We consider a single server infinite capacity queueing system, where
the arrival process is a batch Markovian arrival process (BMAP).
Particular BMAPs are the batch Poisson arrival process, the Markovian
arrival process (MAP), many batch arrival processes with correlated
interarrival times and batch sizes, and superpositions of these processes.
We note that the MAP includes phase-type (PH) renewal processes and
non-renewal processes such as the Markov modulated Poisson process
(MMPP).The server applies Kella's vacation scheme, i.e., a vacation policy
where the decision of whether to take a new vacation or not, when the
system is empty, depends on the number of vacations already taken in
the current inactive phase. This exhaustive service discipline includes the
single vacation T-policy, T(SV), and the multiple vacation T-policy,
T(MV). The service times are i.i.d. random variables, independent of
the interarrival times and the vacation durations. Some important
performance measures such as the distribution functions and means of
the virtual and the actual waiting times are given. Finally, a numerical
example is presented.
Multi-server queueing system with reserve servers
