Queueing systems on a circle

Queueing systems on a circle

Consider a ring on which customers arrive according to a Poisson process. Arriving customers drop somewhere on the circle and wait there for a server who travels on the ring. Whenever this server encounters a customer, he stops and serves the customer according to an arbitrary service time distribution. After the service is completed, the server removes the client from the circle and resumes hi...

Stability and weakly convergent approximations of queueing systems on a circle

We rst consider a `non-greedy' queueing system on a circle. We present a new and very simple proof of the stability of this system (under the appropriate condition) based on the average travel times between customers. Next we show that the same non-greedy system, with a restricted number of customers, converges weakly to this system when the restricted number goes to innnity. Finally we conside...

Queueing Systems

On fluid queueing systems with strict priority

We consider priority fluid queueing systems where high priority class has strict priority access to service. Sample path analysis tools, such as Poisson Counter Driven Stochastic Differential Equation, are employed to study system queueing behavior in steady state. We are able to obtain various analytical results for different fluid traffic models and system configurations. Those results can be...

The Impact of Dependence on Queueing Systems

The effect of dependence is mostly ignored in queueing systems due to the difficulty in its analysis; the existing studies about dependent queueing systems have restrictive assumptions, such as considering only the M/M/1 queue with order of dependence lag-1 in interarrival and service times. In this paper, we conduct a simulation study to observe the impact of dependence in a single server queu...