Consider a service system in which each entering customer must be served first by server 1, then by server 2, and finally by server 3. The amount of time it takes to be served by server i is an exponential random variable with rate μi, i = 1, 2, 3. Suppose that you enter the system when it contains a single customer who is being served by server 3. Find the probability that server 3 will still be busy when you move over to server 2. Find the probability that server 3 will still be busy when you move over to server 3. Find the expected amount of time you spend in the system. (whenever you encounter a busy server, you must wait for the service in progress to end before you can enter the service) Suppose that you enter the system when it contains a single customer who is being served by server 2. Find the expected amount of time that you spend in the system.

Consider a service system in which each entering customer must be served first by server 1, then by server 2, and finally by server 3. The amount of time it takes to be served by server i is an exponential random variable with rate μi, i = 1, 2, 3. Suppose that you enter the system when it contains a single customer who is being served by server 3. Find the probability that server 3 will still be busy when you move over to server 2. Find the probability that server 3 will still be busy when you move over to server 3. Find the expected amount of time you spend in the system. (whenever you encounter a busy server, you must wait for the service in progress to end before you can enter the service) Suppose that you enter the system when it contains a single customer who is being served by server 2. Find the expected amount of time that you spend 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 11P

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