Time-dependent analysis of a single-server retrial queue with state-dependent rates

Parthasarathy, P. R.; Sudhesh, R.

doi:10.1016/j.orl.2006.12.005

Cited by 16 publications

(7 citation statements)

References 8 publications

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“…The methodology can be extended to more general queuing models combining retrials and other queuing phenomena: unreliable queues [8,14,[18][19][20], discrete-time models [8,20], etc. The consideration of the new descriptors in a time dependent context [16] could be the subject matter of a forthcoming study. Such a study will allow us to compute our descriptors in any time interval (0, t] rather than in a busy period.…”

Section: Resultsmentioning

confidence: 99%

“…We also remark the paper by Artalejo and Falin [3] where two structural characteristics of the orbit, namely, the orbit busy period and the orbit idle period, were investigated. To illustrate the active role of the retrial queues over the last few years, we mention a recent paper published in this journal [21] as well as some other recent publications [1,[8][9][10][11][12][14][15][16][18][19][20].…”

Section: Example 2 Random Access Protocols In Communication Networkmentioning

confidence: 99%

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The M/G/1 retrial queue: New descriptors of the customer’s behavior

Amador

Artalejo

2009

Journal of Computational and Applied Mathematics

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We consider queuing systems where customers are not allowed to queue; instead of that they make repeated attempts, or retrials, in order to enter service after some time. The performance of telephone systems and communication networks modelled as retrial queues differs from standard waiting lines because typically the retrial group is an invisible queue which cannot be observed. As a result, the original flow of primary arrivals and the flow of repeated attempts become undistinguished. Our aim in this paper is to consider some aspects of this problem. Thus, we focus on the main retrial model of M/G/1 type and investigate the distribution of the successful and blocked events made by the primary customers and the retrial customers.

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Section: Resultsmentioning

confidence: 99%

Section: Example 2 Random Access Protocols In Communication Networkmentioning

confidence: 99%

The M/G/1 retrial queue: New descriptors of the customer’s behavior

Amador

Artalejo

2009

Journal of Computational and Applied Mathematics

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“…They have computed the queue length distributions using supplementary variable and recursive techniques. Parthasarathy and Sudhesh [15] considered a time-dependent single server retrial queue with state dependent rates. They have obtained the time-dependent system size probabilities by employing continued fractions analytically in closed form in terms of convolutions.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time State Dependent Bulk Service Queue with Multiple Vacations and Changeover Times

Laxmi

Demie

2014

ISRN Operations Research

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This paper presents the analysis of a discrete-time renewal input multiple vacations queue with state dependent service and changeover times under ( , , ) policy. The service times, vacation times, and changeover times are geometrically distributed. The server begins service if there are at least units in the queue and the services are performed in batches of minimum size and maximum size ( ≤ ≤ ). At service completion instant, if the queue size is less than but not less than a secondary limit , the server continues to serve and takes vacation if the queue size is less than − 1. The server is in changeover period whenever the queue size is − 1 at service completion instant and − 1 at vacation completion instant. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at prearrival and arbitrary epochs. Based on the queue length distributions, some performance measures of the system have been discussed. A cost model has been formulated and optimum values of the service and vacation rates have been evaluated using genetic algorithm. Numerical results showing the effect of model parameters on the key performance measures are presented.

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“…SDQs are realistic models for discrete-event dynamic systems with a human server, whose speed may be affected by the number of jobs or customers waiting in line. These types of queueing systems have been studied by many researchers, see for example, Courtois and Georges (1971), Cheng (1993), Macgregor Smith (1994), Gupta and Srinivasa Rao (1998), Chao and Rahman (2006), Parthasarathy and Sudhesh (2007).…”

Section: Introductionmentioning

confidence: 99%

Mathematical programming representations for state-dependent queues

Chan

Schruben

2008

2008 Winter Simulation Conference

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Discrete-event dynamic systems with feedback, where the behavior of the system depends on the system state, are difficult to model due to the uncertainties and dependencies of system performance on the system state. Service systems, in particular, tend to exhibit this behavior where servers may work faster (or slower) when facing an increasingly long line of impatient customers. A common example is a state-dependent queue where the service rate depends on the queue size, which can change during service. In this paper, we present a mathematical programming representation for the sample path dynamics of a state-dependent queue, and illustrate its application in sensitivity analysis.

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Time-dependent analysis of a single-server retrial queue with state-dependent rates

Cited by 16 publications

References 8 publications

The M/G/1 retrial queue: New descriptors of the customer’s behavior

The M/G/1 retrial queue: New descriptors of the customer’s behavior

Discrete-Time State Dependent Bulk Service Queue with Multiple Vacations and Changeover Times

Mathematical programming representations for state-dependent queues

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