Optimal strategy analysis of an N-policy two-phase MX/M/1 queueing system with server startup and breakdowns

Vemuri, Vasanta Kumar.; Boppana, Venkata Siva Nageswara Hari Prasad; Kotagiri, Chandan; Bethapudi, Ravi Teja

doi:10.1007/s12597-011-0046-1

Cited by 11 publications

(5 citation statements)

References 15 publications

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“…Thus, various extensions are possible. N-policy queuing systems with server breakdowns (both working and non-working breakdowns) are studied extensively in the queuing literature (for example, [5][6][7]).…”

Section: Introductionmentioning

confidence: 99%

The k-out-of-n:G System Viewed as a Multi-Server Queue

Krishnamoorthy,

Joshua,

Mathew

2024

Mathematics

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This paper extends the k-out-of-n:G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N-policy of repair. The queuing system considered here has n servers, each of which has identically and exponentially distributed service times with parameter μ. Servers are subject to breakdown at an exponential rate γ. The repair process follows the N-policy of repair. Although these servers work independently of each other, service can be provided only when k functional servers are available in the system. We study the model in the steady state, using the matrix analytic method. We evaluate some associated performance measures and provide graphical/numerical illustrations. We consider an optimization problem, and the results of the study are presented.

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Section: Introductionmentioning

confidence: 99%

The k-out-of-n:G System Viewed as a Multi-Server Queue

Krishnamoorthy,

Joshua,

Mathew

2024

Mathematics

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“…Queueing theory plays a vital role with respect to the repair of the machines to optimize the system. Gupta [6], Hsieh and Wang [7], Vemuri et al [13], Jain [8], Devi et al [4], and Vedala et al [12] have significantly contributed this domain of server breakdowns and repair facilities.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of \(M^X/M/1\) Queue With Working Vacation, \(N\)-Policy and Customer Impatience

Sridhar

Devi²,

Chandan

2022

Comm. Math. Appl.

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This paper deals the transient analysis of a queueing system with working vacation in which the server may encounter with breakdowns. Customers enter in batches according to a Poisson process and receive service in FCFS mode. Whenever the server finds nobody, the server starts a working vacation during which the server renders service at a slower rate than the normal one. Further, we considered two types of customer's impatience balking and reneging. We solved the system of differential equations to find transient state probabilities and computed various performance indices like average queue length of system, the mean waiting time etc. We then executed sensitivity analysis and observed the impact on different parameters.

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“…In continuation of the above studies, the two stages M/M/1 queueing system with N-policy and gating, Vasanta Kumar & Chandan [30] presented an optimal operational policy. The detailed and performance examination of the two-phase M/Ek/1 and M X /M/1 server breakdown and gating N-policy systems were extensively and exhaustively explored by Vasanta Kumar et al [31,32]. As a consequence of the above studies, batch arrival and Erlangian service two-phase controllable M X /M/1 and M X /Ek/1 queueing systems with server startup and breakdowns were discussed by Vasanta Kumar et al [33,34].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Sama¹,

Vemuri²,

Boppana³

2021

ISI

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The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

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Optimal strategy analysis of an N-policy two-phase MX/M/1 queueing system with server startup and breakdowns

Cited by 11 publications

References 15 publications

The k-out-of-n:G System Viewed as a Multi-Server Queue

The k-out-of-n:G System Viewed as a Multi-Server Queue

Performance Analysis of \(M^X/M/1\) Queue With Working Vacation, \(N\)-Policy and Customer Impatience

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

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