A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.a. How many customers would you expect to see, on average, at the coffee urn?b. How long would you expect it to take to get a cup of coffee?c. What percentage of time is the urn being used?d. What is the probability that three or more people are in the cafeteria?e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constanttime of 15 seconds, how does this change your answers to (a) and (b)?

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.a. How many customers would you expect to see, on average, at the coffee urn?b. How long would you expect it to take to get a cup of coffee?c. What percentage of time is the urn being used?d. What is the probability that three or more people are in the cafeteria?e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constanttime of 15 seconds, how does this change your answers to (a) and (b)?

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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