MULTI Phase M/G/1 Queue with Bernoulli Feedback and Multiple Server Vacation

Maragathasundari, S.; Srinivasan, S.

doi:10.5120/8165-1390

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…Doshi (1986) and Takagi (1991) have done excellent survey works on vacation queues. Maragathasundari S et al (2018) analyzed a single server general service queue with compulsory vacation. In today's world, the concept of unreliable servers is very common in any type of service.…”

Section: Introductionmentioning

confidence: 99%

M[X]/G(1,K)/1queue with Unreliable Server and with Compulsory Vacation

2023

SCRS Proceedings of International Conference of Undergraduate Students 2023

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A batch arrival and batch service queue have been considered. The arrival pattern is Poisson. After completion of each service, the server takes a compulsory vacation, and the server may also break down at random time epochs during service. For this queuing model, using the supplementary variable technique, the probability-generating function of the number of customers in the queue at different server states has been obtained. The mean queue size and the probability of the server being idle have been derived. Some particular models have been derived. Some numerical models have been derived.

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Section: Introductionmentioning

confidence: 99%

M[X]/G(1,K)/1queue with Unreliable Server and with Compulsory Vacation

2023

SCRS Proceedings of International Conference of Undergraduate Students 2023

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“…S.Maragathasundari and S.Srinivasan [15], they studied about analysis of triple stage of service having compulsory vacation and service interruptions. S.Maragathasundari and S.Srinivasan [16], they studied about three phase M/G/1 queue with Bernoulli feedback and multiple server vacation.…”

Section: Introductionmentioning

confidence: 99%

Batch arrival queueing system with two stages of service

Maragathasundari¹,

Srinivasan²,

Ranjitham³

2014

ijma

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This Paper studies batch arrival queue with two stages of service. Random breakdowns and Bernoulli schedule server vacations have been considered here .After a service completion, the server has the option to leave the system or to continue serving customers by staying in the system. It is assumed that customers arrive to the system in batches of variable size, but served one by one. After completion of first stage of service, the server must provide the second stage of service to the customers. Vacation time follows general distribution, while we consider exponential distribution for repair time.We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers ,and the average waiting time in the queue.

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“…S. Maragathasundari and S. Srinivasan [15] analyzed the M/G/1 feedback queue with three stages multiple server vacations. S. Maragathasundari and S. Srinivasan [16] analyzed the triple stages of service having compulsory vacation and service interruptions. S. Maragathasundari and S. Srinivasan [17] studied the three phase M/G/1 queue with Bernoulli feedback and multiple server vacation.…”

Section: Introductionmentioning

confidence: 99%

“…S. Maragathasundari and S. Srinivasan [16] analyzed the triple stages of service having compulsory vacation and service interruptions. S. Maragathasundari and S. Srinivasan [17] studied the three phase M/G/1 queue with Bernoulli feedback and multiple server vacation. Various aspects like phase vacations, stages of services, and phases of service have been discussed by S. Maragathasundari and S. Srinivasan [18,19,20,21,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions

Sundari¹,

Srinivasan²,

Ranjitham³

2014

Missouri J. Math. Sci.

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We study a batch arrival queueing system of phase vacation with two stages of service based on a Bernoulli schedule. A single server provides essential service to all arriving customers with service time following a general distribution. After two stages of service completion, the server leaves for phase one vacation of random length with probability p or to continue staying in the system with probability 1−p. As soon as the completion of phase one vacation, the server undergoes phase two vacation. On completion of two heterogeneous phases of vacation the server returns back to the system. The vacation times are assumed to be general. The server is interrupted and the service interruption follows an exponential distribution. The arrivals follow a Poisson distribution. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived. From this we deduce the steady state results. We also obtain the average queue size and average waiting time.

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MULTI Phase M/G/1 Queue with Bernoulli Feedback and Multiple Server Vacation

Cited by 3 publications

References 22 publications

M[X]/G(1,K)/1queue with Unreliable Server and with Compulsory Vacation

M[X]/G(1,K)/1queue with Unreliable Server and with Compulsory Vacation

Batch arrival queueing system with two stages of service

Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions

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