HW4Soln - IEOR 161 - Introduction to Stochastic Processes...

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IEOR 161 - Introduction to Stochastic Processes Spring 2010 HW4 Solutions ** Note that the numbering is from Ross 9th Edition 5.20 Denote X = the service time of the new customer, A = the service time of customer A, and B = the service time of customer B. (a) P A = P { service time at server 1 < service time at server 2 for A } = P { X < A } = μ 1 μ 1 + μ 2 . (b) P B = P { service time at server 1 < service time at server 2 for A and B } = P { X < A + B } = P { X < A + B | X < A } P { X < A } + P { X < A + B | X > A } P { X > A } = P { X < A } + P { X < B } P { X > A } by memoryless of exponential distribution = μ 1 μ 1 + μ 2 + μ 1 μ 1 + μ 2 μ 2 μ 1 + μ 2 = μ 2 1 + 2 μ 1 μ 2 ( μ 1 + μ 2 ) 2 . (c) E[ T ] = E[ S 1 + S 2 + W A + W B ] = E[ S 1 ] + E[ S 2 ] + E[ S A ] P A + E[ S B ] P B = 1 μ 1 + 1 μ 2 + 1 μ 2 μ 1 μ 1 + μ 2 + 1 μ 2 μ 2 1 + 2 μ 1 μ 2 ( μ 1 + μ 2 ) 2 .
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This note was uploaded on 03/17/2011 for the course IEOR 161 taught by Professor Lim during the Spring '08 term at University of California, Berkeley.

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HW4Soln - IEOR 161 - Introduction to Stochastic Processes...

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