An approximation method for the M/G/1 retrial queue with general retrial times

Yang, Tao; Posner, M. J. M.; Templeton, J. G. C.; Li, H.

doi:10.1016/0377-2217(94)90286-0

Cited by 52 publications

(27 citation statements)

References 5 publications

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“…The literature on vacation models recognises this property as one of the most interesting features in this mater, e.g., see Doshi (1986), and Fuhrmann and Cooper (1985). Stochastic decomposition for retrial models is also found in Yang et al (1994) and Yang and Templeton (1987). The existence of the stochastic decomposition property for our model can be demonstrated easily by showing that…”

Section: Stochastic Decompositionmentioning

confidence: 78%

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A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

Choudhury

Deka

2015

IJMOR

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This paper deals with the steady state behaviour of an Mx/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with first come, first served (FCFS) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or may serve the next unit, if any, with probability (1 -p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property.Reference to this paper should be made as follows: Choudhury, G. and Deka, M. (2015) 'A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times', Int.

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Section: Stochastic Decompositionmentioning

confidence: 78%

“…However, this methodology was found to be incorrect by Falin (1986). Subsequently, Yang et al (1994) have developed an approximation method to obtain the steady state performance for the model of Kapyrin. Later, Gomez-Corral (1999) discussed extensively an M/G/1 retrial queue with FCFS discipline and general retrial times.…”

Section: Introductionmentioning

confidence: 98%

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

Choudhury

Deka

2015

IJMOR

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“…Stochastic decomposition property of classical M/G/1 retrial queues with exponential and general retrial times states that the number of customers in the system is equal to the sum of two independent random variables: the number of customers in the ordinary M/G/1 queue with infinite waiting space and the number of customers in the M/G/1 retrial queue given that the server is idle [15,16]. Aissani and Artalejo [2] introduced an auxiliary queue without retrials to establish the stochastic decomposition property of M/G/1 retrial queues with breakdowns and exponential retrial times.…”

Section: Stochastic Decompositionmentioning

confidence: 99%

On the M/G/1 retrial queue subjected to breakdowns

Djellab

2002

RAIRO-Oper. Res.

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“…Therefore, the analysis of retrial queueing systems is very difficult. In order to analyze the performance of these systems, an important number of different approximating approaches and algorithms are proposed (Abramov 2006;Artalejo and Gomez-Corral 1995;Artalejo and Pozo 2002;Berjdoudj and Aïssani 2004;Gomez-Corral 2006;Lopez-Herrero 2006;Stepanov 1983;Yang et al 1994).…”

Section: Introductionmentioning

confidence: 99%

MRSPN analysis of Semi-Markovian finite source retrial queues

2015

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In this paper, the analysis of Semi-Markovian single server retrial queues by means of Markov Regenerative Stochastic Petri Nets (MRSPN) is considered. We propose MRSPN models for the two retrial queues M/G/1/N/N and M/G/1/N/N with orbital search. By inspecting the reduced reachability graph of both MRSPN models, the qualitative analysis is obtained. The quantitative analysis is carried out after constructing their one step transition probability matrix and computing the steady state probability distribution of each tangible marking. As an example, the queue M/H ypo 2 /1/2/2 is treated in order to illustrate the functionality of the MRSPN approach. The exact performance measures (mean number of customers in the system, mean response time, mean waiting time,…) are computed for different parameters of the two systems by an algorithm elaborated in Matlab environment.

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An approximation method for the M/G/1 retrial queue with general retrial times

Cited by 52 publications

References 5 publications

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

On the M/G/1 retrial queue subjected to breakdowns

MRSPN analysis of Semi-Markovian finite source retrial queues

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