Queuing on a continuous circle

In this thesis we analyze a queueing model on a continuous circle. The model is motivated by an application in optical data transport. A processor moves with constant speed on this circle. Jobs arrive at the current location of the processor, according to a Poisson process of fixed intensity. If the server is not occupied, it immediately takes the new job into service and releases it after completing exactly one turn on the circle. If the server is occupied with a another service at the moment a job arrives, this job waits at the position of its arrival, until the first time that the server passes by without being occupied with another job. It is possible to describe the model as a polling model. An earlier study used this approach to obtain the first two moments of the queue content distribution, although the full distribution remained unknown [12]. Because exact analysis of this model proves difficult, we propose an approximation that significantly decreases the complexity of the problem. Besides presenting a performance analysis of the original model with the use of simulations, it will also be shown that the distribution of the queue content of this approximation is very similar to that of the original model. Since the approximation is based on simple arguments, the fact that the behavior of the original model matches the original model so well, is very remarkable. Therefore, the approximation contributes to a better understanding of the model. Title: Queueing on a continuous circle a mathematical analysis of a void-avoiding optical fiber-loop Author: Pim Bongers, [email protected], 10452621 Supervisors: dr. J.L. Dorsman, prof. dr. R. Núñez Queija Second Examiner: dr. A.V. den Boer Examination date: October 06, 2017 Korteweg-de Vries Institute for Mathematics University of Amsterdam Science Park 105-107, 1098 XG Amsterdam http://kdvi.uva.nl