Stochastic comparisons for fork-join queues with exponential processing times

Stochastic comparisons for fork-join queues with exponential processing times

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Article ID: iaor1998972
Country: United Kingdom
Volume: 34
Issue: 2
Start Page Number: 487
End Page Number: 497
Publication Date: Jun 1997
Journal: Journal of Applied Probability
Authors: ,
Abstract:

Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single server. Service times are independent, exponentially distributed random variables. Server i works at rate μi, Σi=1k μi = μ, where μ is constant. We prove that the departure process becomes stochastically faster as the service rates become more homogeneous in the sense of stochastic majorization. Consequently, when all k servers work with equal rates the departure process is stochastically maximized.

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