Stochastic modeling and analysis of a discrete-time bulk-service vacation queue with second optional service

Minimization of energy consumption and quality of service are two significant aspects of wireless telecommunication systems, which are adequately modeled using discrete-time queueing framework. System’s delay can be reduced with the effective use of service and vacation policies. In this article, the modeling and analysis of a discrete-time bulk-service vacation queue with first essential service (FES) and second optional service (SOS) has been carried out. In FES, general bulk-service rule has been incorporated. A part of already served group in FES will join the SOS following binomial distribution. In both the phases, service time distributions are considered to be general distribution with service rates being dependent on batch-size. Here, we derive the bivariate probability generating functions of queue and server size distribution just after FES and SOS completion which are key components of this analysis. We also provide complete joint distribution at arbitrary, vacation completion slots. Various performance indices such as energy saving factor, throughput of the system, mean delay etc. have been sketched. The trade-off between energy consumption and system’s throughput has also been depicted which may produce the optimal energy consumption. Numerical illustrations exhibit the implementation of our proposed methodology as well as include an example in which deviation in average power consumption is discussed. Through the graphical representation, sensitivity analysis of key parameters on numerous marginal system’s probability and performance metrics have been investigated.