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Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes

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  • Jesus R. Artalejo
  • Srinivas R. Chakravarthy

Abstract

Two-dimensional continuous-time Markov chains (CTMCs) are usefultools for studying stochastic models such as queueing, inventory,and production systems. Of particular interest in this paper isthe distribution of the maximal level visited in a busy periodbecause this descriptor provides an excellent measure of thesystem congestion. We present an algorithmic analysis for thecomputation of its distribution which is valid for Markov chainswith general-block structure. For a multiserver batch arrivalqueue with retrials and negative arrivals, we exploit theunderlying internal block structure and present numerical examplesthat reveal some interesting facts of the system.

Suggested Citation

  • Jesus R. Artalejo & Srinivas R. Chakravarthy, 2006. "Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-15, March.
    • Handle: RePEc:hin:jnlmpe:053570
    DOI: 10.1155/MPE/2006/53570
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