A new method for deriving waiting-time approximations in polling systems with renewal arrivals
نویسندگان
چکیده
We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings.
منابع مشابه
Closed-Form Waiting Time Approximations for Polling Systems
A typical polling system consists of a number of queues, attended by a single server in a fixed order. The vast majority of papers on polling systems focusses on Poisson arrivals, whereas very few results are available for general arrivals. The current study is the first one presenting simple closed-form approximations for the mean waiting times in polling systems with renewal arrival processes...
متن کاملPolling models with renewal arrivals: A new method to derive heavy-traffic asymptotics
We consider asymmetric cyclic polling systems with an arbitrary number of queues, general service-time distributions, zero switch-over times, gated service at each queue, and with general renewal arrival processes at each of the queues. For this classical model, we propose a new method to derive closed-form expressions for the expected delay at each of the queues when the load tends to 1, under...
متن کاملEvaluation and optimization of polling systems
Throughout this internship report, polling systems play a central role. Polling systems are queueing systems consisting of multiple queues, attended by a single server. The server can only serve one queue at a time. Whenever the server moves from one queue to another, a stochastic, non-zero switch-over time is incurred. The server never idles; even when there are no customers waiting in the who...
متن کاملPolling systems with periodic server routing in heavy traffic: renewal arrivals
This paper considers heavy-traffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waiting-time distribution in a general parameter setting when the load tends to 1, under proper heavy-traffic scalings. The resul...
متن کاملEnschede Waiting times at periodically switched one - way traffic lanes
We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules, i.e. the driving dire...
متن کامل