Engineering Physics and Mathematics
Cost inspection of a Geo/G/1 retrial model using particle swarm optimization and Genetic algorithm

https://doi.org/10.1016/j.asej.2020.11.012Get rights and content
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Abstract

We have studied a Geo/G/1 retrial model with state-dependent and voluntary services in discrete-time frame. The concept of Bernoulli vacation is also considered wherein, after the execution of each service, the server may hold back for next unit or it may leave for a vacation of arbitrary duration. Priority and impatient units are also analysed. This system is applicable in digital and communication fields where the data is transferred in packets like broadband integrated services digital network (B-ISDN) and all those areas where time is considered as a discrete random variable. All necessary performance indices are established for the developed model. Stochastic decomposition laws for the system size are also provided. The calculated results are verified by performing numerical examples and a detailed illustration. We have further carried out a comparative analysis to obtain minimum cost using direct search method (DSM), Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) techniques.

Keywords

Discrete-time queue
Bernoulli vacation
Preferred and Impatient units
Cost optimization
GA
PSO

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Geetika Malik has done her masters in Mathematics from Delhi University. She is currently a PhD scholar in Amity University, Noida (U.P) under the guidance of Dr. Shweta Upadhyaya and co-guidance of Dr. Richa Sharma. Her research is focussed on probability theory, optimization, queueing analysis and precisely retrial queues. She has published one research paper in a UGC approved reputed journal and has presented her work in 7 reputed national/international conferences and workshops.

Dr. Shweta Upadhyaya did her MPhil and PhD in Mathematics from Dr. B.R. Ambedkar University, Agra. Currently she is an Assistant Professor in Amity University, Noida (U.P). Her research areas of interests include probability theory, stochastic models and queueing theory. She has published 25 research papers in international/national journals of repute and has participated and presented her research papers in twelve international/national conferences.

Dr. Richa Sharma is an Assistant Professor of Mathematics in JK Lakshmipat University, Jaipur. She received her M. Sc. and Ph. D. degrees in Mathematics from Dr B. R. Ambedkar University, Agra. She has nine years of research and teaching experience. Her research area includes queueing theory, probability theory, reliability theory, stochastic modelling and optimization. She has published thirty-six research papers in refereed International/National journals. She has participated and presented her research papers in forty-five International/National conferences and workshops.

Peer review under responsibility of Ain Shams University.