WHY QUEUING ANALYSIS? ......................................................................................2 QUEUING MODELS......................................................................................................3 The Single-Server Queue.....................................................................................3 Queue Parameters .............................................

This paper compares two discrete-time single-server queueing models with queues. In both models, the server is available to a queue probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for joint moments not feasible, we rely on heavy-traffic limit approach. The correlation coefficient of queue-contents computed via solution two-dimensional functional equatio...

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...

In a single server polling system, the server visits the queues according to a routing policy and while at a queue serves some or all of the customers there according to a service policy. A polling (or scheduling) policy is a sequence of decisions on whether to serve a customer, idle the server, or switch the server to another queue. The goal of this paper is to nd polling policies that stochas...

— We consider in this paper the steady state behaviour of a Queueing System with queue length dependent additional server facility wherein arrivais occur in batches of variable size. Whenever the queue length in front of the first server reaches a certain lenght, the system adds another server. Steady state probabilities and expected queue lengths in Single Server System and Additional Server S...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

We study the average Age of Information (AoI) and peak AoI (PAoI) a dual-queue status update system that monitors common stochastic process through two independent channels. Although double queue parallel transmission is instrumental in reducing AoI, out order data arrivals also imposes significant challenge to performance analysis. consider settings: M-M where service time servers exponentiall...