ASYMPTOTIC WAITING TIME ANALYSIS OF A FINITE-SOURCE M/M/1 RETRIAL QUEUEING SYSTEM
Copyright policy )ASYMPTOTIC WAITING TIME ANALYSIS OF A FINITE-SOURCE M/M/1 RETRIAL QUEUEING SYSTEM
The aim of the paper is to derive the distribution of the number of retrial of the tagged request and as a consequence to present the waiting time analysis of a finite-source M/M/1 retrial queueing system by using the method of asymptotic analysis under the condition of the unlimited growing number of sources. As a result of the investigation, it is shown that the asymptotic distribution of the number of retrials of the tagged customer in the orbit is geometric with given parameter, and the waiting time of the tagged customer has a generalized exponential distribution. For the considered retrial queuing system numerical and simulation software packages are also developed. With the help of several sample examples the accuracy and range of applicability of the asymptotic results in prelimit situation are illustrated showing the effectiveness of the proposed approximation.
- Peoples' Friendship University of Russia Russian Federation
- National Research University of Electronic Technology Russian Federation
- University of Debrecen Hungary
- National Research Tomsk State University Russian Federation
асимптотический анализ, время ожидания, finite-source queueing system, 650, Queueing theory (aspects of probability theory), asymptotic analysis, системы массового обслуживания, closed queueing system, accuracy and area of applicability of approximations, retrial queue, Queues and service in operations research, waiting time, limiting distribution, number of retrials
асимптотический анализ, время ожидания, finite-source queueing system, 650, Queueing theory (aspects of probability theory), asymptotic analysis, системы массового обслуживания, closed queueing system, accuracy and area of applicability of approximations, retrial queue, Queues and service in operations research, waiting time, limiting distribution, number of retrials
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