limit) are used in the model. All are used to
report total system time of some entities, and characteristic of student entities. If more
were permitted, more would have been used. The attributes are as follows:
Entry_Floor – The floor a student enters on. It is used to permit calculation of system
times.
Time12
- Total system time for student entering at floor 1 and exiting at floor 2.
Time13
- Total system time for student entering at floor 1 and exiting at floor 3.
Time14
- Total system time for student entering at floor 1 and exiting at floor 4.
Time24
- Total system time for student entering at floor 2 and exiting at floor 4.
13
If I had chosen to use only a single type of student, then more attributes would have been
required to control the operation of the elevator.
[In hindsight, I did not realize until working on Lab 11 that attributes do not have to
defined for each entity. I could have used one attribute to record system times for
different entities, but I would have required more if statement to log in the proper label.]
3.11 Variables
Twenty five variables were used to model this simple elevator. Twenty two are
absolutely necessary to control the operation of the elevator. If more floors or elevators
are added, the number of variables would have increased. Two of the variables are used
as constants so that I do not have to change lines of code at many locations. One of these
variables is used for the summarizing data.
The variables are not described hear but are described in the promodel files The one
variable used for summarizing data is “MaxNumElev”, which represent the maximun
number of passenger on the elevator during a simulation. The maximum number
passengers was not automatically checked, but it was monitored during the simulations to
determine the reasonableness of the results. It was very useful for detecting logic
problems.
The number of variables and the process control coding could, perhaps, be improved or
made more efficient with more promodel experience and by the use of arrays, macros
and a different model approach.
3.12 Processing
The basic operation of the elevator is the elevator/pallet waits around for requests. Once
requested, it picks up the passengers and delivers them to the appropriate floor. If a new
request comes in between the time of first call and the delivery, it is assumed the elevator
will try to satisfy the request so long as it the elevator does not have to change directions.
It is also assumed that passengers in the elevator have priority over other call requests.
I have no ideas if this is the intended operational procedure of RH elevator’s, but it seams
reasonable based upon my own experience.
It is not know if calls for different floors are put into a first in first out queue. Keeping
track of such a request queue is beyond the scope of this study.
Promodel does not have an elevator like resource, or a resource type which permits
programming in control logic. The control operation logic must be incorportated into the
process logic of promodel.
14
The process control is provided in the promodel files. The only difference among the
different promodel files is in the logic. The …home1 and the …. home2 files send the
elevator to floors 1 or 2, if it is idle.
An elevator like resource is created with this logic, but promodel has some limitations
which affect the operation.
Promodel does not allow an entity (pallet/elevator) to be loaded after unloading at a
location. Suppose an elevator has passengers who want to get off at floor 2, but floor 2
also has passengers waiting to get on. If I unload first, the passengers are not permitted
to be loaded. The simple solution is to load the passengers first and then unload the
passenger. If new requests arrive during this process, they are not immediately satisfied
at this floor. They will be picked the next time. This is the process selected for this
simulation.
A possible solution is to temporary move the pallet to a temporary location and
immediately return back. This would create the need for more locations, more process
routes, and more logic. This option was not pursued.
This limitation results in other complications. The maximum number in the elevator is
not necessarily reported accurately. If the elevator is loaded prior to unloading, then the
number in the elevator is temporary incorrect (too high). This could be corrected with
more coding logic, but time did not permit this to be corrected.
Another complication is if students are delivered (unloaded) to a floor and no one is in
the elevator, and no one is waiting at this floor, the elevator can not wait at this floor to
load more students ( loads after unloads are not permitted). The simple solution is move
the elevator to the nearest floor to wait for a request.
4.0 Stairwell Travel
It was not necessary to model the stairwell with promodel. Few students use the stairwell
there is no competition for resources. The stairwell travel times are assumed constant
based on a single observation (myself). Within an individual, there is not expected to be
much variability and it is assumed the rate of climbing a flight of stairs is independent of
the number of flight
The Stairwell paths and travel times for the north stairwell are shown in Tables 8 and 9.
