Analysis of the MAP/G(a,b)/1/N queue

The Markovian arrival process (MAP) is used to represent the bursty and cor related traffic arising in modem telecommunication network. In this paper. we consider a single server finite capacity queue with general bulk service rule in which arrivals are governed by MAP and service times are arbitrari ly distributed. The distributions of the number of customers in the queue a t arbitrary, post-departure and pre-arrival epochs have been obtained using the supplementary variable and the embedded Markov chain techniques. Compu tational procedure has been given when the service time distribution is of phase type.