A study on the behaviour of the server breakdown without interruption in a Mx/G(a, b)/1 queueing system with multiple vacations and closedown time

Jeyakumar, S.; Senthilnathan, B.

doi:10.1016/j.amc.2012.08.096

Cited by 12 publications

References 11 publications

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“…In queueing literature, a few researchers considered the server breakdown situations in their studies. Together with the concept of server breakdown and vacation presented by Jeyakumar and Senthilnathan (2012) analyze server breakdown without interruption in an M x /G(a, b)/1 queueing system with multiple vacations. Ye and Liu (2017) analyzed Markovian arrival single server queueing model with working breakdown by employing the matrix geometric method to determine the steady state equations.…”

Section: Introductionmentioning

confidence: 99%

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

Thakur

Jain

2021

Int J Math, Eng, Manag Sci

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In this paper, we investigate the M/M/1/N single server finite capacity Markovian queueing model with operational vacation and impatient behavior of the customers. To recover the server broken down during a busy period, M-threshold recovery policy along with set-up is used. Using the inflow and outflow transition rates, the state probabilities equations for different system states are constructed. For computing the stationary queue length, matrix-geometric analytic is performed. The sensitivity analysis is carried for the validation of the system performance measures. To examine the scope of the adaptive neuro-fuzzy inference system (ANFIS), computational results are presented using matric-geometric and ANFIS approaches.

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Section: Introductionmentioning

confidence: 99%

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

Thakur

Jain

2021

Int J Math, Eng, Manag Sci

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“…These type of queues are known as vacation queues which have potential applications in polling protocols frequently used in high-speed telecommunication networks, designing of local area networks, processor schedules in computer and switching systems, shared resources maintenance, manufacturing system with server breakdown etc. The literature clearly exhibits the extensive studies on vacation queues, for example see Doshi [25], Lee et al [26], Chang et al [10], Sikdar et al [27,28], Gupta et al [29,30,31], Reddy et al [32,33], Madan et al [34], Banik et al [35,36], Arumuganathan and Jeyakumar [37,38], Ke Jau-Chuan [39], Jeyakumar and Arumuganathan [40,41] and the references therein. It should be noted here that none of these analysis provides the server content distribution which is an essential tool to increase the serving capability of the server.…”

Section: Introductionmentioning

confidence: 99%

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Nandy,

Pradhan

2020

Preprint

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Due to the widespread applicability of discrete-time queues in wireless networks or telecommunication systems, this paper analyzes an infinite-buffer batch-service queue with single and multiple vacation where customers/messages arrive according to the Bernoulii process and service time varies with the batch-size.The foremost focal point of this analysis is to get the complete joint distribution of queue length and server content at service completion epoch, for which first the bivariate probability generating function has been derived. We also acquire the joint distribution at arbitrary slot. We also provide several marginal distributions and performance measures for the utilization of the vendor. Transmission of data through a particular channel is skipped due to the high transmission error. As the discrete phase type distribution plays a noteworthy role to control this error, we include numerical example where service time distribution follows discrete phase type distribution. A comparison between batch-size dependent and independent service has been drawn through the graphical representation of some performance measures and total system cost.

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“…These type of queues are known as vacation queues and has potential applications in processor schedules in computer and switching system, shared resource maintenance, designing of local area networks (LAN), manufacturing system with server breakdown etc. Various type of vacation queueing models for both discrete-and continuous-time set-up can be found in Dhosi [9], Baba [10], Takagi [11], Lee et al [12], Tian [13], Reddy et al [14], Gupta et al [15,16], Sikdar et al [17], Jeyakumar et al [18] etc. Batch-service queues have applications in mobile crowdsourcing app for smart cities, recreational devices in amusement park, group testing of blood samples for detecting HIV/Influenza/viruses or to eliminate defective items in manufacturing systems etc.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of a discrete-time group-arrival and batch-size-dependent service queue with single and multiple vacation

Pradhan¹,

Nandy²

2020

Preprint

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Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze an infinite-buffer discrete-time group-arrival queue with single and multiple vacation policy where processing/transmission/service times dynamically vary with batch-size under service.The bivariate probability generating function of queue length and server content distribution has been derived first, and from that we extract the probabilities in terms of roots of the characteristic equation. We also find the joint distribution at arbitrary and pre-arrival slot. Discrete phase type distribution plays a noteworthy role in order to regulate the high transmission error through a particular channel. In view of this, numerical illustrations include the service time distribution to follow the discrete phase type distribution.

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A study on the behaviour of the server breakdown without interruption in a Mx/G(a, b)/1 queueing system with multiple vacations and closedown time

Cited by 12 publications

References 11 publications

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Modeling and analysis of a discrete-time group-arrival and batch-size-dependent service queue with single and multiple vacation

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