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The Embedded Random Walk in the Stationary M/M/1 Queue

Author

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  • W. Stadje

    (University of Osnabrück)

Abstract

We consider the stationary queue length process of the standard M/M/1 queue just after its jump times (i.e., the times of arrivals or departures). Simple formulas for the distribution of this embedded random walk with immediate reflection at zero are derived. We study the monotonicity properties of the corresponding expected values and point out an asymmetry between the number of arrivals and the number of departures until the n-th jump time.

Suggested Citation

  • W. Stadje, 2002. "The Embedded Random Walk in the Stationary M/M/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 4(2), pages 143-151, June.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:2:d:10.1023_a:1020685423386
    DOI: 10.1023/A:1020685423386
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