A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

Thangaraj, V.; Vanitha, S.

doi:10.1080/07362990903259934

Cited by 8 publications

(3 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Define, P n (1) ( x, t ) = Probability that at time t, there are n ( ≥ 0 ) customers in the queue excluding the one being provided the first essential service and the elapsed service time of this customer is x. P n (2) ( x, t ) = Probability that at time t, there are n ( ≥ 0 ) customers in the queue excluding the one being provided the second essential service and the elapsed service time of this customer is x. V n (t) = Probability that at time t, there are n ( ≥ 0 ) customers in the queue and the server is on vacation. The system is then governed by the following set of differential difference equations.…”

Section: Governing Equationsmentioning

confidence: 99%

A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

Hemamalini¹,

Abinaya²

2014

IOSRJM

View full text Add to dashboard Cite

show abstract

Section: Governing Equationsmentioning

confidence: 99%

A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

Hemamalini¹,

Abinaya²

2014

IOSRJM

View full text Add to dashboard Cite

show abstract

“…Thangaraj and Vanitha [28] have considered a two phase M/G/1 feedback queue with multiple server vacations. Subsequently these authors [27] studied an M/G/1 feedback queue with two types of service. Shahkar and Badamchizadeh [23], and Salehirad and Badamchizadeh [24], have studied queueing systems with k phases of heterogeneous service and random feedback.…”

Section: Introductionmentioning

confidence: 99%

A priority retrial queue with second multi optional service and m immediate Bernoulli feedbacks

Kalidass

Ramanath

2011

Proceedings of the 6th International Conference on Queueing Theory and Network Applications

View full text Add to dashboard Cite

We consider an M/G/1 retrial queueing system with two phases of heterogeneous service and a finite number of immediate Bernoulli feedbacks. If an arriving customer finds an idle server, service commences immediately. Otherwise, the blocked customer either joins the infinite waiting room with probability p or leaves the service area and enters the retrial group with complementary probability q. All arriving customers are provided with the same type of service in the first phase. In the second phase, the customer has to choose from one of the several optional services which are available in the system. After having completed both phases of service, the customer is allowed to make an immediate feedback. The feedback service also consists of two phases. In the feedback, the first phase of service is of the same type as in the previous service. However, in the second phase the customer may be permitted to choose an optional service different from one chosen earlier. In this way, the customer is permitted to make a finite number feedbacks. We employ the embedded Markov chain technique to obtain a sufficient condition for the system to attain the steady state. We obtain the probability generating function of the system size and the marginal probability generating functions of the queue size and orbit size. We also obtain the distribution of the server state and some useful performance measures. We also obtain the stochastic decomposition law. We study the asymptotic behaviour under high rate of retrials. Finally, numerical calculations are used to observe system performance.

show abstract

“…Some of the authors who concentrated on M/G/1 type queues with second optional service are Madan [10], Krishnakumar et al [8], Medhi [13], Choudhury [4] and Thillaigovindan et al [15]. Vacation models under various service disciplines have been investigated by Madan [9], Choudhury [3], Kalyanaraman and Pazhani Bala Murugan [7] and Thangaraj and Vanitha [14]. A study on M/G/1 type queueing system with optional second vacation have been carried out by Choudhury [5].…”

Section: Introductionmentioning

confidence: 99%

An M/G/1 reneging queueing system with second optional service and with second optional vacation

Manoharan¹,

Sasi²

2015

ams

View full text Add to dashboard Cite

We study an M/G/1 queueing system where the arrival follows Poisson Process. The server provides service in two stages, the first stage service is essential and the second stage of service is optional. If the system is empty then the server goes for a vacation of random duration and after returning from vacation the server decides to take a second vacation which is optional. When the server is on vacation the customer may decide to renege. We treat reneging in this paper when the server is on vacation as the service is unavailable. Using supplementary variable technique we derive the probability generating function for the number of customers in the system. Some performance measures are derived. A Particular case is discussed. Numerical study is also presented.

show abstract

A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

Cited by 8 publications

References 19 publications

A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

A Two Phase M/G/1 Feedback Queue with Multiple Server Vacation

A priority retrial queue with second multi optional service and m immediate Bernoulli feedbacks

An M/G/1 reneging queueing system with second optional service and with second optional vacation

Contact Info

Product

Resources

About