Simulation and Optimization of the UC's most frequented Transport Service

1. Shivaram Prakash
M08744020 | BANA 6035
Simulation of UC’s
North Route Shuttle
FINAL PROJECT

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TABLE OF CONTENTS
Introduction 2
Objective 2
Data Collection 2
Modelling in Arena
3
Analysis
- Important Facets of the Model
- Scenarios of Operation
- Determining the best scenario
based on statistical significance
4
5
7
Conclusion 8
Appendix 9

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INTRODUCTION
The University of Cincinnati’s Bearcat Transportation System operates shuttles in seven regular
routes every day. The North Route is considered as the busiest of all the routes since most
international students live to the North of the University. Due to heavy demand and long
waiting times, BTS has had to the number of buses during peak times (7 am to 11 am, 4 pm to 8
pm). Hence, simulating this particular route makes sense, so as to try and identify areas of
improvement and increase the efficiency of the system. The shuttle operates from 6 am to
midnight with three different shifts of operation.
OBJECTIVE
To reduce the average waiting time of passengers at all stops and to increase the utilization of
buses (reduce the number of empty Seats).
DATA COLLECTION
Data was collected during different times of the day at the four significant stops of the north
route shuttle viz. The University, Cincinnati Children’s Hospital, Clifton and Dixysmith Avenue.
The Arrival for every half an hour interval was noted and the respective distributions for each
stop was incorporated into the model. Model fitting was done using the input analyzer (Refer
appendix for the plots)
Passenger arrival Time University Cincinnati Children’s Clifton Dixysmith
7.00 – 7.30 am 6 10 10 3
7.30 – 8.00 am 7 8 11 2
8.00 – 8.30 am 8 6 12 3
8.30 – 9.00 am 10 8 10 2
9.00 – 9.30 am 12 6 8 1
9.30 – 10.00 am 13 8 7 2
Average arrival for 30 mins 9.33 7.67 9.67 2.17
Inter-arrival/min 3.214 3.913 3.103 13.884
Since roughly the same number of people take the shuttle during peak time in the evenings, we
can assume the same inter-arrival times for passengers. The people who take the shuttle in the
morning will almost always use the shuttle in the evenings. So it is logical to simulate the model
for one peak duration and assume the same for the other peak duration.

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MODELLING IN ARENA - Model Walkthrough
PART 1:
FIGURE 1 – Passenger arrival at the university
 1 - Create modules at each stop simulate passenger arrival at respective stops
 2 - An assign module after the create module, assigns the final stop for each passenger
with different discrete probabilities for each stop
 3 - A hold module after the assign module, holds all passengers in queue till the arrival
of the bus (when the bus arrives at a stop, it sets a logical variable to ‘0’, thus satisfying
the condition for the hold module – explained in PART 2)
 4 – The passengers who board the bus and then get down due to non-availability of
seats, will arrive at this station and continue queueing
 5 -The passengers proceed to board the bus
 Figure 1 shows the arrival of passenger at the University stop. There will be three similar
models for the remaining three stops
PART 2:
FIGURE 2 – Bus at the University Stop

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 Different stops are represented using the station module
 1 - The separate module after the station, separates the grouped entity ‘Bus’
(individuals are grouped as a Bus in the previous stop)
 2 – The group is separated and the assign module that follows separation, gives the
signal for the passengers to board (Hold at part 1 is released)
 3 - A decide module then separate passengers who alight at the stop from the
passengers who continue onward with their journey
 4 - The secondary decide module then checks if there are seats left in the bus (the
shuttle services do not allow passengers to stand in the aisle when there are not seats
left)
 5 - Upon passing the decide module, another assign module counts the number of
passengers who have boarded the bus (condition for the previous decide module)
 6 - Process module – specifies the amount of time the bus waits at a particular stop
(varies from stop to stop)
 7 - Batch module – groups all passengers into a bus
 8 - Record – For the final statistic – Counting the number of empty seats in the bus at
each iteration
 9 - Assign module – Sets the ‘number of passengers’ variable to zero
 10 - Route module – Routing the bus to the next station ( Cincinnati Children’s hospital
in this case)
 Similar to part 2 for university (as shown in Figure 2), three more parts represent the
other three stops
ANALYSIS
Two important factors namely “The average waiting time of all passengers” and “Number of
Empty Seats in the Bus” form the focus of study. These two factors are calculated as a part of
the simulation and different scenarios are introduced to try and find the best possible condition
for operation.
Important Facets of the model
1. Variables and attributes:
Name Type Function
Alight at Attribute Specifies the alighting point of all passengers
StopFlow1/2/3/4 Variables Logical variables that specifies if the passengers can board
Num Pass at Univ/
Hospital/ Clifton/ Dix
Variables Variables that calculate the number of passengers who
have boarded the bus at respective stops
Ppl sent back at Univ/
Hospital/ Clifton/ Dix
Variables Counts the number of people who have got out of the bus
because of non-availability of seats
NumSeats Variable Specifies the number of seats in the bus

