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A BATCH ARRIVAL RETRIAL QUEUE WITH starting failureS,FEEDBACK AND ADMISSION CONTROL

Journal of Systems Science and Systems Engineering 2010年第3期19卷 306-320页

作者： Jinting WANG Peng-Feng ZHOU Department of Mathematics,School of Science,Beijing Jiaotong University,Beijing,China Department of Mathematics School of Science Beijing Jiaotong University Beijing China

This paper is concerned with the analysis of a feedback M^[X]/G/1 retrial queue with starting failures and general retrial times. In a batch, each individual customer is subject to a control admission policy upon arrival. If the server is idle, one of the customers admitted to the system may start its service and the rest joins the retrial group, whereas all the admitted customers go to the retrial group when the server is unavailable upon arrival. An arriving customer （primary or retrial） must turn-on the server, which takes negligible time. If the server is started successfully （with a certain probability）, the customer gets service immediately. Otherwise, the repair for the server commences immediately and the customer must leave for the orbit and make a retrial at a later time. It is assumed that the customers who find the server unavailable are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server. The Markov chain underlying the considered queueing system is studied and the necessary and sufficient condition for the system to be stable is presented. Explicit formulae for the stationary distribution and some performance measures of the system in steady-state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.

关键词： Batch arrival feedback repair retrial queue starting failure

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A RepairableGeoX/G/1 Retrial Queue with Bernoulli Feedback and Impatient Customers

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 205-222页

作者： Shan GAO Zai-ming LIU Department of Mathematics Fuyang Normal College School of Mathematics and Statistics Central South University

Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting *** from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov ***,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary *** also derive a stochastic decomposition *** the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit ***,we investigate the relation between our discrete-time system and its continuous ***,some numerical examples show the influence of the parameters on the mean orbit size.

关键词： discrete-time queue retrial queue starting failure steady state Bernoulli feedback

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维普期刊数据库

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