Measurement and performance of the strong stability method. (English) Zbl 1125.60094

Bouallouche, Louiza; Aissani, Djamil

Teor. Jmovirn. Mat. Stat. 72, 1-9 (2005) and Theory Probab. Math. Stat. 72, 1-9 (2006).

The strong stability method is a tool of investigation of the ergodicity and stability of stationary, as well as non-stationary, characteristics of Markov chains with the help of small permutations of the transition kernels of Markov chains. The method gives a possibility to derive conditions under which characteristics of complex queuing systems can be approximated by the corresponding characteristics of simpler queuing systems. See M. Benaouicha and D. Aissani [Teor. Jmovirn. Mat. Stat. 71, 22–32 (2004) and Theory Probab. Math. Stat. 71, 25–36 (2005; Zbl 1097.60076)] for more details.
In this paper the authors show how to use in practice the strong stability method and illustrate its efficiency with the help of approximation of the \(GI/M/1\) system by the \(M/M/1\) system. An algorithm is proposed which verifies the approximation conditions of the \(GI/M/1\) system and determines conditions under which the minimal approximation error is possible. A numerical example is proposed which illustrates application of the algorithm in practice. The accuracy of the approach is demonstrated by comparison with some known exact results.

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

60K25	Queueing theory (aspects of probability theory)
68M20	Performance evaluation, queueing, and scheduling in the context of computer systems
90B22	Queues and service in operations research

Keywords:

Markov chain; transition kernel; queuing system; strong stability method; ergodicity

Citations:

Zbl 1097.60076