Table 8 – Stairwell Travel Times
Path
Time (sec)
15
Time to travel to/from elevator to stairwell
Time to travel up one flight of stairs
20
12
Table 9 – Stairwell climb
From
1(Floor 2)
1(Floor 2)
1(Floor 2)
2(floor3)
To
2 (floor3)
3(floor 4)
4(floor 6)
4(floor 6)
Travel Time
sec
min
52
0.87
64
1.07
88
1.47
76
1.27
5.0 Results
One basic model was created which does not have home location for waiting for a
request. Three other variation are made of this model. The first variation is the home
location of the elevator is floor2. This was achieved by changing the process logic to
sent the elevator to the home floor rather than wait for a request. The third variation is
the home location is Floor1. The fourth variation is a very approximate model of the
North elevator to approximate no other demand other than students from floor1 going to
floor 4. This was achieved by disabling all arrivals except for students going to floor4
from floor 1.
Table 10 Summarized the different models.
Table 10 Different Models
File Name
elevator11-1dig.MOD
elevator11-1dig_home2.MOD
elevator11-1dig_home1.MOD
elevator11-1dig-noth.MOD
Description
Original – no home location
Home is Floor2
Home is Floor1
North Elevator
5.1 Verification and Validation of the Model
16
Clearly there are many required simplifying assumption which limit the validity of the
model. The first floor location is ignored, but the student at that location are included in
floor1. This is approximate. In addition several other floors were ignored. Only one
elevator is used, and this may be a significant approximation. Quite honestly I do not
know if a second elevator will improve the throughput on a per student basis or decrease
it. It is possible that two elevators decrease the efficiency of individual elevators. For
example if two elevators are called to a floor and one elevator gets there first, then the
second elevator will arrive and there will be no one to pick up. This would be a wasted
travel. When only one elevator is present, there are no wasted requests.
During development of the model the animation was carefully monitored to observe the
behavior. Many of the variables for controlling the operation of the elevator are
displayed in the animation. This animation was very useful for detecting and correcting
errors in the process instructions/coding.
Two variables/parameters were monitored during execution of the 1st replications (not all
replications). The variables are the total throughput of student delivered and the
Maximum (Within a replication) passengers in the elevator.
Based on the activity during data collection, most of the students had been delivered to
the destination within about 30 minutes. The simulation should exhibit similar behavior.
Figure 12 shows a plot of the student throughput for the 1st replication of the first model
(no home). It shows most of the students delivered within about 30 minutes, which is
consistent with the observation. This is a sanity check on the model
(processing/logic/flow) and arrivals.
Figure 12 – Total Student Throughput
17
The second parameter monitored is the maximum number of passengers in the elevator
for a entire replication. This data was purposely collected during the simulation. A plot
of this quantity is shown in Figure 13 for the 1 replication of the 1st model (no home).
Figure 13 – Maximum Elevator Contents for 1 Replication
No warm up periods are used in the simulation. The elevator system quickly gets to a
steady state condition. In addition, the total number of arrivals is specified which
represents total students in class rooms.
Table 11 summarizes MaxNumElve variable for all cases run. The Maximum Number is
the maximum number for the all 20 replications. Obviously there are times when the
elevator is empty or has smaller numbers. For the normal case consider (no home) the
maximum number varies between 7 and 13. This range is considered reasonable.
[Remember this number may be reported slightly high due to the load/unload limitation]
no home
9.70
2.23
7.00
Table 11 Maximum Number in Elevator 20 Replications
Home Floor 2 Home Floor 1 North Elevator
9.45
9.45
0.95
(Average)
2.21
1.8489
0.22
(Std. Dev
6.00
7
0.00
(Min)
18
13.00
8.84
10.56
15.00
8.59
10.31
13
8.73519
10.1648
1.00
0.86
1.04
(Max)
(90% C.I. Low)
(90% C.I. High)
5.2 Results of the Simulation
The average result for 20 replication each for the system time of students going form
floor 1 to 2, floor 1 to 3, floor 1 to 4 and floor 2 to 4 are shown in Table12.
