Vacation time queues with Markovian arrival process (MAP) are
mainly useful in modeling and performance analysis of
telecommunication networks based on asynchronous transfer mode
(ATM) environment. This paper analyzes a single-server finite
capacity queue wherein service is performed in batches of maximum
size “b” with a minimum threshold “a” and arrivals are
governed by MAP. The server takes a single vacation when he finds
less than “a” customers after service completion. The
distributions of buffer contents at various epochs (service
completion, vacation termination, departure, arbitrary and
pre-arrival) have been obtained. Finally, some performance
measures such as loss probability and average queue length are
discussed. Numerical results are also presented in some cases.
