Unreliable M&lt;SUP align="right"&gt;x&lt;/SUP&gt;/G/1 retrial queue with multi-optional services and impatient customers

Bhagat, Amita; Jain, Madhu

doi:10.1504/ijor.2013.053614

Cited by 18 publications

(5 citation statements)

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“…Jain et al (2012a) investigated a batch arrival retrial queuing system with essential and optional services with server breakdown. Recently, M X /G/1 retrial queue with unreliable server and general retrial times was examined by Bhagat and Jain (2013).…”

Section: Literature Reviewmentioning

confidence: 99%

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Jain

Sharma

2015

IJISE

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This paper deals with the maximum entropy principle (MEP) to explore the steady state behaviour of the bulk arrival retrial queuing system. The concepts of Bernoulli vacation schedule and second optional service are taken into consideration. After the completion of first essential service (second optional service), the server has an option to go for vacation with probability ( ) p q or may continue to serve the next customer, if any with complementary probability. During vacation, the server is allowed to do some secondary work and is called on working vacation. By introducing supplementary variables and using generating function technique, we obtain the expected number of the customers and expected waiting time of the customers in the retrial group. By employing the maximum entropy approach, we derive various system performance measures. By taking the numerical illustrations we perform a comparative study between the exact waiting time and the approximate waiting time based on MEP analysis. The sensitivity analysis is also carried out to validate the analytical results.

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Section: Literature Reviewmentioning

confidence: 99%

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Jain

Sharma

2015

IJISE

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“…Wang and Li (2010) studied an M [X] /G/1 queue with second multi-optional service and unreliable server and both of the transient and steady-state solutions for queueing and reliability measures of interest were obtained. One may refer to Bhagat and Jain (2013) for recent advance in this area.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, this paper was extended to a more general model as an M/G/1 retrial queue (Lakshmi and Ramanath, 2014b). Bhagat and Jain (2013) studied the queueing measures of the M [x] /G/1 retrial queue with batch arrival customers and unreliable server which provides the second optional phase service after the FPS to only those customers who opt for it.…”

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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“…In this work, they considered the threshold level to start the repair of the failed server. Using supplementary variable approach, the single server retrial queue with bulk input and balking was investigated by Bhagat and Jain [11]. In this paper, they assumed that second optional phase service is provided to the customers after availing first phase essential service.…”

Section: Introductionmentioning

confidence: 99%

MX/G/1 unreliable retrial queue with option of additional service and Bernoulli vacation

Singh

Jain

Kumar³

2016

Ain Shams Engineering Journal

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In this paper, retrial queue with unreliable server and bulk arrivals is investigated. The server is capable of providing m-optional services and any one of these available services, may be rendered to the customer after the first essential service if the customer opts for the same. It is assumed that the server may fail while rendering any phase of service and undergoes for the immediate repair. After the completion of the service of a customer, the server may either take a vacation for a random period or may continue to provide the service to the other customers waiting in the queue. The supplementary variables corresponding to service time, repair time and retrial time are incorporated to determine the queue size distribution. To examine the effect of different parameters on the performance measures of the system, the numerical illustration is given which is supported by numerical simulation and sensitivity analysis. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Unreliable M<SUP align="right">x</SUP>/G/1 retrial queue with multi-optional services and impatient customers

Cited by 18 publications

References 0 publications

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Finite source retrial queues with two phase service

MX/G/1 unreliable retrial queue with option of additional service and Bernoulli vacation

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