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A cafeteria can seat a maximum of 20 persons. Each customer arrives in a Poisson stream with mean value 4 minutes. They are serviced at the rate of 10 per hour. For simplicity, assume that customers are serviced one at a time by one waiter. c) Suppose that two customers (with random arrival times) would like to be seated together. What is the probability that their wish can be fulfilled? Assume that arrangements can be made to seat them together as long as there are three empty seats anywhere in the cafeteria. d) Determine the expected number of customers waiting but currently not being served

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.4: Important Queueing Relationships

Problem 6P

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A cafeteria can seat a maximum of 20 persons. Each customer arrives in a Poisson stream with mean value 4 minutes. They are serviced at the rate of 10 per hour. For simplicity, assume that customers are serviced one at a time by one waiter.

c) Suppose that two customers (with random arrival times) would like to be seated together. What is the probability that their wish can be fulfilled? Assume that arrangements can be made to seat them together as long as there are three empty seats anywhere in the cafeteria.

d) Determine the expected number of customers waiting but currently not being served

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