A two phase batch arrival queueing system with a vacation time under Bernoulli schedule

We consider a batch arrival queueing system, where the server provides two phases of heterogeneous service one after the other to the arriving batches under Bernoulli schedule vacation. After completion of both phases of service the server either goes for a vacation with probability r(0 less than or equal to r less than or equal to 1) or may continue to serve the next unit, if any, with probability (1 - r). Otherwise, it remains in the system until a new batch of customers arrives. We derive the queue size distribution at a random epoch as well as a departure epoch under the steady state conditions. Further, we derive some important performance measures of this system. This extends the model studied by Madan [Egyptian Statist. J. 44 (2000) 39; Int. J. Syst. Sci. 32 (2001) 837]. (C) 2003 Published by Elsevier Inc.