A Tandem Queueing System with Batch Session Arrivals

We consider a tandem queueing system with session arrivals. Session means a group of customers which should be sequentially processed in the system. In contrast to the standard batch arrival when a whole group of customers arrives into the system at one epoch, we assume that the customers of an accepted session arrive one by one in exponentially distributed times. Generation of sessions at the first stage is described by a Batch Markov Arrival Process (

BMAP

). At the first stage of tandem, it is determined whether a session has the access to the second stage. After the first stage the session moves to the second stage or leaves the system. At the second stage having a finite buffer the customers from sessions are serviced. A session consists of a random number of customers. This number is geometrically distributed and is not known at a session arrival epoch. The number of sessions, which can be admitted into the second stage simultaneously, is subject to control. An accepted session can be lost, with a given probability, in the case of any customer from this session rejection.