SIMULATION
IN INTERNATIONAL SERVICE – ANALYSIS
OF
WINDSOR-DETROIT TUNNEL TRAFFIC
Edward J. Williams
Drew Podges
2230 Engineering Complex,
Industrial & Manufacturing Systems Engineering
University of Michigan –
Dearborn
4901 Evergreen Road
Dearborn, Michigan 48128,
United States
williame@umdsun2.umd.umich.edu
Discrete-process simulation, at first most heavily
used for analyses of manufacturing operations, has steadily expanded its areas
of application into provision of health care, service industries, supply and
logistics, and transportation facilities.
In the application described here, simulation documented quantitatively,
and provided suggestions for ameliorating, severe delays at a publicly accessible
transportation facility, the tunnel between Windsor, Ontario, Canada; and
Detroit, Michigan, United States.
INTRODUCTION
Soon after the general availability of specialized
simulation languages and subsequent software package tools (historically first
on mainframe computers), simulation analysis was most frequently used to
analyze, and improve the efficiency of, manufacturing operations (Law and
McComas 1999). Since the ability of
discrete-process simulation to provide accurate abstractions of numerous
real-world systems is high, simulation analysis subsequently proved its value
in the study, design, and enhancement of health care delivery systems
(Standridge 1999), service systems and the hospitality industry (e.g., banks,
stores, restaurants, hotels, and entertainment parks) (Starks and Whyte 1998),
and transportation systems (harbors, railroads, highways, and airlines, for
example) (Fishburn, Golkar, and Taaffe 1995).
Excellent and specific examples of simulation to design and improve
transportation systems appear in (Nanthavanij et al. 1996), (Tolujev,
Straußburger, and Schulze 2000), and (García, Gutiérrez, and Moreno 2001). The analysis described here was devoted to
quantitative assessment of the delays involved in traveling from Windsor, Ontario,
Canada to Detroit, Michigan, United States via the Detroit-Windsor Tunnel; the
study was motivated in part by the increased concern about and emphasis on
security of international borders provoked by the attacks upon New York City on
11 September 2001.
BACKGROUND
CONCERNING THE TUNNEL
The cities of Windsor, Ontario, Canada and Detroit,
Michigan, United States are separated by the Detroit River, which joins two of
the five Great Lakes (Huron, via much smaller Lake St. Clair) and Erie. The Detroit-Windsor Tunnel runs under the
Detroit River, and the nearby Ambassador Bridge spans it. Before these vital international links were
built, vehicles crossed the river on ferries.
The tunnel, opened in 1930, was privately financed, built, and
operated. The tunnel itself is slightly
less than two kilometers long (Poremba 2001).
Some two dozen buildings, housing tollbooths, customs offices, and
immigration offices, represent infrastructure supporting this international
tunnel. The tunnel itself accommodates
one lane of traffic in each direction.
CURRENT
IMPORTANCE OF THE TUNNEL – MOTIVATIONS FOR THE STUDY
The tunnel carries 17% of all vehicular traffic
between the province of Ontario (Canada’s largest province in an
economic-output sense) and the United States.
This traffic comprises about 4.4 million vehicles and 8.7 million
travelers annually. “Vehicles” in this
context includes not only privately owned automobiles, but also omnibuses and
large lorries [trucks] hauling industrial and commercial goods for hire.
A significant underlying motivation of this study
was the tragic attack upon the United States, via airplanes seized in flight,
which occurred on 11 September 2001.
Subsequently, the United States government greatly tightened security at
border entry points, including the tunnel.
Dramatic increases in delays to vehicles traveling from Windsor to
Detroit proved very costly to commercial enterprises, especially in view of the
recent popularity of lean manufacturing, which is intolerant of high
inventories. Successful implementation
of lean manufacturing requires frequent and strictly to-schedule delivery of
goods, often, in the context of this study, via heavy lorry. Long delays also infuriated the traveling
public and alarmed officials of Windsor’s municipal government, since fire
engines and ambulances were blocked on emergency runs by lines of vehicles on
Windsor’s thoroughfares awaiting access to the tunnel.
DATA
COLLECTION
Significant data collection efforts were required in
support of this study, despite the availability of some historical data. Tunnel management shared long-term data
specifying weekly counts of vehicles through the tunnel over a year (January
and April are the lightest traffic months; August the heaviest) and recent
distributions of vehicles per day of the week (traffic volume rises gradually
from Monday to Saturday by nearly 30%, then drops back rapidly to the Monday
value). Since the client tunnel
managers had requested a study of acknowledged limitations in scope to demonstrate
feasibility of simulation use and to obtain quantitative results within eight
weeks, additional short-term arrival data was collected. These data showed that the increase in
traffic flow during “morning rush hour” from 5AM to 9AM was nearly independent
of day of the week (Monday through Friday).
Therefore, the client managers and the simulation analysts jointly
decided to limit the scope of the study to the development of congestion within
the tunnel each weekday morning.
