Maximum entropy analysis to the N policy M/G/1 queueing system with server breakdowns and general startup times

Wang, Kuo-Hsiung; Wang, Tsung-Yin; Pearn, W. L.

doi:10.1016/j.amc.2004.04.115

Cited by 28 publications

(9 citation statements)

References 25 publications

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“…(1) proposed in [24]. Later, Wang et al [25,26] further used the same method to deal with some single-arrival M/G/1 controllable systems with various features: server breakdown and startup. Wang et al [27] analyzed the exact and approximate steady-state results for the M [x] /M/1 queueing system with multiple vacations and server breakdowns using birth-and-death process and maximum entropy approach.…”

Section: Introductionmentioning

confidence: 92%

Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation

Lin

2008

Journal of Computational and Applied Mathematics

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We consider the M [x] /G/1 queueing system, in which the server operates N policy and a single vacation. As soon as the system becomes empty the server leaves for a vacation of random length V . When he returns from the vacation and the system size is greater than or equal to a threshold value N , he starts to serve the waiting customers. If he finds fewer customers than N . he waits in the system until the system size reaches or exceeds N . The server is subject to breakdowns according to a Poisson process and his repair time obeys an arbitrary distribution. We use maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length. We perform a comparative analysis between the approximate results with established exact results for various batch size, vacation time, service time and repair time distributions. We demonstrate that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems.

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Section: Introductionmentioning

confidence: 92%

Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation

Lin

2008

Journal of Computational and Applied Mathematics

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“…The N-policy M/M/1 queue with heterogeneous arrival rates, server breakdowns, and vacations was analyzed by Ke and Pearn [8]. Wang et al [9] utilized the principle (1) We derive several system performance measures, as well as the stability condition of this queueing model; (2) We establish a cost model to find the optimal threshold N, the optimal service rate during the normal period, and the optimal service rate during the working breakdown period under the stability condition; (3) We apply the two-stage optimization method to search for the minimum expected cost. Numerical examples are given to illustrate the effectiveness of the two-stage optimization method.…”

Section: Introductionmentioning

confidence: 99%

Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

2020

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This paper deals with the N policy M/G/1 queue with working breakdowns. The supplementary variable and probability generating function techniques are implemented to develop the steady-state results. The stability condition of a stable queue, as well as several system performance measures, are also derived. A two-stage optimization method is employed to determine the optimal threshold N and the optimal joint values of two mean service rates until the stability constraint is satisfied. To demonstrate the effectiveness of two-stage optimization method, some numerical results are presented. Finally, we carry out sensitivity analysis for the expected cost function with numerical illustrations.Symmetry 2020, 12, 583 2 of 16 of maximum entropy to investigate the N-policy M/G/1 queue with server breakdowns and general startup times. Using the same approach, Ke and Lin [10] approximated the steady-state probability distributions of the queue length for the N-policy M [x] /G/1 queue with an unreliable server and a single vacation. The optimal control of the N-policy M/G/1 queueing system with server breakdowns and general startup times was examined by Wang et al. [11]. They applied the direct search method to determine the optimal threshold N at the minimum cost. Jain and Bhargava [12] performed cost analysis of the N-policy for the machine repair problem with mixed standbys and an unreliable server. An N-policy M X /M/1 queueing system with server startup and breakdowns was analyzed by Vemuri et al. [13], where service was in two phases. Singh et al. [14] focused on the investigation of the N-policy queue with an unreliable server, state-dependent arrival rates, two phases of service, and m phases of repair. Moreover, Yang and Ke [15] applied the supplementary variable technique to analyze the (p, N)-policy M/G/1 queue with an unreliable server and a single vacation. Chen and Wang [16] address the sensitivity analyses of a retrial machine repair problem with warm standby units and a single server under the N-policy.Over the years, there has been extensive literature on N-policy queues with server breakdowns, in which the server stops working completely during the breakdown period. However, there are no studies investigating the N-policy queue with working breakdowns. This queueing model accommodates many real-world systems, such as computer systems, assembly systems, and manufacturing systems. Thus, it motivates us to focus on the analysis of the N-policy M/G/1 queue with working breakdowns. The purpose of this paper is three-fold.

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“…Tadj and Hamdi [18] applied the MEP to obtain the approximate solutions for a quorum queueing system. Wang et al [23] used the MEP to study the N policy M/G/1 queueing system with server breakdowns and general startup times.…”

Section: Introductionmentioning

confidence: 99%

Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup

Yang

Wang

Pearn

2009

J. Appl. Math. Comput.

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This paper deals with the N, p -policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution. The server breaks down according to a Poisson process and his repair times obey a general distribution in the first essential service channel and second optional service channel, respectively. The server operation starts only when N (N ≥ 1) customers have accumulated, he requires a startup time before each busy period. When the system becomes empty, turn the server off with probability p (p ∈ [0, 1]) and leave it on with probability (1 − p). The method of maximum entropy principle is used to develop the approximate steady-state probability distribution of the queue length in the M/G(G, G)/1 queueing system. A study of the derived approximate results, compared to the established exact results for three different N, p -policy queues, suggests that the maximum entropy principle provides a useful method for solving complex queueing systems.

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Maximum entropy analysis to the N policy M/G/1 queueing system with server breakdowns and general startup times

Cited by 28 publications

References 25 publications

Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation

Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation

Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup

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