We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

We consider a model of two M/M/1 queues, served by a single server. The service policy for this polling model is of threshold type: the server serves queue 1 exhaustively, and does not remain at an empty queue if the other one is non-empty. It switches from queue 2 to queue 1 when the size of the latter queue reaches some level T , either preemptively or non-preemptively. All switches are insta...

Queuing theory is the study of queues for managing process and objects. In this paper we analyze various models of the Single server queuing system with.Single-sever service node consists of a server plus its queue. If only one service technician, the machine shop model from section 1. 1 is a single-server queue.Queueing theory is the mathematical study of waiting lines, or queues. The MM1 queu...

We consider a single-server polling system consisting of two queues of fluid with arrival process generated by a big number of heavy-tailed On/Off sources, and application in road traffic and communication systems. Classj fluid is assigned to queue j, j = 1,2. Server 2 visits both queues to process or let pass through it the corresponding fluid class. If there is class-2 fluid in the system, it...

this paper analyzes renewal input state dependent queue with $n$- policy wherein the server takes exactly one vacation. using the supplementary variable technique and recursive method, we derive the steady state system length distributions at various epochs. various performance measures has been presented. finally, some numerical  computations in the form of graphs are presented to show the par...