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.

(a) Let X1 , X2 and X3 be the measure of time taken by worker 1, 2 and 3 individually. Likelihood…

Answered: Consider a service system in which each…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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.

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