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Hitting-time and occupation-time bounds implied by drift analysis with applications

  • Bruce Hajek (a1)
Abstract

Bounds of exponential type are derived for the first-hitting time and occupation times of a real-valued random sequence which has a uniform negative drift whenever the sequence is above a fixed level. The only other assumption on the random sequence is that the increments satisfy a uniform exponential decay condition. The bounds provide a flexible technique for proving stability of processes frequently encountered in the control of queues.

Two applications are given. First, exponential-type bounds are derived for a GI/G/1 queue when the service distribution is exponential type. Secondly, geometric ergodicity is established for a certain Markov chain in which arises in the decentralized control of a multi-access, packet-switched broadcast channel.

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Corresponding author
Postal address: Coordinated Science Laboratory, University of Illinois, 1101 West Springfield Ave., Urbana, IL 61801, U.S.A.
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This work was supported by U.S. Navy contract N00014–80-C-0802.

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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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