A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium

This paper studies the operating characteristics of an M X /H k /1 queueing system under multiple vacation policy. It is assumed that the server goes for vacation as soon as the system becomes empty. When he returns from a vacation and there is one or more customers waiting in the queue, he serves these customers until the system becomes empty again, otherwise goes for another vacation. The breakdown and repair times of the server are assumed to follow a negative exponential distribution. By using a generating function, we derive various performance indices. The approximate formulas for the probability distribution of the waiting time of the customers in the system by using the maximum entropy principle (MEP) are obtained. This approach is accurate enough for practical purposes and is a useful method for solving complex queueing systems. The sensitivity analysis is carried out by taking a numerical illustration.

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“…Following El-Affendi and Kouvatsos (1983), the entropy function y can be mathematically formulated as…”

Section: The Maximum Entropy Modelmentioning

confidence: 99%

Multiple vacation policy for MX/Hk/1 queue with un-reliable server

Jain

Sharma

Sharma³

2013

J Ind Eng Int

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“…We may refer to early papers by Shore (1982) and El-Affendi and Kouvatsos (1983) who obtained information theoretic approximation for some ordinary queueing models, and also to the survey paper by Kouvatsos (1994). More recently the applications include the paper by Tadj and Hamdi (2002) for single server queues with quorum, and Wang, Chuang, and Pearn (2002) for an M/G/1 queue operating under N -policy; in the context of retrial queues, Lopez-Herrero (2002) and Artalejo, Falin and Lopez-Herrero (2002) determine maximum entropy approximations for the distribution of the number of customers served during the busy period and the waiting time of an M/G/1 retrial queue, respectively.…”

Section: Introductionmentioning

confidence: 98%

A maximum entropy approach for the busy period of the M/G/1 retrial queue

Lopez-Herrero

2006

Ann Oper Res

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This paper concerns the busy period of a single server queueing model with exponentially distributed repeated attempts. Several authors have analyzed the structure of the busy period in terms of the Laplace transform but, the information about the density function is limited to first and second order moments. We use the maximum entropy principle to find the least biased density function subject to several mean value constraints. We perform results for three different service time distributions: 3-stage Erlang, hyperexponential and exponential. Also a numerical comparative analysis between the exact Laplace transform and the corresponding maximum entropy density is presented.

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“…With respect to queuing theory, the principle of maximum entropy has been applied to solving numerous systems including, but not limited to, and queues ([1], [2]), finite and infinite capacity queues ([3], [4]), multi-server queues ([5], [6]), multiple class queues with priorities ([7]), and queues with vacation ([8]–[10]) and queuing networks ([11]–[13]). In fact, since the early 1970's many attempts have been made to apply the method of maximum entropy in the field of queuing theory.…”

Section: Introductionmentioning

confidence: 99%

Maximum Entropy Principle Based Estimation of Performance Distribution in Queueing Theory

Huang

et al. 2014

PLoS ONE

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In related research on queuing systems, in order to determine the system state, there is a widespread practice to assume that the system is stable and that distributions of the customer arrival ratio and service ratio are known information. In this study, the queuing system is looked at as a black box without any assumptions on the distribution of the arrival and service ratios and only keeping the assumption on the stability of the queuing system. By applying the principle of maximum entropy, the performance distribution of queuing systems is derived from some easily accessible indexes, such as the capacity of the system, the mean number of customers in the system, and the mean utilization of the servers. Some special cases are modeled and their performance distributions are derived. Using the chi-square goodness of fit test, the accuracy and generality for practical purposes of the principle of maximum entropy approach is demonstrated.

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A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium

Cited by 77 publications

References 8 publications

Multiple vacation policy for MX/Hk/1 queue with un-reliable server

Multiple vacation policy for MX/Hk/1 queue with un-reliable server

A maximum entropy approach for the busy period of the M/G/1 retrial queue

Maximum Entropy Principle Based Estimation of Performance Distribution in Queueing Theory

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