Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 2 2021 11 01 On fluctuation analysis of different kinds of n-policy queues with single vacation 2029 2040 5340 10.22075/ijnaa.2021.5340 EN Hind Saad Kazem Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq Ali Hussein Mahmood Al-Obaidi Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq 0000-0003-4221-7622 Journal Article 2021 03 04 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 2 geometric batch input. We derive the probability generating function of the number of units in the system in two cases by using fluctuation analysis. N-policy single vacation fluctuation theory input batches bulk input marked delayed renewal process delayed renewal process point process marked point process random walk https://ijnaa.semnan.ac.ir/article_5340_cce625699519dd5713ca68f9d290c000.pdf