MAP/G/1/K queue with multiple thresholds on buffer (Q2717129)

As the title indicates, the paper examines a single server, finite capacity queue with a Markovian arrival process (MAP), for which the service time distribution depends on the queue length at the start of service. The work is motivated by discarding schemes for ameliorating congestion in ATM networks; it generalizes previous studies by the author and others. An embedded chain at departure epochs is considered, first. Then, using the supplementary variable method, the stationary queue length distribution is obtained in terms of the MAP parameters, the service time distributions and the stationary distribution for the embedded chain.