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<p>A retrial multi-server queue is considered in the paper. In our previous study, we found asymptotic results for similar model with two-phase hyper-exponential distribution of service time. In the current study, we consider the model with service times that have various non-exponential distributions: gamma, Weibull, lognormal, Pareto. The main idea is to build hyper-exponential approximations for these distributions and substitute them into the result of the study obtained for retrial queue with hyper-exponential service time. In the paper, we propose algorithms for building such approximations and evaluate the results. For estimation of accuracy of the results, we compare them with distributions built basing on the simulations of the corresponding models. As the results show, proposed approach allows to obtain quite accurate results for various values of parameters of the original distributions of service time except small regions. It works even though for some values of parameters of the chosen original distributions, their approximations are not hyper-exponential distributions or probability distributions at all.</p>

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Hyper-exponential Approximation in the Analysis of a Multi-server Retrial Queue with Non-exponential Service Time Distribution

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Alexander Moiseev,
  • Anatoly Nazarov,
  • Svetlana Paul

摘要

A retrial multi-server queue is considered in the paper. In our previous study, we found asymptotic results for similar model with two-phase hyper-exponential distribution of service time. In the current study, we consider the model with service times that have various non-exponential distributions: gamma, Weibull, lognormal, Pareto. The main idea is to build hyper-exponential approximations for these distributions and substitute them into the result of the study obtained for retrial queue with hyper-exponential service time. In the paper, we propose algorithms for building such approximations and evaluate the results. For estimation of accuracy of the results, we compare them with distributions built basing on the simulations of the corresponding models. As the results show, proposed approach allows to obtain quite accurate results for various values of parameters of the original distributions of service time except small regions. It works even though for some values of parameters of the chosen original distributions, their approximations are not hyper-exponential distributions or probability distributions at all.