On fluctuation analysis of different kinds of n-policy queues with single vacation

In this paper, we debate queueing systems with N-policy and single vacation. We consider these systems when the vacation times have Erlang distribution. Moreover, we adapted the input by studying two different kinds: first, an ordinary Poisson input, and second, type ۲ geometric batch input. We derive the probability generating function of the number of units in the system in two cases by using fluctuation analysis.

Keywords:

N-policy , single vacation , fluctuation theory , input batches , bulk input , marked delayed renewal process , delayed renewal process , point process , marked point process , random walk