Consider a two-server system in which a customer is served first by server 1, then by server 2, and then departs. The service times at server i are exponential random variables with rates μi , i = 1, 2. When you arrive, you find server 1 free and two customers at server 2 — customer A in service and customer B waiting in line • (a) Find P , the probability that A is still in service when you move A over to server 2. • (b) Find PB, the probability that B is still in the system when you move over to 2. • (c) Find E[T], where T is the time that you spend in the system.

Consider a two-server system in which a customer is served first by server 1, then by server 2, and then departs. The service times at server i are exponential random variables with rates μi , i = 1, 2. When you arrive, you find server 1 free and two customers at server 2 — customer A in service and customer B waiting in line • (a) Find P , the probability that A is still in service when you move A over to server 2. • (b) Find PB, the probability that B is still in the system when you move over to 2. • (c) Find E[T], where T is the time that you spend in the system.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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