A two phase batch arrival queueing system with a vacation time under Bernoulli schedule. (Q1427868)

The authors study the steady state behaviour of the queue size distribution of a batch arrival queueing system, where the server provides two phases of heterogeneous service one after the other under Bernoulli schedule vacation. They obtain the queue size distribution at a departure epoch as a classical generalization of Pollaczek-Khinchin formula. They also derive some important measures. This paper is an extension of the model studied by \textit{K. C. Madan} [Int. J. Syst. Sci. 32, 837--844 (2001; Zbl 1006.90021)].