Vehicles arrive according to a Poisson process (random arrival) to a parking lot with mean arrival rate of 3 vehicles/min, and are processed (they pay parking fee) at a Poisson process (random Departure) rate of 240 vehicles/hour. (1) What type of queuing is this problem? D/D/1 M/D/1 M/M/1 (2) What is the traffic intensity? (3) Determine (I) the average waiting time and (II) the average length of the que

Vehicles arrive according to a Poisson process (random arrival) to a parking lot with mean arrival rate of 3 vehicles/min, and are processed (they pay parking fee) at a Poisson process (random Departure) rate of 240 vehicles/hour. (1) What type of queuing is this problem? D/D/1 M/D/1 M/M/1 (2) What is the traffic intensity? (3) Determine (I) the average waiting time and (II) the average length of the que

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter6: Fundamental Principles Of Traffic Flow

Section: Chapter Questions

Problem 26P: The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson...

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The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson with a mean of 30 mi/h. It takes an average of 1.5 min for the necessary tickets to be bought for occupants of each car. (a) What is the expected length of queue at the ticket gate, not including the vehicle being served? (b) What is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c) What will be the average waiting time of a vehicle?
The arrival rate at a parking lot is 6 veh/ min. Vehicles start arriving at 6:00 P. M., and when the queue reaches 36 vehicles, service begins. If company policy is that total vehicle delay should be equal to 540 veh-min, what is the service rate? (Assume D/ D/ 1 queuing and a constant service rate.)
Vehicles arrive according to a Poisson process (random arrival) to a parking lot with mean arrival rate of 180 veh/hour, and are processed (they pay parking fee) at a uniform deterministic rate of 4 veh/min. (1) What type of queuing is this problem? D/D/1 M/D/1 M/M/1 (2) Determine: (I) the average waiting time and (II) the average length of the queue
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?
3-The arrival rate at a parking lot is 6 veh/min. Vehicles start arriving at 6:00 P.M., and when the queue reaches 36 vehicles, service begins. If company policy is that total vehicle delay should be equal to 500 veh min, what is the departure rate? (Assume D/D/1 queuing and a constant service rate.)
The average queue length at the intersection of the two roads with a stop sign is 4 vehicles. If the arrival rate of vehicles at the stop sign is 300 veh/hr, determine the service rate of the road in veh/hr. Assume both arrival and departure rates are exponentially distributed.
Vehicles arrive at a single toll booth beginning at8:00 A.M. They arrive and depart according to a uniformdeterministic distribution. However, the toll booth doesnot open until 8:10 A.M. The average arrival rate is 8veh/min and the average departure rate is 10 veh/min.Assuming D/D/1 queuing, when does the initial queueclear and what are the total delay, the average delay pervehicle, longest queue length (in vehicles), and the waittime of the 100th vehicle to arrive (assuming first-infirst-out)?
The arrival rate at a parking lot is 6 veh/min. Vehicles start arriving at 6:00 P.M., and when the queue reaches 36 vehicles, service begins. The company policy states that the total vehicle delay should be equal to 500 veh-min. Assuming D/D/1 queuing and a constant service rate, at what time did the queue clear?
QUESTION 1 3 booths, each of which can handle one vehicle every 6 second. a. If D/D/1 model is used, what is total service rate of the system? (you can express this in total vehicles that can be handled in 10 minutes) 6. Draw the queuing diagram (cumulative traffic volumes vs. time) with traffic upstream arriving volume and this service rate. C. Using the queuing diagram, determine the max queue, the longest delay to an individual vehicle and total delay (veh-min). Time Period 10-min Volume 7:00-7:10 200 स 7:10-7:20 400 7:20-7:30 500 7:30-7:40 250 7:40-7:50 200 7:50-8:00 150
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?
6. 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?
Vehicles 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)?