Stability analysis of a multiclass retrial system with classical retrial policy

Morozov, Evsey; Phung-Duc, Tuan

doi:10.1016/j.peva.2017.03.003

Cited by 30 publications

(13 citation statements)

References 31 publications

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“…In a fairly general class of retrial queues (both single and multiple class models) with classical retrial rate, the coincidence in the stability conditions between retrials models and non-retrial models is confirmed by Morozov et al [89,90] for more general non-Markovian models (i.e., arbitrary renewal arrivals and arbitrary service time) using the regenerative approach. The regenerative approach of Morozov et al is also used to prove other models with constant retrial rate [3,4].…”

Section: Stability Conditionsmentioning

confidence: 78%

Retrial Queueing Models: A Survey on Theory and Applications

Phung-Duc¹

2019

Preprint

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Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these systems. We investigate the state of the art of the theoretical researches including exact solutions, stability, asymptotic analyses and multidimensional models. We present an overview on retrial models arising from real world applications. Some open problems and promising research directions are also discussed.

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Section: Stability Conditionsmentioning

confidence: 78%

Retrial Queueing Models: A Survey on Theory and Applications

Phung-Duc¹

2019

Preprint

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“…It has been widely known in fairly general settings that the stability condition for a retrial model is the same with that of the corresponding model without retrials [13,14]. The stability condition of our multiserver retrial queue is a new finding in the sense that it is different from that of the corresponding queue without retrials.…”

Section: Tuan Phung-duc and Ken'ichi Kawanishimentioning

confidence: 80%

“…The stability conditions of the models with and without buffer are different. It is well known that the stability condition for a retrial queue without setup time and with classical (linear) retrial rate is the same as that of the corresponding model without retrials [13,14]. This is evident because in the saturated situation where there are many customers in the orbit and all the servers are active.…”

Section: Remarkmentioning

confidence: 84%

Multiserver retrial queue with setup time and its application to data centers

Phung-Duc¹,

Kawanishi²

2019

Journal of Industrial &Amp; Management Optimization

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This paper considers a multiserver retrial queue with setup time which is motivated from application in data centers with the ON-OFF policy, where an idle server is immediately turned off. The ON-OFF policy is designed to save energy consumption of idle servers because an idle server still consumes about 60% of its peak consumption processing jobs. Upon arrival, a job is allocated to one of available off-servers and that server is started up. Otherwise, if all the servers are not available upon arrival, the job is blocked and retries in a random time. A server needs some setup time during which the server cannot process a job but consumes energy. We formulate this model using a threedimensional continuous-time Markov chain obtaining the stability condition via Foster-Lyapunov criteria. Interestingly, the stability condition is different from that of the corresponding non-retrial queue. Furthermore, exploiting the special structure of the Markov chain together with a heuristic technique, we develop an efficient algorithm for computing the stationary distribution. Numerical results reveal that under the ON-OFF policy, allowing retrials is more power-saving than buffering jobs. Furthermore, we obtain a new insight that if the setup time is relatively long, setting an appropriate retrial time could reduce both power consumption and the mean response time of jobs.

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“…In particular, in this work we focus on the fundamental problem of investigating the queueing delay in multiclass retrial systems with constant retrial policy, and arbitrarily distributed class dependent service times, which remains an open problem. The only available results refer to the investigation of the stability conditions [9,10,29,30]. More precisely, for the two orbit scenario, we generalize the seminal paper in [7] by allowing arbitrarily distributed class dependent service times, and obtain the generating function of the stationary joint orbit queue-length distribution in terms of a solution of a Riemann boundary value problem 1 .…”

Section: Our Contributionmentioning

confidence: 99%

A two-class queueing system with constant retrial policy and general class dependent service times

Dimitriou

2018

European Journal of Operational Research

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A single server retrial queueing system with two-classes of orbiting customers, and general class dependent service times is considered. If an arriving customer finds the server unavailable, it enters a virtual queue, called the orbit, according to its type. The customers from the orbits retry independently to access the server according to the constant retrial policy. We derive the generating function of the stationary distribution of the number of orbiting customers at service completion epochs in terms of the solution of a Riemann boundary value problem. For the symmetrical system we also derived explicit expressions for the expected delay in an orbit without solving a boundary value problem. A simple numerical example is obtained to illustrate the system's performance.

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Stability analysis of a multiclass retrial system with classical retrial policy

Cited by 30 publications

References 31 publications

Retrial Queueing Models: A Survey on Theory and Applications

Retrial Queueing Models: A Survey on Theory and Applications

Multiserver retrial queue with setup time and its application to data centers

A two-class queueing system with constant retrial policy and general class dependent service times

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