Suppose a supermarket uses a system in which allcustomers wait in a single line for the first available cashier.Assume that the service time for a customer who purchasesk items is exponentially distributed, with mean k seconds.Also, a customer who purchases k items feels that the costof waiting in line for 1 minute is $k1. If customers can beassigned priorities, what priority assignment will minimizethe expected waiting cost incurred by the supermarket’scustomers? Why would a customer’s waiting cost per minutebe a decreasing function of k?

Suppose a supermarket uses a system in which allcustomers wait in a single line for the first available cashier.Assume that the service time for a customer who purchasesk items is exponentially distributed, with mean k seconds.Also, a customer who purchases k items feels that the costof waiting in line for 1 minute is $k1. If customers can beassigned priorities, what priority assignment will minimizethe expected waiting cost incurred by the supermarket’scustomers? Why would a customer’s waiting cost per minutebe a decreasing function of k?

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 9P

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