PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 32P
To determine
The uniform deterministic arrival rate.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
At 10 am, vehicles arrive at a toll booth facility at the rate of 480vehicles/hour. Initially, the toll booth is closed from 10:00 am until 10:15 am. Then it opens from 10:15with a service rate of 6 seconds per vehicle. Assuming D/D/1 queuing, determine:(1) At what time queue disappears? (2) What is the total delay? (3) What is the maximum Queuelength? (4) What is the queue length at 10:00 am? (5) What is maximum delay? (6) What is thedelay for the 140th and 170th vehicle?
At 9 am, vehicles arrive at a toll booth facility at the rate of 480 vehicles/hour.
Initially, the toll booth is closed from 9:00 am until 9:15 am. Then it opens from 9:15 with a service rate of 600 vehicles/hour. Assuming D/D/1 queuing, determine:
(1) At what time queue disappears?
(2) What is the total delay?
(3) What is the maximum Queue
length?
(4) What is the queue length at 10:00 am? (5) What is maximum delay?
(6) What is the delay for 160th vehicle?
2.) 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.
Chapter 5 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
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
Similar questions
- At 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_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? What is the longest waiting time in the system?arrow_forwardAt 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_forward
- Note: 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_forwardVehicles begin to arrive to a parking lot at 7:00 AM at a rate of 2000 veh/hour, but the demand reduces to 1000 veh/hour at 7:30 AM and continues at that rate. The ticketing booth to enter the parking lot can only serve the vehicles at 1000 veh/hour until 7:15 AM, after which the service rate increases to 2000 veh/hour. Assuming D/D/1 queuing, draw a queuing diagram for this situation. Find: a) the time at which the queue clears, b) the total delay, c) the longest queue length, and d) wait time of the 500th and 2000th vehicles to arrive to the parking lot (assuming FIFO conditions)?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
- Question. 2Propagation speed of 45 km/hr and that each toll booth takes 6 seconds to service a car.Suppose the caravan of 10 cars begins immediately in front of the first toll booth, travels 20 km to a second toll booth, then another 40 km to a third toll booth, and finally stops immediately after the third tool booth. Thus, they travel a total of 60 km. What is the total end to-end delay?arrow_forwardVehicles begin arriving at Allen fieldhouse at 6:30 PM, at a constant rate of 4 per minute. One gate opens at 7:00 PM and processes cars at a rate of 5 vehicles per minute. At 7:10 PM, a second gate opens, doubling the rate at which cars are processed. What is the average vehicle delay? Assume D/D/1 queuing.arrow_forwardVehicles arrive at a recreational park booth at a uniform deterministic rate of 4 veh/min. If uniform deterministic processing of vehicles (collecting fees) begins 30 minutes after the first arrival and the total delay is 3600 veh-min, how long after the arrival of the first vehicle will it take the queue to dissipate?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_forward6. Vehicles begin to arrive at a toll booth at 8:50AM with an arrival rate of (t)=4.1+0.01t with t in minutes and 2(t) in vehicles per minute. The toll booth opens at 9:00AM and process vehicle at a rate of 12 veh/min throughout the day. When will the queue dissipate?arrow_forwardA student records the number of vehicles that pass through a toll road lane, as shown in the following list Calculate: (c) what is the busiest flow rate for a 15-minute period in this lane?arrow_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