Perturbation Analysis of M/M/1 Queue
This paper treats the problem of evaluating the sensitivity of performance measures to changes in system parameters for a specific class of stochastic models. Motivated by the problem of the coexistence on transmission links of telecommunication networks of elastic and unresponsive traffic, we study in this paper the impact on the stationary characteristics of an M/M/1 queue of a small perturbation in the server rate. For this model we obtain a new perturbation bound by using the Strong Stability Approach. Our analysis is based on bounding the distance of stationary distributions in a suitable functional space.
KeywordsMarkov Chain Service Rate Perturbation Analysis Markov Chain Modeling Strong Stability
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- Aïssani, D., Kartashov, N.: Ergodicity and stability of Markov chains with respect to operator topology in the space of transition kernels. Doklady Akademii Nauk Ukrainskoi SSR 11 (seriya A) 11, 3–5 (1983)Google Scholar
- Heidergott B (2008) Perturbation analysis of Markov chains. In: Proceedings of the International Workshop on DES, Göteborg, SwedenGoogle Scholar
- Hordijk, A., Spieksma, F.: A new formula for the deviation matrix. In: Kelly, F. (ed.) Probability, Statistics and Optimization, Wiley, Chichester (1994)Google Scholar
- Kartashov N (1996) Strong stable Markov chains. VSP/TbiMC, Utrecht/Kiev, Utrecht/KievGoogle Scholar
- Whitt W (1981) Quantitative continuity results for the GI/G/1 queue. Tech. rep., Bell Laboratories ReportGoogle Scholar
- Zolotarev V (1977) General problems of the stability of mathematical models. Proceedings of the session the 41st International Statistical Institute: New DehliGoogle Scholar