An M/G/1 retrial queue with balking and retrials during service

Wu, Xin; Brill, Percy H.; Hlynka, Myron; Wang, Jinting

doi:10.1504/ijor.2005.007432

Cited by 28 publications

(15 citation statements)

References 13 publications

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“…All models considering retrial queues with server breakdowns assume an M/G/1/1 loss system with the exception of [6] and [21]. [2,3,7,16,20,23,24,27]) force these customers into the orbit, whereas others [4][5][6]11,15,26] provide the option of joining the orbit or departing the system. For retrial models with no waiting room and server breakdowns, customers arriving to find the server unavailable (busy or failed) join the orbit.…”

Section: Introductionmentioning

confidence: 99%

“…For retrial models with no waiting room and server breakdowns, customers arriving to find the server unavailable (busy or failed) join the orbit. A variety of failure types are considered in the literature, including starting failures [16,20,27], vacations [7,23], active breakdowns [6,24,26], and, like our model, both active and idle breakdowns [2][3][4][5]11,15]. [2,3,7,16,20,23,24,27]) force these customers into the orbit, whereas others [4][5][6]11,15,26] provide the option of joining the orbit or departing the system.…”

Section: Introductionmentioning

confidence: 99%

“…Some models (cf. [7,16,26]) consider orbits as first come-first served (FCFS) queues. With the exception of two cases ( [3,24]), these models also either force or provide the option for in-service customers interrupted by a server failure to join the orbit.…”

Section: Introductionmentioning

confidence: 99%

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AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS

Sherman

Kharoufeh

Abramson

2009

Prob. Eng. Inf. Sci.

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As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS

Sherman

Kharoufeh

Abramson

2009

Prob. Eng. Inf. Sci.

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“…Chakravarthy and Dudin (2003) studied a retrial queuing model in which two types of customers arrive according to a Markovian arrival process. Wu et al (2005) studied the retrial queues with general service times and non-exponential retrial time distribution. Sherman and Kharoufeh (2006) analysed an unreliable M/M/1 retrial queue with infinitecapacity orbit.…”

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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“…As examples of recent treatments of the waiting time under other queueing policies, we mention Refs. [7,9,13].…”

Section: Introductionmentioning

confidence: 99%

Waiting time analysis of the M/G/1 queue with finite retrial group

Artalejo

Gómez‐Corral

2007

Naval Research Logistics

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Abstract:We consider an M/G/1 retrial queue with finite capacity of the retrial group. First, we obtain equations governing the dynamic of the waiting time. Then, we focus on the numerical inversion of the density function and the computation of moments. These results are used to approximate the waiting time of the M/G/1 queue with infinite retrial group for which direct analysis seems intractable.

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An M/G/1 retrial queue with balking and retrials during service

Cited by 28 publications

References 13 publications

AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS

AN M/G/1 RETRIAL QUEUE WITH UNRELIABLE SERVER FOR STREAMING MULTIMEDIA APPLICATIONS

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

Waiting time analysis of the M/G/1 queue with finite retrial group

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