Principles of Highway Engineering and Traffic Analysi (NEW!!)
6th Edition
ISBN: 9781119305026
Author: Fred L. Mannering, Scott S. Washburn
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 55P
To determine
The probability of waiting in queue.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The
service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also
random with an average rate of 22 vehicles per minute.
Estimate average waiting time of vehicles
O 0.45
0.35
O 0.65
0.55
At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute.Estimate average time vehicles spent in the systemGroup of answer choices0.400.500.450.35
Vehicles arrive at a toll bridge at a rate of 420 veh/h (the time between arrivals is exponentially distributed). Two toll booths are open and each can process arrivals (collect tolls) at a mean rate of 12 seconds per vehicle (the processing time is also exponentially distributed). What is the total time spent in the system by all vehicles in a 1-hour period?
Final Answer should be: 164.706 min
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Similar questions
- 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?arrow_forwardAt 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)arrow_forwardVehicles arrive at a toll system at random at an average rate of 12 vehicles per minute. If there are 2 tollbooths each at random at an average of 6 seconds after services are done for every vehicle at the tollsystem, calculate the following:1. Queuing characteristics2. If one toll ticket booth is closed and service time is reduced by 3 seconds, what are theQueuing characteristics?3. Plot the arrival distribution curve for the traffic conditions stated above.arrow_forward
- Vehicles arrive at a toll booth with a mean arrival rate of 2 veh/min (the time between arrivals is exponentially distributed). The toll booth operator processes vehicles (collect tolls) at a uniform deterministic rate of one every 20 seconds. What is the average length of queue (in vehicles), time spent in the system and waiting time spent in the queue?arrow_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_forward2.) Queuing Theory: At a single toll booth, you were able to observe an average vehicle arrival rate of 10 vehicles per minute starting from 7:00 AM. 30 minutes later, average vehicle arrival rate has become 4 vehicles per minute and continues throughout the day at that rate. If the toll booth is able to process one vehicle every 10 seconds, how many minutes after 7:00 AM will the first queue clear up? What is the longest queue length, expressed in number of vehicles? Assume a D/D/1 queuing model.arrow_forward
- Vehicles 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:1.1 Average length of queue of vehicles1.2. Average waiting time in a queue1.3. Average time spent in a queue1.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the queuing characteristics of the system? And plot the arrival distribution curve for this traffic conditionarrow_forwardDrivers arrive at a toll booth at a rate of 5 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take a) more one minute between consecutive drivers? b) between 30 seconds and 90 seconds between consecutive drivers?arrow_forwardAt exactly 8:00 AM, vehicles start to enter a single toll gate at a rate of 8 veh/min following a deterministic distribution. Due to the teller being late, the toll booth opened at 8:10 AM having a service rate of 10 veh/min following a deterministic distribution. What is the Maximum Queue Length in the system? o 70 vehicles o 90 vehicles o 80 vehicles o 60 vehiclesarrow_forward
- At exactly 7:45 AM, vehicles start to enter a single toll gate at a rate of 7.5 veh/min following a deterministic distribution. Due to the teller being late, the toll booth opened at 8:00 AM having a service rate of 10 veh/min following a deterministic distribution. At what time does the queue clear? 9:00 AM 9:30 AM 8:30 AM 8:45 AMarrow_forwardNote: Read the question carefully and give me BOTH right solutions with clear calculations. Vehicles begin to arrive at a toll booth at 5 vehicles per minute from 7 AM to 8 AM. The booth opens at 7:15 AM and services at a rate of 3 vehicles per minute until 7:45 AM. From 7:45 AM until 8 AM the service rate is 6 vehicles per minute. Assuming D/D/1 queuing, (A) have all vehicles that arrived between 7AM and 8AM exited the queue? and (B) what is the total vehicle delay while the queue exists?arrow_forwardAt the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute. Estimate average length of queue formed at the toll gate Group of answer choices 7.09 8.09 9.09 6.09arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Traffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning