At a parking lot, vehicles arrive according to a Poisson process and are processed (parking fee collected) at an exponentially distributed rate at a single station. The mean arrival rate is 4 veh.min and the processing rate is 5 veh/min. Determine the average length of queue (in vehicles), time spent in the system and waiting time spent in the queue.

At a parking lot, vehicles arrive according to a Poisson process and are processed (parking fee collected) at an exponentially distributed rate at a single station. The mean arrival rate is 4 veh.min and the processing rate is 5 veh/min. Determine the average length of queue (in vehicles), time spent in the system and waiting time spent in the queue.

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...

See similar textbooks

Similar questions

The 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.?
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
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)?
vehicles start to arrive at a parking area at 6 am with an arrival rate function(vehicles per minute) of lambda(t)=1.2+(0.3)t, where t is in minutes. At 6:15 am, the parking area opens and processed vehicles at a rate of 12 per minute. a)Determine when does the queue clear? b)find the total delay? c)find the maximum queue length?
A parking garage has a single processing booth where cars pay for parking. The garage opens at 6:00 A.M. and vehicles start arriving at 6:00 A.M. at a deterministic rate of 3(t)= 6.1-0.22t where 3(t) is in vehicles per minute and t is in minutes after 6:00A.M. What is the minimum constant departure rate (from 6:00 A.M. on) needed to ensure that the queue length does not exceed 10 vehicles? Answer in veh/min.
Vehicles arrive according to a Poisson process (random arrival) to a parking lotwith 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 at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 8:00 A.M., the average arrival rate be 240 veh/h and Poisson distributed (exponential times between arrivals) over the entire period from park opening time (8:00 A.M.) until closing at dusk. If the time required to distribute the brochure is 10 seconds, the distribution time varies depending on whether park patrons have questions relating to park operating policies, assuming M/M/1 queuing. a.) Compute the average length of queue (express in veh), b.) Average waiting time in the queue (express in min/veh), c.) and average time spent in the system(express in min/veh)
A parking garage has a single processing booth where cars pay for parking. The garage opens at 6:00 A.M. and vehicles start arriving at 6:00 A.M. at a deterministic rate of Ȝ(t) = 6.1 − 0.22t where Ȝ(t) is in vehicles per minute and t is in minutes after 6:00 A.M. What is the maximum constant departure rate (from 6:00 A.M. on) needed to ensure that the queue length does not exceed 10 vehicles? Answer in veh/min. final answer: 8.21
Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes free brochures. The park opens at 8:00 AM. At which vehicles begin to arrive at a rate of 480 veh/h. After 20 minutes, the arrival flow rate declines to 120 veh/h and corrtinues at that level for the remainder of the day. If the time required to distribute the brochure is 15 seconds, and assuming D/D/1 queuing (a) draw the queuing diagram (b) describe the operational characteristics of the queue (maximum queue length, maximum queuing time, average queuing time per vehicle etc.)
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
in the entrance of car parking, the vehicle arrival in each counting period of 100 sec. is shown in table below, check whether the arrival distribution of vehicle can be assumed random or not
Passenger car arrive at the stop sign at an average rate of 280 per hour. Average waiting time at the stop sign is 12 sec. If both arrivals and departure are exponentially distributed, what would be the average queue length in vehicles. Answer in whole number.