Abstract
In this work, we discuss various (stochastic) orderings between random variables, with focus on the failure rate comparison. Then these results are applied to construct a coupling of random variables. In particular, it is shown how to compare the failure rates of various distributions, including Exponential, Weibull, Pareto and Burr distributions. These results are then applied to establish some monotonicity properties of the multiserver queueing systems with finite waiting room. These theoretical results are illustrated by a numerical simulation of M/G/c/n and M/M/c/n queueing systems.
The research is supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 05.577.21.0293, unique identifier RFMEFI57718X0293). The research is supported by Russian Foundation for Basic Research, projects No. 19-57-45022, 19-07-00303, 18-07-00156, 18-07-00147.
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Morozov, E., Peshkova, I., Rumyantsev, A. (2019). On Failure Rate Comparison of Finite Multiserver Systems. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science(), vol 11965. Springer, Cham. https://doi.org/10.1007/978-3-030-36614-8_32
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