Therefore, the simulation team, having obtained
special clearance from the tunnel and customs authorities, gathered data on
hourly vehicle arrival rates between 5AM and 9AM weekdays, including data on
the (non-constant) relative proportions of automobiles, omnibuses, and lorries
during those four-hour periods. Data
collection also included the times required to pay the toll and the travel
speeds of various vehicles through the tunnel (when unimpeded, automobiles
travel faster than either omnibuses or lorries) and the average lengths of
these three vehicle types. These lengths
(about 5 meters for automobiles, 12 meters for omnibuses, and 18 meters for
large commercial lorries) were of importance to calculate how many vehicles
(automobiles, omnibuses, and lorries interspersed) could fit into the queues on
the Windsor side of the tunnel to pay the tunnel toll. Next, the simulation team gathered
observational data on customs-passage times for automobiles and omnibuses. These data comprised the following:
a)
Distribution
of time required to ask an automobile driver routine questions such as
nationality; length of time spent in Canada; and value, nature, and quantity of
items purchased while in Canada
b)
Distribution
of time required to search an automobile and its occupants thoroughly (the
historical data are proprietary to the United States government, not the
Detroit-Windsor Tunnel Corporation)
c)
Fraction
of automobiles pulled aside for thorough search (deciding to do so is at the
discretion of customs officers, who may use random search and/or their
intuition based on experience); an average of four automobiles are thus
detained hourly
d)
Distribution
of time required for passengers to exit an omnibus, answer questions and show
credentials, and reenter the omnibus.
On the United States side, heavy commercial lorries
enter a separate lane for inspection of cargo manifests and possible extensive
search. Due to both time constraints on
the study and high secrecy attached to those data, quantitative analysis of the
queuing performance relative to heavy commercial lorries was excluded from this
study.
These empirical data were fitted to closed-form
distributions using the BestFit® distribution-fitting software tool (Jankauskas
and McLafferty 1996); the Pearson V, Pearson VI, and gamma distributions (Law
and Kelton 2000) often characterized empirical data well for this model. In cases where no closed-form distribution
fitted the data well, an empirical sampling distribution based directly on the
data was used.
CONSTRUCTION,
VERIFICATION, AND VALIDATION OF THE MODEL
The model was constructed, using the SIMUL8®
software model-building tool (Hauge and Paige 2001), as a series of storages
(queues), work centers, and conveyors.
Vehicles entering the system are provided three attributes (called
“Labels” in SIMUL8®) specifying their length, customs queue to use, and whether
they are fated for an extensive search at United States customs. A vehicle traveling from Windsor to Detroit
first queues for a tollbooth, which may be either automatic (accepting exact
change or a previously purchased special token) or manned (hence able to make
change). Omnibuses and lorries must
pass through a designated tollbooth equipped to weigh them automatically and
thence determine the correct toll.
Vehicles from all tollbooths then converge upon the tunnel, which is
modeled as an accumulating conveyor, inasmuch as no vehicle is permitted to
overtake another within the tunnel.
This characterization of the tunnel as a conveyor is an example of
stepping mentally from reality to a conceptual model to a computer model (Krug
2001), inasmuch as “conveyor” is a primitive construct in SIMUL8® usually used
in the simulation of manufacturing processes.
At the far end of the tunnel, vehicles fan out to an appropriate customs
queue. Lorries must go to queue #1;
omnibuses, to queue #2. Automobiles
choose the shortest of remaining queues.
As a result of increasingly stringent security, vehicles are not allowed
to wait within the tunnel (Capeloto and Windsor 2001). Therefore, the model implements logic which,
upon sensing a queue for customs extending back to the tunnel exit, blocks
vehicles on the Windsor side from entering the tunnel.
Model verification was undertaken primarily via desk
checking and close examination of the animation corresponding to the simulation
(Banks et al. 2001). Examples of errors
thus detected and corrected were:
a)
Misrepresentation
of a work center’s routing-out logic caused vehicles to stay indefinitely in an
upstream work center
b)
Misrepresentation
of a work center’s routing-out logic caused lorries and omnibuses to wrongly
enter queues reserved for automobiles
c)
An
incorrectly specified work center cycle time caused maximum time-in-system to
be preposterously long.
The most fundamental validation undertaken by the
simulation team was to enter the tunnel from the Windsor side during each of
the hourly intervals (5AM to 6AM, 6AM to 7AM, 7AM to 8AM, and 8AM to 9AM) and
note the time taken to clear customs on the Detroit side. The actual times required, when compared to
required times as predicted by the model, did not differ at the α = 0.05
level, as determined by both parametric and non-parametric statistical tests
(the latter as a precaution due to mild-to-moderate deviations from normality).
Additional validation was done in collaboration with
the client tunnel managers; they were shown both model animation and
quantitative model predictions. Upon
successful completion of this step, the model had attained not only validity,
but also face validity, and hence credibility with the client.
