This paper deals with a finite capacity queue with workload dependent service. The ar-
rival of a customer follows Markovian arrival process ( MAP ). MAP is very effective arrival process
to model massage-flow in the modern telecommunication networks, as these messages are very bursty
and correlated in nature. The service time, which depends on the queue length at service initiation
epoch, is considered to be generally distributed. Queue length distribution at various epoch and key
performance measures have been obtained. Finally, some numerical results have been discussed to
illustrate the numerical compatibility of the analytic analysis of the queueing model under consider-
ation.