Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

Madan, Kailash C.; Abu–Dayyeh, Walid; Tayyan, Firas

doi:10.22237/jmasm/1051748340

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…The study on batch arrival batch service queue with some other assumptions is carried out by some authors. Madan et al(2003) considered the steady state analysis of batch arrival batch service queue with breakdown. A Batch arrival queue with variant vacation policy and balking was studied by Ke (2007).…”

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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“…Franx et al [8] study the multiserver system M=D=c. Madan and Saleh [9] study the queue M=D=1 with general vacations. Choi et al in [3,10] investigate the transient and sensitivity analysis of DSPN.…”

Section: Introductionmentioning

confidence: 99%

Performance Modeling of Finite Sources Retrial Queue using Markov Regenerative Approach

Ikhlef¹

2023

Markov Model - Theory and Applications

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We study a finite source retrial queue with deterministic service times using an approach based on the theory of Markov Regenerative Process (MRP). A Deterministic Stochastic Petri Net (DSPN) model which copes with the complexity of this queue is given. For the steady state of this model, we construct the one step transition probability matrix of embedded Markov chain and the conversion matrix. As an example the retrial system M/D/1/2/2 is detailed. We establish an algorithm in Matlab environment based on the theoretic results obtained in order to compute efficiently various performance measures and to study the effect of system parameter's on the characteristics of the DSPN models the retial queue M/D/1/N/N.

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“…The server may also interrupt right away if trouble arises. Yet, in the majority of instances, it is impossible to disturb the server before it has completed providing its bulk services [9]. Jeyakumar and Senthilnathan also studied breakdown without carrier disruption in a bulk carrier queue model and a bulk arrival queue model.…”

Section: Introductionmentioning

confidence: 99%

Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation

Niranjan,

Devi Latha,

Mahdal

et al. 2023

Mathematics

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In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size ′a′ and maximum bulk size ′b′. In the first essential service (FES) completion epoch, if the server fails, with probability ′δ′, then the renewal of the service station is considered. On the other hand, if there is no server failure, with a probability ′1−δ′, then the server switches to a second essential service (SES) in succession. A customer who requires further service as feedback is given priority, and they join the head of the queue with probability β. On the contrary, a customer who does not require feedback leaves the system with a probability ′1−β′. If the queue length is less than ′a′ after SES, the server may leave for a single vacation with probability ′1−β′. When the server finds an inadequate number of customers in the queue after vacation completion, the server becomes dormant. After vacation completion, the server requires some time to start service, which is attained by including setup time. The setup time is initiated only when the queue length is at least ′a′. Even after setup time completion, the service process begins only with a queue length ‘N’ (N > b). The novelty of this paper is that it introduces an essential two-phase bulk service, immediate Bernoulli feedback for customers, and renewal service time of the first essential service for the bulk arrival and bulk service queueing model. We aim to develop a model that investigates the probability-generating function of the queue size at any time. Additionally, we analyzed various performance characteristics using numerical examples to demonstrate the model’s effectiveness. An optimum cost analysis was also carried out to minimize the total average cost with appropriate practical applications in existing data transmission and data processing in LTE-A networks using the DRX mechanism.

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Steady State Analysis Of An M/D/2 Queue With Bernoulli Schedule Server Vacations

Cited by 3 publications

References 12 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

Performance Modeling of Finite Sources Retrial Queue using Markov Regenerative Approach

Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation

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