RESULTS
Multiple replications (at least ten replications per
scenario) of the model were run and compared under two scenarios typical at the
time of the study: (1) five tollbooths
open in Windsor and five customs booths open in Detroit; (2) five tollbooths
open in Windsor and six customs booths open in Detroit. The two most significant performance
measures of the tunnel are time-in-system and the percentage of time that
access to the tunnel must be temporarily prohibited to vehicles wishing to
enter it from Windsor to uphold the prohibition against vehicles queuing within
the tunnel itself. During the first
half of the morning period (5AM – 7AM), scenario 1 was adequate. During the second half of the morning period
(7AM – 9AM, characterized by rapidly increasing traffic levels due primarily to
commuter traffic), scenario 2 quickly became dramatically superior to scenario
1, as shown in the following table.
Performance Metric |
|
Scenario One |
Scenario Two |
Time in System |
Mean |
281 sec. |
498 sec. |
Min |
193 sec |
195 sec. |
|
Max |
1411 sec. |
2502 sec. |
|
% Blockage Time |
2.9% |
21.1% |
Table 1. Comparison of Scenario Results
Hence, the closure of just one booth on the Detroit
side nearly doubles the average time-in-system and multiplies by more than
seven the probability that the tunnel will be closed to entry from the Windsor
side at any given moment of time.
Tunnel management quickly began to use these results in negotiations
with the United States government relative to reassigning, at least temporarily,
some military personnel from their regular duties to border patrol and customs
duties to prevent severe increases in queuing times (Gray 2001).
LIMITATIONS
AND INDICATIONS FOR FURTHER WORK
Due to the short time frame of this study, it
concerned itself only with traffic flow on weekday mornings. Extensions of the study to other time
periods would, as a practical matter, require automated data collection (e.g.,
via roadway sensors), inasmuch as traffic flow is too fast and complex for even
several analysts observing simultaneously to monitor manually.
Also, automobiles, omnibuses, and lorries all have a
fixed length in this model; a more detailed model would rely on probability
distributions, based on extensive observations, to characterize vehicle
lengths. Similarly, vehicle speed is either
zero (when a vehicle is in queue) or 40 kilometres per hour.
Since travel in the opposite direction (Detroit ® Windsor) is not currently troublesome or
delay-prone, due largely to high levels of customs staffing provided by the
Canadian government, it was not modeled at all; that is, the tunnel was modeled
as unidirectional.
CONCLUSION
This study proved itself an excellent example of
using discrete-process simulation to model a publicly accessible transportation
facility. The tunnel managers, now that
they have become acquainted with the availability of and power of simulation
analysis, are much more likely to extend its use in the future as changing
conditions warrant. Also of high
importance, the industrial engineering students who contributed to this project
obtained valuable insight into the challenges of an entire simulation
project (particularly data collection and analysis), versus the overly narrow
view of “simulation as model building.” (Black and Chick 1996). Furthermore, the results of this study were
a significantly contributing factor to the United States government’s decision
to add 97 customs officers to Michigan’s border crossings vis-à-vis Canada
(Angel 2000).
ACKNOWLEDGMENTS
Professor Onur M. Ülgen, professor and senior
simulation analyst at the University of Michigan – Dearborn, provided valuable
guidance to students and the instructor of the senior-level simulation course
which furnished the context of this project.
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AUTHOR
BIOGRAPHIES
EDWARD J. WILLIAMS holds bachelor’s and
master’s degrees in mathematics (Michigan State University, 1967; University of
Wisconsin, 1968). From 1969 to 1971, he
did statistical programming and analysis of biomedical data at Walter Reed Army
Hospital, Washington, D.C. He joined
Ford Motor Company in 1972, where he worked until retirement in December 2001
as a computer software analyst supporting statistical and simulation
software. After retirement from Ford,
he joined Production Modeling Corporation, Dearborn, Michigan, as a senior
simulation analyst. Also, since 1980,
he has taught evening classes at the University of Michigan, including both
undergraduate and graduate simulation classes using GPSS/HÔ, SLAM IIÔ, SIMANÔ, ProModelÒ, or SIMUL8Ò. He
is a member of the Institute of Industrial Engineers [IIE], the Society for
Computer Simulation International [SCS], and the Michigan Simulation Users'
Group [MSUG]. He serves on the
editorial board of the International
Journal of Industrial Engineering – Applications and Practice. During the last several years, he has given
invited plenary addresses on simulation and statistics at conferences in
Monterrey, México; İstanbul, Turkey; Genova, Italy; and Rīga, Latvia.
DREW PODGES is a senior At the
University of Michigan – Dearborn, studying Manufacturing Engineering. He is an active member of SME and IIE and
Alpha Pi Mu (engineering honor fraternity); his professional interests include
Simulation and Rapid Prototyping.
Recreational interests include playing ice hockey, broomball, mountain
biking, and running.