Time12 in System
Time13 in System
Time14 in System
Time24 in System
Table 12 Average Time in System (Min)
nohome
home Floor2
Home Floor1
1.05
1.15
1.09
1.59
1.67
1.55
2.11
2.21
1.95
2.11
2.09
2.15
North Elevator
0.89
Stairs
0.87
1.07
1.47
1.27
The time for taking the stairs and the north elevator are considered constant with no
significant statistical variation. There is effectively no competition for resources. This is
certainly true for the stairs. There would be slight variation in the stairs depending on
individual people and how much effort they want to but into climbing stairs. But this
variation is considered small when compared to the variation caused by waiting for
resources to become available.
The north vlevator model is only approximate and assumes there is no other demands
place upon it other than going from floor 1 to 4. This is very approximate, but the field
observations indicate that this elevator is barely used.
Table 13 provides the 90% confidence lower bound travel times for 20 replications.
These result show (assuming no variation on the stairs or the north elevator) that with
90% confidence we can state the north elevator (.89 min) is the fastest way to floor 4
(Real floor 6) from floor 1 (Real Floor 2). It takes .89 minutes using the north elevator
and it take 1.47 minutes using the stairs. The north elevators take between 1.73 and 2.0
minutes, depending the elevator waiting logic.
19
Time12 in System
Time13 in System
Time14 in System
Time24 in System
Table 13 - 90% Confidence Lower Bound Travel Time (Min)
nohome
home Floor2
Home Floor1
North Elevator
1.01
1.12
1.05
1.51
1.60
1.48
1.85
2.00
1.73
0.89
1.93
1.92
1.98
Stairs
0.87
1.07
1.47
1.27
Table 14 provides the 90% Confidence upper bound travel time.
Time12 in System
Time13 in System
Time14 in System
Time24 in System
Table 14 - 90% Confidence upper Bound Travel Time (Min)
nohome
home Floor2
Home Floor1
North Elevator
1.09
1.19
1.13
1.66
1.74
1.62
2.37
2.42
2.18
0.89
2.29
2.26
2.31
Stairs
0.87
1.07
1.47
1.27
The 90 % high and low confidence band for travel from 1 to floor 4 overlap for the no
home, home at Floor2 and home at floor 1, hence there is no significant difference in the
changing the programming logic of the elevator which will improve the transport of
students from floor 1 (real floor2) to floor4 (Real Floor 6).
6.0 Summary and Conclusions
A very simple simulation model of the Rensselear Hartford elevator system has been
completed. The simulation models the arrival and transport of students during peak
times. Several simplifications were necessary to accommodate limitations of Promodel
Students version. The focus of the review was to determine the fastest way to class on
the sixth floor from the second floor.
The review show that the fastest way to class is to use the south elevator, which is hardly
used. The conclusion could have reached by simply observing the usage of the 3 elevator
systems.
The second fastest way to class (if the students are up to it) is to take the stairwell.
Taking the stairs does not compete with other student for use of the elevator and it not
20
affected by the arrival and transport of other students. This method should be very
consistent and reliable.
The slowest method to class is to take one of the north elevators. The north elevators
transport a large percentage of the student, and they are constantly being utilized during
peak demand periods.
The home location of the elevator does not significantly affect the results. The animation
reveals the reason. During peak times there are constant calls for the elevator and the
elevator rarely waits for a call. The request come so quickly, it is never idle during peak
times.
Promodel can model elevators, however it is extremely difficult. It requires significant
amount of coding to capture the elevator’s behavior. As recommended in section 6, there
are several improvement that can be made to make the elevator’s behavior more realistic.
Promodel needs an elevator like resource, or at least a resource which permits it behavior
to be coded into a resource characteristic. In this study the behavior was coded into the
process. This makes it more difficult to monitor and control. One has to be careful were
wait commands are issued, especially if state variables are going to be redefined or reset.
If one is not careful with the coding, these variables may change due to some other
activity (if a wait command is issued).
7.0 Improvements to the Model
The following suggestions for improvement in the model:
1) Model the students as one entity and used attributes to keep track of entry and
departure locations. This will change the programming code.
2) Use a single attribute to record and track system time. At the time the model was
developed I was unaware that one attribute can be used to track system time on all
entities.
3) Using the improvements above, more entities are available. This will permit
another elevator to be modeled.
4) Correct the limitation(due to unload/load restrictions in promodel) on reporting
MaxNumElev.
21
22