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Reliability analysis of M/G/1 queues with general retrial times and server breakdowns

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Progress in Natural Science:Materials International 2006年第5期16卷 464-473页

作者： WANG Jinting (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China) Department of Mathematics Beijing Jiaotong University Beijing 100044 China

This paper concerns the reliability issues as well as queueing analysis of M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a first-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained.

关键词： retrial queues general retrial times reliability server breakdowns and repairs.

Optimal Design for a retrial Queueing System with State-Dependent Service Rate

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Journal of Systems Science & Complexity 2017年第4期30卷 883-900页

作者： ZHANG Xuelu WANG Jinting MA Qing Department of Mathematics Beijing Jiaotong University School of Science Qilu University of Technology Department of Basic Courses Shandong Women’s University

This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.

关键词： Particle swarm optimization algorithm retrial queues social optimal strategy statedependent service policy

ON THE SINGLE SERVER retrial QUEUE WITH PRIORITY SUBSCRIBERS AND SERVER BREAKDOWNS

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Journal of Systems Science & Complexity 2008年第2期21卷 304-315页

作者： Jinting WANG Department of Mathematics Beijing Jiaotong University Beijing 100044 China

The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.

关键词： Priority queues reliability retrial queues server breakdowns.

OPTIMAL CONTROL OF AN M/G/1 retrial QUEUE WITH VACATIONS

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Journal of Systems Science and Systems Engineering 2008年第4期17卷 487-502页

作者： Amar AISSANI University of Science & Technology Houari Boumediene BP 32 El Alia Bab-Ez-Zouar 16111Algeria

In this note, we consider an M/G/1 retrial queue with server vacations, when retrial times, service times and vacation times are arbitrary distributed. The distribution of the number of customers in the system in stationary regime is obtained in terms of generating function. Next, we give heavy traffic approximation of such distribution. We show that the system size can be decomposed into two random variables, one of which corresponds to the system size of the ordinary M/G/1 FIFO queue without vacation. Such a stochastic decomposition property is useful for the computation of performance measures of interest. Finally, we solve simple problems of optimal control of vacation and retrial policies.

关键词： retrial queues vacation optimal control stochastic decomposition ageing distribution heavy traffic

An M^([X])/G/1 retrial G-queue with Single Vacation Subject to the Server Breakdown and Repair

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 579-596页

作者： Shu-ping YANG Jin-biao WU Zai-ming LIU The School of Mathematics and Statistics Central South University

An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.

关键词： Batch arrivals in a compound poisson process G-queues retrial queues single vacation reliability

AN M/G/1 retrial QUEUE WITH SECOND MULTI-OPTIONAL SERVICE,FEEDBACK AND UNRELIABLE SERVER

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Applied Mathematics(A Journal of Chinese Universities) 2006年第3期21卷 252-262页

作者： Li Jianghua Wang Jinting Department of Mathematics Beijing Jiaotong University Beijing 100044 China.

An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.

关键词： retrial queues two-phase service feedback server breakdown and repair starting failures.