Answered: Average time each tractor must wait to…

Average time each tractor must wait to be repaired. b) Probability that a tractor is in the workshop for more than one day. c) Average time that a vehicle is in the system.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 26P

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Question

A tractor shop that is staffed only by one employee. Suppose that the arrival table corresponds to a Poisson process, so that service times follow exponential distributions. Let us consider that, after observing the evolution of the workshop, it is estimated that the arrival rate is 10 vehicles per day and that the service time is one hour. Assuming that the employee fixes the tractors in strict order of arrival and taking a 12-hour working day, the following questions are asked:

a) Average time each tractor must wait to be repaired.

b) Probability that a tractor is in the workshop for more than one day.

c) Average time that a vehicle is in the system.

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