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T.J.'s small local grocery store

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T.J.'s market is a small local grocery store with only one checkout counter. Assume that the shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag.

a) If T.J. does not want the average time waiting for service to exceed 5 minutes, what would you tell T.J. about the current system? Is the current system working well?

b) One of the ways to meet this requirement is to improve the current service rate. But he does not know how much to do it. What would be the new service rate to meet his 5 minutes or less waiting time?

c) Another option is to hire a full-time person to assist in the checkout operation. T.J. believes that if the new employee assists the checkout cashier, average service time could be reduced to 2 minutes. Will this satisfy his goal of 5 minutes or less waiting time?

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Solution Summary

M/M/1 queuing model is integrated in this solution.

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In this problem we are dealing with an M/M/1 queuing model with:
Arrival rate λ = 15/hour = 1/4 per minute
Service rate µ = 1/3 per minute

a) As per the theory of M/M/1 queuing model average waiting ...

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