Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/Gn(a,b)/1

Discrete-time queueing models find a large number of applications as they are used in modeling systems arising digital platforms like telecommunication and computer networks. In this paper, we analyze an infinite-buffer model with discrete Markovian arrival process. The units on served batches by single server according to the general bulk-service rule, service time follows distribution rate depending size batch being served. We mathematically formulate using supplementary variable technique obtain vector generating function at departure epoch. is turn extract joint queue content terms roots characteristic equation. Further, develop relationship between epoch arbitrary, pre-arrival outside observer’s epochs, where first latter ones. evaluate some essential performance measures system also discuss computing process extensively which demonstrated numerical examples.