Jl Jan-Pieter Dorsman

A New Method for Deriving Waiting-Time Approximations in Polling Systems with Renewal Arrivals

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.

The impact of scheduling policies on the waiting-time distributions in polling systems

We consider polling models consisting of a single server that visits the queues in a cyclic order. In the vast majority of papers that have appeared on polling models, it is assumed that at each of the individual queues, the customers are served on a first-come-first-served (FCFS) basis. In this paper, we study polling models where the local scheduling policy is not FCFS but instead is varied as last-come-first-served (LCFS), random order of service (ROS), processor sharing (PS), and shortest-job-first (SJF). The service policies are assumed to be either gated or globally gated. The main result of the paper is the derivation of asymptotic closed-form expressions for the Laplace–Stieltjes transform of the scaled waiting-time and sojourn-time distributions under heavy-traffic assumptions. For FCFS service, the asymptotic sojourn-time distribution is known to be of the form

Analysis of fibre-loop optical buffers with a void-avoiding schedule

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Parallel queueing networks with Markov-modulated service speeds in heavy traffic

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Scheduling in polling systems in heavy traffic

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Heavy traffic analysis of a polling model with retrials and glue periods

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