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

Jesus R. Artalejo and Srinivas R. Chakravarthy

Mathematical Problems in Engineering, 2006, vol. 2006, 1-15

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:053570

DOI: 10.1155/MPE/2006/53570

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