Single server queues with a batch Markovian arriva

Authors: A D Banik

Publish Date: 2015/03/26

Volume: 24, Issue: 3, Pages: 337-363

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Abstract

We first consider an infinitebuffer single server queue where arrivals occur according to a batch Markovian arrival processBMAP The server serves customers in batches of maximum size ‘b’ with a minimum threshold size ‘a’ The service time of each batch follows general distribution independent of each other as well as the arrival process The proposed analysis is based on the use of matrixanalytic procedure to obtain queuelength distribution at a postdeparture epoch Next we obtain queuelength distributions at various other epochs such as prearrival arbitrary and preservice using relations with postdeparture epoch Later we also obtain the systemlength distributions at postdeparture and arbitrary epochs using queuelength distribution at postdeparture epoch Some important performance measures like mean queuelengths and mean waiting times have been obtained Total expected cost function per unit time is also derived to determine the locally optimal values of a and b Secondly we perform similar analysis for the corresponding infinitebuffer single server queue where arrivals occur according to a BMAP and service process in this case follows a nonrenewal one namely Markovian service process MSPA D Banik is presently an assistant professor in the Indian Institute of Technology Bhubaneswar India He received the BSc and MSc degrees in mathematics from the Jadavpur University West Bengal India in the year 1998 and 2000 respectively He received his PhD from the Department of Mathematics Indian Institute of Technology Kharagpur India in the year 2007 He visited a few places as research associate and earned research fellowships viz INRIA France one year postdoc fellowship at IRISA Rennes France two year visiting fellowships at TIFR Mumbai India one year FCT Portugal postdoc fellowship at IST Lisbon Portugal etc His main research interests include continuoustime queueing theory and its applications He has published research articles in Operations Research Letters Applied Mathematics and Computation Journal of Applied Mathematics and Stochastic Analysis Applied Mathematical Modelling Methodology and Computing in Applied Probability Stochastic Analysis and Applications etc He is a life member of the operational research society of India ORSI

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