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

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.

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 |