9.A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a meanrate of 15 per hour. However, if the pump already is being used, these potential customers may balk (drive onto another service station). In particular, if there are n cars already at the service station, the probability that annarriving potential customer will balk is for n = 1, 2, 3. The time required to service a car has an exponential3distribution with a mean of 4 minutes.(a) Construct the rate diagram for this queueing system.(b) Find the steady-state probability distribution of the number of cars at the station.(c) Find the expected waiting time (including service) for those cars that stay.

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Answered: (a) Construct the rate diagram for this…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) Construct the rate diagram for this queueing system. (b) Find the steady-state probability distribution of the number of cars at the station. (c) Find the expected waiting time (including service) for those cars that stay.