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Unformatted text preview: Fall 2011 CEE 3604: Introduction to Transportation Engineering Assignment 8: intersection Analysis and Queueing Theory
Date Due: November 18, 2009 Instructor: Trani Problem 1
The intersection shown in Figure 1 is to be studied for level of service characteristics. The intersection has a cycle length of 55
seconds. After consulting with the traffic engineer in town, you are told the green time for University Avenue traffic is 35 seconds.
The intersection has two phases: 1) phase 1 allows green time for the traffic on University Avenue and 2) phase 2 allows green
time for traffic on Elmo Street. The traffic flows recorded in a recent survey are shown in Figure 1. Assume that the D/D/1
queueing system adequately describes each lane for each approach at the intersection. In other words, in your analysis
assume that each lane is independently studied as a D/D/1 queueing system. Assume no time loss in the cycle. The saturation
flows for straight approaches (i.e., when cars move in straight line through the intersection) are 1,900 vehicles per hour. The
saturation flows for turning movements are 1,600 veh/hr.
a) Estimate the average delay per vehicle for every approach and every lane. Show a set of sample calculations by hand if
using a Matlab or Excel.
b) Find the average queue length at the end of the red signal for every approach.
c) Find the percent of vehicles stopped for each approach.
d) Are the green times for this intersection optimal? Explain.
e) Allocate effective red and green times among approaches in such a way to minimize the total delay of all approaches at
f) For the optimal allocation of green times derived in part (e) estimate the total delay at the intersection.
g) Modify the analysis if “amber” times are considered in the problem. Assume the typical amber time for each approach is 3
seconds. Consider the worst case scenario is that during the amber times no vehicles flow through the intersection.
Calculate the delays for the intersection considering loss times (two per cycle) using the green times of part(a). Comment
on the results. Figure 1. Intersection for Problem 1. CEE 3604 A8 Trani Page 1 of 3 Problem 2
The Port Authority of Acapulco (in México) is planning to expand its limited cruise ship port facility. Figure 2 shows the current
situation with only two positions to accommodate large cruise ships of up to 70,000 metric tons. During the peak season, cruise
ships arrive to the port randomly at a rate of 7.5 per week. Ships arrive to port every day of the week. The average ship docks in
port 1.25 days allowing visitors to enjoy the weather and the local hospitality. Assume the service times to be negative
exponentially distributed. Cruise ships wait in Acapulco Bay when the two docking positions at the cruise ship terminal are busy
(see Figure 2).
a) Under the current conditions, estimate the expected number of cruise ships waiting in Acapulco Bay and unable to dock
during the peak season.
b) Under the current conditions, estimate the average waiting time (in hours) for a cruise ship waiting in the bay.
c) Find how often three (3) or more cruise ships will have to wait for service in Acapulco Bay.
d) How often is the port facility empty? Explain.
The port authority forecasts 15 cruise ships per week in the year 2025.
e) Estimate the number of docking positions needed in the year 2025 if the port authority wants to maintain the average
waiting times for a ship to 10 hours or below.
f) Using your engineering economics, study the tradeoff between waiting times at this port as measured by loss of revenue
to the local economy and the cost of building more docking positions. Building a new docking position is estimated to cost
$80 million dollars that could be amortized over 40 years at 5% interest rate. Every hour a ship waits for service costs the
local economy and the cruise operator an estimated $11,000. Calculate the yearly delay costs vs capital costs to build
more berthing positions over a 10 year period. Assume the demand function increase linearly from today (year 2011 to
year 2025). Figure 2. Acapulco, México Cruise Ship Port Facility. Source: Google Earth. CEE 3604 A8 Trani Page 2 of 3 Problem 3
A 4-lane divided freeway (2 lanes each direction) near Detroit has a free flow speed u f =120 (km/hr). During the morning peak period (5 AM-10 AM) the volume of traffic flowing to the city center on the two inbound lanes of the highway is recorded by
cameras and shown in Table 1. Table 1. Trafﬁc Volumes Recorded for Two Inbound Lanes.
Time (hrs) Recorded Trafﬁc Volume
(vehicles/hr) 6:00 1850 6:30 3300 7:00 3890 7:30 3600 8:00 2340 8:30 2500 9:00 2200 9:30 1900 10:00 and later 1380 a) Using the level of service values provided in the notes (i.e., Level_of_Service_Notes.pdf) in Exhibit 23-2 of the Highway
Capacity Manual (HCM), determine the level of service of this freeway during the peak period spanning from 6:00 to
10:00 AM. Do your calculations of level of service for each interval recorded and shown in Table 1. Make a plot of the
expected speed vs. service flow rate and indicate the level of service in your plot.
b) Find the level of service at 10:00 AM.
c) One morning a minor accident blocks the inbound right lane for 45 minutes until emergency crews clear the accident
scene. The accident occurs at 7:30 AM.
d) Plot the demand and supply rates for the highway on day of the accident vs. time.
e) Find the total delay for vehicles traveling on the road in the day of the accident. In this analysis employ the Maximum
Service Flow Rate (measured in passenger cars per hour) provided by the HCM as the capacity of each lane.
f) Find the maximum queue length in the day of the accident. Calculate the total queue distance (km) from the accident site
to the last vehicle in the queue.
g) Find the average queue length and average waiting time in the day of the accident. CEE 3604 A8 Trani Page 3 of 3 ...
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This note was uploaded on 12/31/2011 for the course CEE 3604 taught by Professor Katz during the Fall '08 term at Virginia Tech.
- Fall '08