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.
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