<i>N</i>-Policy for State-Dependent Batch Arrival Queueing System with<i>l</i>-Stage Service and Modified Bernoulli Schedule Vacation

Jain, Madhu; Agarwal, PK

doi:10.1080/16843703.2010.11673229

Cited by 14 publications

(3 citation statements)

References 20 publications

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“…Retrial queue, bulk arrival, starting failure, stochastic decomposition, and -stage service Jain and Agrawal [16,17] Probability generating function Retrial queue, feedback, and phase service Liu and Gao [165] Geo/Geo/1 Second optional service Lin et al [166] Matrix analytic approach, quasi-Newton method MAP/PH/1 Discrete time, multiple working vacations, and two-phase service Goswami and Selvaraju [167] M a t r i x a n a l y t i c m e t h o d GI/D-MSP/1 Discrete time, multiple vacations, Samanta and Zhang [168] Matrix geometric method…”

Section: Special Features Authors Methodologymentioning

confidence: 99%

“…To illustrate, this phenomenon we can cite a clinical physical examination procedure as a doctor's clinic wherein the patient goes through a series of physical checkup such as ear, nose and throat examination, blood test, electrocardiogram, eye examination which all are considered as essential phases of service to reach the final decision by any medical doctor to declare a candidate to be fit. Recently, Jain and Agrawal [16,17] examined a batch arrival queueing system with modified Bernoulli vacation under -policy wherein the customer needs -stage of service in succession that is, the first stage service (FSS) is followed by the second stage service (SSS), the second stage service followed by third stage service (TSS) and so on up to -stages of service.…”

Section: Multiphase Essential Servicementioning

confidence: 99%

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Mathematical Analysis of Queue with Phase Service: An Overview

Sharma

2014

Advances in Operations Research

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We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent.

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Section: Special Features Authors Methodologymentioning

confidence: 99%

Section: Multiphase Essential Servicementioning

confidence: 99%

Mathematical Analysis of Queue with Phase Service: An Overview

Sharma

2014

Advances in Operations Research

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“…Vasanta Kumar et al [8,9] examined the performance of two-phase M X /M/1 and M X /Ek/1 queueing systems with N-policy and unreliable server, respectively. Madhu Jain and Agarval [6] dealt with a state dependent batch arrival queueing system with modified Bernoulli vacation under N-policy. They proposed a method to find the optimal value of the threshold parameter to minimize the total expected cost.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an N-policy MX/M/1 Two-phase Queueing System with State-dependent Arrival Rates and Unreliable Server

Sama¹,

Vemuri²,

Talagadadeevi³

et al. 2019

ISI

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The aim of this paper is to analyze the performance of the two-phase MX/M/1 queueing mechanism. The other conditions of the queueing system under study are state-dependent arrival rates, N-policy, unreliable server and delayed repair. A single server provide service in two stages. The first stage is batch service and the second one is individual to each customer in the batch. The client's arrival rate depends upon the state of the server. We developed the steady state equations. Probability generating functions were used to solve the equations. The expected size of the queue while the server is at different states are derived. Cost function has been developed to determine the optimal threshold of N. Sensitivity analysis is presented to study the effect of the system parameters at the threshold of N for the geometric batch size distribution. The findings of this research help in designing two-phase queueing systems that occur in telecommunication networks, production etc. at a low cost.

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