A single server retrial queue with general retrial times and two-phase service

Wang, Jinting; Li, Jianghua

doi:10.1007/s11424-009-9164-8

Cited by 23 publications

(5 citation statements)

References 13 publications

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“…In some queueing situations all arriving customers require the essential service, whereas a few of them may further demand the subsidiary service provided by the same server immediately after completion of the regular service. Several researchers have studied the concept of additional optional service with queues [11,19,20]. Jeganathan [9] investigated a continuous review perishable (s, S) inventory system with N optional services, in which some of the arriving customers asked for second optional service as soon as the completion of first essential service and the second service is multi-optional.…”

Section: Introductionmentioning

confidence: 99%

A retrial queueing-inventory system with J-additional options for service and finite source

Yadavalli

Jeganathan

Venkatesan

et al. 2017

ORiON

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A continuous review (s, S) inventory system at a service facility with finite homogeneous sources of demands and retrial is analysed. The lifetime of each item is assumed to be exponential. Before items are delivered to the customers, some basic service on the item must be performed. It is known as a regular or main service. The service may get interrupted according to a Poisson process and it restarts after an exponentially distributed time. If the server is idle at the time of arrival of a customer and the inventory level is positive, then the service begins immediately. After the completion of regular service, a customer may either abandon the system forever or demand for a second service from the same server, which is multi-optional. If any arriving customer finds that the server is busy or inventory level is zero, he/she either enters into the orbit with probability p or balks (does not enter) with probability 1 − p. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by the matrix method. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. A numerical illustration is given.

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Section: Introductionmentioning

confidence: 99%

A retrial queueing-inventory system with J-additional options for service and finite source

Yadavalli

Jeganathan

Venkatesan

et al. 2017

ORiON

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“…Retrial queues with quasi-random input are of recent interest in modelling magnetic disk memory systems, telephony, cellular mobile networks, computer networks and localarea networks with non-persistent CSMA/CD protocols (see for example, Falin and Artalejo, 1998). Due to their wide applications in above areas, there has been a rapid growth in the literature on retrial queues with a quasi-random input, readers may refer to Do et al (2014b), Dragieve (2013Dragieve ( , 2014, Roszik et al (2007), Wang and Li (2009), Wang et al (2011), Zhang and Wang (2013) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…They also provided some interesting applications of the model. Wang and Li (2009) studied a single server retrial queue with general retrial times and two-phase service. Choudhury and Kalita (2009) dealt with the steady behaviour of an M/G/1 retrial queue which the server provides two phases of heterogeneous service under Bernoulli vacation.…”

Section: Introductionmentioning

confidence: 99%

Finite source retrial queues with two phase service

Wang

Sztrik

et al. 2017

IJOR

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This paper is concerned with a single server retrial queue with a finite number of sources with second optional service. This queueing system assumes that each source can generate a primary call to request service when it is free. After the first phase service, the customer will choose the second phase service with probability p. Our analysis extends previous work on this topic and we can use method of discrete transformation to get some more general results on the length of the queue, busy period and waiting time. Numerical examples show the influence of key parameters on the performance of the system.

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“…Later, Gomez-Corral (1999) discussed extensively an M/G/1 retrial queue with FCFS discipline and general retrial times. In recent years, several retrial models have been analysed with general retrial times, details of which may be found in Atencia and Moreno (2005), Chang and Ke (2009), Krishnakumar et al (2002b), Moreno (2004) and Wang and Li (2009).…”

Section: Introductionmentioning

confidence: 99%

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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A single server retrial queue with general retrial times and two-phase service

Cited by 23 publications

References 13 publications

A retrial queueing-inventory system with J-additional options for service and finite source

A retrial queueing-inventory system with J-additional options for service and finite source

Finite source retrial queues with two phase service

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

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