Bounds For Performance Characteristics; A Systematic Approach Via Cost Structures

02/1999; DOI: 10.1080/15326349808807467
Source: CiteSeer

ABSTRACT In this paper we present a systematic approach for the construction of bounds for the average cost in Markov chains with infinitely many states. The technique to prove the bounds is based on dynamic programming. Most performance characteristics of Markovian systems can be represented by the average cost for some appropriately chosen cost structure. Therefore, the approach can be used to generate bounds for relevant performance characteristics. The approach is demonstrated for the shortest queue model. It is shown how for this model several bounds for the mean waiting time can be constructed. We include numerical results to demonstrate the quality of these bounds. 1 INTRODUCTION In this paper we consider an irreducible N-dimensional Markov chain with states m = (m 1 ; Delta Delta Delta ; mN ), where each m i is an integer, and transition probabilities p(m;n). Let ß denote its equilibrium distribution (which we assume to exist). If c(m) is the cost per period in state m, then the ...