Principles of Highway Engineering and Traffic Analysi (NEW!!)
6th Edition
ISBN: 9781119305026
Author: Fred L. Mannering, Scott S. Washburn
Publisher: WILEY
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Question
Chapter 5, Problem 37P
To determine
The departure rate so that the queue length does not exceed
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At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1200
veh/h, and at the booth, drivers take an average of 10 seconds to pay their tolls. Both the arrival and departure
rates can be assumed to be exponentially distributed. How would the average queue length, time in the system
change if a fifth toll booth were opened?
Queue Analysis - Numerical
M/M/N
- Average length of queue
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- Average time waiting in queue
- Average time spent in system
A = arrival rate
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M/M/N - More Stuff
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- Probability of having no vehicles
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n = n! N!(1-p/N)
- Probability of having n vehicles
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n!
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- Probability of being in a queue
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At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears?
At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears? (Also Draw the D/D1)
Chapter 5 Solutions
Principles of Highway Engineering and Traffic Analysi (NEW!!)
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - The arrival rate at a parking lot is 6 veh/min....Ch. 5 - Prob. 16PCh. 5 - At the end of a sporting event, vehicles begin...Ch. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Vehicles begin arriving at a single toll-road...Ch. 5 - Vehicles begin to arrive at a toll booth at 8:50...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Vehicles begin to arrive at a parking lot at 6:00...Ch. 5 - At a parking lot, vehicles arrive according to a...Ch. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Vehicles arrive at a recreational park booth at a...Ch. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - A truck weighing station has a single scale. The...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Vehicles leave an airport parking facility (arrive...Ch. 5 - Vehicles begin to arrive at a parking lot at 7:45...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - A theme park has a single entrance gate where...Ch. 5 - Prob. 54PCh. 5 - Prob. 55P
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- QUESTION 12 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed. How would the average waiting time in the queue change if a fifth toll booth were opened? The waiting time is reduced by 2.5 seconds. O The waiting time is reduced by 4.7 seconds. The waiting time is reduced by 6.1 seconds. The waiting time is reduced by 7.9 seconds. O The waiting time is reduced by 9.8 seconds.arrow_forwardThe Arrival time of vehicles at the entrance of a baseball stadium has a mean value of 30 veh/ hr. If it takes 1.5 min for the issuance of parking tickets to be bought for occupants of each car. a.) Determine the expected length of queue , not including the vehicle being served. b.) What will be the average waiting time of a vehicle in the queue in min.?arrow_forwardThe arrival function and departure functions at a traffic facility are given below: Arrival function, A(t) = 8t+0.95t2 • Departure function, D(t) = 2t+1t2 where, t = time in minutes. Determine the value of t (in minutes) at which the queue length is the maximum.arrow_forward
- Passenger cars arrive at the stop sign at an average rate of 280 per hour. Average departure time at the stop sign is 12 sec. If both arrivals and departure are exponentially distributed, what would be the average waiting time per vehicle in minutes? Answer in one-decimal place.arrow_forwardQuestion 1 In studying traffic flow at a highway toll booth over a course of 60 minutes, it is determined that the arrival and departure rates are deterministic, but not uniform. The arrival rate is found to vary according to the function of A (t) = 1.8 2 +0.25t -0.0030t. The departure rate function is u(t) =1.4 + 0.11 t. In both of these functions, t is in minutes after the beginning of the observation and X(t) and u(t) are in vehicles per minutes. (i) When will the queue that forms be cleared? (ii) What time does the maximum queue length occur and what will be the corresponding queue length? (iii) Determine the total delay (iv) Estimate the average time delay per vehiclearrow_forwardA theme park has a single entrance gate where visitors must stop and pay for parking. The average arrival rate during the peak hour is 150 veh/h and is Poisson distributed. It takes, on average, 20 seconds per vehicle (exponentially distributed) to pay for parking. What is the average waiting time for this queuing system in minute/vehicle? Answer in two-decimal placesarrow_forward
- Suppose that a crash occurs on a two lane highway, blocking one lane for 45 minutes and dropping the capacity of the other lane by 70% for the same time period. After 45 minutes, the crash and emergency vehicles are cleared from the road and capacity of each lane returns to its normal value of 2000 vehicles/hour/lane. If vehicles approach the section at a rate of 2500 vehicles/hour and the queuing system can be assumed to be D/D/1: What is the length of the longest queue? vehicles How many minutes after the crash occurs does the queue clear? minutesarrow_forwardVehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following: 5.1 Average length of queue of vehicles5.2. Average waiting time in a queue5.3. Average time spent in a queue5.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the system’s Q, W and T? And plot the arrival distribution curve for this traffic conditionarrow_forwardAt time ? = 0, when the border inspection station was scheduled to open, eight vehicles were already waiting in a queue in front of an inspection booth. Vehicles continued to arrive at a rate of 4 veh/minute. The officer did not start the inspection until ? = 4 minutes. When ?≥4 minutes, the barrier was lifted and vehicles left at a rate of 7.5 veh/minute. Draw the vehicle arrival and departure curves in the following graph. From the graph, determine the maximum queue length and the time the queue disappears. Assume D/D/1 queuing.arrow_forward
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