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Some martingales related to cumulative sum tests and single-server queues

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  • Kennedy, Douglas P.

Abstract

Martingales involving the maximum or minimum of skip-free random walks are derived. Continuous time analogues are used to study first passage times for the M/M/1 queue and stopping times for Brownian motion.

Suggested Citation

  • Kennedy, Douglas P., 1976. "Some martingales related to cumulative sum tests and single-server queues," Stochastic Processes and their Applications, Elsevier, vol. 4(3), pages 261-269, August.
    • Handle: RePEc:eee:spapps:v:4:y:1976:i:3:p:261-269
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    Cited by:

    1. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.

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