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2. Travel times between stops:
The time taken between stops was noted for the four stops for one peak hour interval and a
distribution for the travel time was arrived at using the input analyzer. The following
distributions were obtained. (Refer to appendix for distributions)
Stops Time in minutes
University – Cincinnati Children’s Hospital 3.5 + GAMM(2.1, 2.2)
Cincinnati Children’s Hospital - Clifton 1.65 + 1.8 * BETA(1.83, 1.39)
Clifton – Dixysmith Avenue 1.35 + 1.48 * BETA(2.1, 1.7)
Dixysmith Avenue – University 1.06 + ERLA(0.342, 2)
3. Entities:
Entity 1 – Passenger
The create module simulates the arrival of passengers at each stop. Passengers are
represented by pictures as shown below:
Entity 2 – Bus
Once the passengers are batched, they are grouped into another entity named as ‘Bus’.
It is represented by the picture shown below:
Scenarios of Operation:
Scenario 1: One Big Bus
This is the base scenario. A large 26 seater bus runs through the route. Upon running the
simulation for 100 replications of 1 day each, the following statistics were observed.
NumSeats (input variable) 26
Average waiting time of all passengers 38.077 minutes
Average number of empty seats 8.48
BTS
NORTH ROUTE

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Scenario 2: Two Big Buses
The second Scenario employs two big buses in service at the same time. Bus 1 starts at the
University and Bus 2 starts at Clifton.
FIGURE 3 - Change in Part 1
Since there are two buses, an extra decision module is added. This is because, when both buses
arrive at the stop at the same time, there is 50-50 chance that either of the buses will be
chosen. The statistics obtained are as follows
NumSeats (input variable) 26
Average waiting time of all passengers 10.821 minutes
Average number of empty seats 17.573
Scenario 3: Two Small Buses
In the third scenario two small buses are used instead of the big ones. The variations in the
Average waiting time and average number of empty seats are noted.
NumSeats (input variable) 14
Average waiting time of all passengers 12.135 minutes
Average number of empty seats 5.630

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Determining the best scenario based on statistical significance – PROCESS ANALYZER
 The aforementioned three scenarios are specified by changing the value of the control
variable “NumSeats” which determines the size of the bus. The output variables concern
two factors viz. Average waiting time of all passengers, Average number of empty seats
 All scenarios are run for 100 replications each and the statistically best scenario is
chosen from the lot.
FIGURE 4. Process Analyzer Results
 As seen from Figure 4, the scenarios are run accordingly and the required statistics are
calculated.
 The variations of average wait time between the scenario of one bus and the scenario of
two buses are considerably large because, the passengers wait longer at the queue
when the bus is full. When one bus is in operation, more often than not, this is true.
 Statistically, the best scenarios for the average wait time of all stops is shown in the
figure below:
Best Scenario for
Minimum Average Wait Time

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CONCLUSION
From the simulation, the following conclusions can be drawn.
1. As expected, the minimum average wait time is reduced considerably when there are
two buses in operation
2. When the number of buses is increased without changing the size of the bus, the
utilization of the buses drop (number of empty seats increases)
3. Considering that two buses operate, the following are the results
a. Two big buses – Wait time = 10.821 minutes, Empty Seats = 17.573
b. Two Small buses – Wait time = 12.135 minutes, Empty Seats = 5.630
SUGGESTION
A better utilization is achieved when employing two smaller buses (14 seaters) in operation.
The university should consider switching bigger buses with smaller ones for operation in the
North Route. By compromising on a small decrease in waiting time, fuel costs and operational
costs can be reduced by using smaller buses instead of the bigger ones.

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APPENDIX
INPUT ANALYZER – MODEL FITTING
TRANSFER TIME: UNIVERSITY TO CINCY CHILDREN’S HOSPITAL
TRANSFER TIME: CINCY CHILDREN’S HOSPITAL TO CLIFTON

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TRANSFER TIME: CLIFTON TO DIXYSMITH AVENUE
TRANSFER TIME: DIXYSMITH AVENUE TO UNIVERSITY

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