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1 results

  • Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

  • Xi-Ren Cao
  • Journal:
    Advances in Applied Probability / Volume 22 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    01 July 2016, pp. 178-210
    Print publication:
    March 1990

  • The paper studies the sensitivity of the throughput with respect to a mean service rate in a closed queueing network with exponentially distributed service requirements and state-dependent service rates. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced. The properties of realization factors are discussed, and a set of equations specifying the realization factors are derived. The elasticity of the steady state throughput with respect to a mean service rate equals the product of the steady state probability and the corresponding realization factor. This elasticity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. The sample path elasticity of the throughput with respect to a mean service rate converges with probability 1 to the elasticity of the steady state throughput. The theory provides an analytical method of calculating the throughput sensitivity and justifies the application of perturbation analysis.