Mathematical Problems in Engineering 
Volume 2006 (2006), Article ID 53570, 15 pages
doi:10.1155/MPE/2006/53570

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

Jesus R. Artalejo1 and Srinivas R. Chakravarthy2

 1Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain
2Department of Industrial and Manufacturing Engineering and Business, Kettering University, Flint 48439, MI, USA
Received 28 February 2005; Revised 11 May 2005; Accepted 20 June 2005

Abstract

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system.