A person entering public transport center to purchase intercity Bus ticket. There is two ticket line to purchase tickets. Each ticket purchase takes an average of 12 seconds. The average arrival rate is 3 persons/minute. Find (a) Probability of having one traveler in the system, (b) the average length of queue, (c)average waiting time in queue, (d) average time spend in system. Arrival follows Poisson distribution and service time follows negative exponential distribution.

A person entering public transport center to purchase intercity Bus ticket. There is two ticket line to purchase tickets. Each ticket purchase takes an average of 12 seconds. The average arrival rate is 3 persons/minute. Find (a) Probability of having one traveler in the system, (b) the average length of queue, (c)average waiting time in queue, (d) average time spend in system. Arrival follows Poisson distribution and service time follows negative exponential distribution.

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

Vehicles arrive at a single park-entrance booth where a brochure is distributed. At 8 A.M., there are 20 vehicles in the queue and vehicles continue to arrive at the deterministic rate of λ(t) = 4.2 − 0.1t, where λ(t) is in vehicles per minute and t is in minutes after 8:00 A.M. From 8 A.M. until 8:10 A.M., vehicles are served at a constant deterministic rate of three per minute. Starting at 8:10 A.M., another brochure-distributing person is added and the brochure-service rate increases to six per minute (still at a single booth). Assuming D/D/1 queuing, determine the longest queue, the total delay from 8 A.M. until the queue dissipates; and the wait time of the 40th vehicle to arrive.
Vehicles arrive at a single park-entrance booth where a brochure is distributed. At 8 A.M., there are 20 vehicles in the queue and vehicles continue to arrive at the deterministic rate of λ(t) = 4.2 − 0.1t, where λ(t) is in vehicles per minute and t is in minutes after 8:00 A.M. From 8 A.M. until 8:10 A.M., vehicles are served at a constant deterministic rate of three per minute. Starting at 8:10 A.M., another brochure-distributing person is added and the brochure-service rate increases to six per minute (still
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?
Trucks begin to arrive at a truck weigh station (with a single scale) at 6:00 A.M. at a deterministic but time-varying rate of λ(t) = 4.3 − 0.22t [λ(t) is in veh/min and t is in minutes]. The departure rate is a constant 2 veh/min (time to weigh a truck is 30 seconds). When will the queue that forms be cleared, what will be the total delay, and what will be the maximum queue length?