A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy

Choudhury, Gautam; Madan, Kailash C.

doi:10.1016/j.mcm.2005.04.003

Cited by 72 publications

(26 citation statements)

References 16 publications

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“…The optimal control and management of such models have also received considerable attention in the literature. For example, Choudhury and Madan (2005) investigated such a type of model for a two-stage batch arrival queue with Bernoulli vacation schedule and Choudhury and Paul (2006) studied a similar type of model for a batch arrival queueing system with two phases of service. They derived the queue size distribution at a random epoch as well as at a departure epoch for an M [x] /G/1 queueing system with second optional channel under N-policy.…”

Section: Introductionmentioning

confidence: 99%

Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Pearn

2011

International Journal of Systems Science

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We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.

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Section: Introductionmentioning

confidence: 99%

Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Pearn

2011

International Journal of Systems Science

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“…The variations and extensions of these vacation models were developed by several researchers such as Lee et al [3,4], Krishna Reddy et al [5], Choudhury [6,7], Ke [8,9], Ke and Chu [10], Ke et al [11,12] and many others. A numbers of papers [13][14][15][16] have recently appeared in queueing literature in which the server provides to each heterogeneous service with Bernoulli schedule vacation (BSV). The so-called BSV means that when the service of a unit is completed, the server may leave for a vacation of random length with probability p or may continue to serve the next unit, if any with probability 1 À p (see Choudhury et al [17]).…”

Section: Introductionmentioning

confidence: 99%

Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule

Pearn

2011

Applied Mathematical Modelling

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a b s t r a c tThis paper considers an infinite-capacity M/M/c queueing system with modified Bernoulli vacation under a single vacation policy. At each service completion of a server, the server may go for a vacation or may continue to serve the next customer, if any in the queue. The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. The explicit closed-form of the rate matrix is derived and the useful formula for computing stationary probabilities is developed by using matrix analytic approach. System performance measures are explicitly developed in terms of computable forms. A cost model is derived to determine the optimal values of the number of servers, service rate and vacation rate simultaneously at the minimum total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures.

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“…Arumuganathan and Jeyakumar [13] analysed a M X / G(a, b)/1 queueing system with multiple vacation, setup time with N-policy and closedown times. Choudhury and Madan [14] considered a batch arrival queueing system, where the server provides two stages of heterogeneous service with a modified Bernoulli schedule under N-policy.…”

Section: Introductionmentioning

confidence: 99%

Transient Analysis of a Telecommunication System Using State Dependent Markovian Queue under Bi-Level Control Policy

Jain¹,

Sharma²,

Saraswat³

et al. 2009

eng

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Abstact. In this paper, we develop a finite queueing model having single and batch service modes for telecommunication system, where two types of traffic, i.e. voice and data arrive in Poisson fashion. The server starts service only when N packets are accumulated in the system. The server performs service singly until there are C packets in the system. After then type 2 packets are discarded and all type 1 packets are served in a batch. The arrival rates of packets depend upon the server's status. The transient state probabilities of system states are obtained by solving a set of linear equations with the help of Laplace Transform technique. Performance indices such as average queue length, expected idle time, and expected busy period are determined. We also investigate the optimal value of threshold parameter N and C after which the server changes the mode of service in order to minimize the expected cost. The numerical illustrations are provided to visualize the effect of various parameters on system performance.

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A two-stage batch arrival queueing system with a modified bernoulli schedule vacation under N-policy

Cited by 72 publications

References 16 publications

Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule

Transient Analysis of a Telecommunication System Using State Dependent Markovian Queue under Bi-Level Control Policy

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