Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations

Jain, Madhu; Sharma, G C; Sharma, Richa

doi:10.1504/ijmor.2013.052458

Cited by 18 publications

(5 citation statements)

References 25 publications

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“…Ke and Chang (2009) investigated a batch arrival retrial queue with general retrial times where the server provides two phases of heterogeneous service to all the customers under Bernoulli vacation schedules. Moreover, unreliable server queue with multi-optional repairs/services was studied by Jain et al (2012dJain et al ( , 2013, respectively in different frameworks.…”

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

Self Cite

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“…( 2010 ), Choudhury and Deka ( 2012 ), Jain et al. ( 2013 ), Kumar et al. ( 2020 ), Gorbunova and Lebedev ( 2020 ), and Kumar et al.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method

Tang

2021

Oper Res Int J

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Motivated by the fault tolerance for manufacturing, we investigate a renewal input bulk arrival queue with a fault-tolerant server, in which the server can keep working with a low service rate even if the partial failure occurs. Only when there are no customers in the system, the partial failure can be removed. To explore the performance measures of the queue, a more generic and simpler algorithm based on the right shift operator method for solving difference equations is employed to obtain the queue-length distributions at different time epochs. The significant feature of this algorithm lies in that it does not require the derivation of the transition probability matrix for the corresponding embedded Markov chain. Furthermore, we can resort to the queue-length distribution at the pre-arrival epoch to quickly get the expected sojourn time for an arbitrary customer. Finally, with the help of Pad approximation, several representative numerical examples are illustrated in tables and graphs, under which we show how to verify the correctness of our theoretical results through Little’s law.

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“…This system is characterised by Bernoulli vacation schedule and an unreliable server with delayed repair. Jain et al (2013) extended the SPS to multi-optional services and servers' vacations were allowed. 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.…”

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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Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations

Cited by 18 publications

References 25 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

Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method

Finite source retrial queues with two phase service

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