Polling and greedy servers on a line
type: Item
instance of: scholarly article
title: Polling and greedy servers on a line
zbMATH Open document ID: 0653.90021
DOI: 10.1007/BF01158396
author: E. N. Gilbert
author: E. G. jun. Coffman
published in: Queueing Systems
publication date: 1987-01-01T00:00:00Z
review text: A single server moves with speed \(\nu\) on a line interval (or a circle) of length (circumference) L. Customers, requiring service of constant duration b, arrive on the interval (or circle) at random at mean rate \(\lambda\) customers per unit length per unit time. A customer's mean wait for service depends partly on the rules governing the server's motion. We compare two different servers; the polling server and the greedy server. Without knowing the locations of waiting customers, a polling server scans endlessly back and forth across the interval (or clockwise around the circle), stopping only where it encounters a waiting customer. Knowing where customers are waiting, a greedy server always travels toward the current nearest one. Except for certain extreme values of \(\nu\), L, b, and \(\lambda\), the polling and greedy servers are roughly equally effective. Indeed, the simpler polling server is often the better. Theoretical results show, in most cases, that the polling server has a high probability of moving toward the nearest customer, i.e. moving as a greedy server would. The greedy server is difficult to analyze, but was simulated on a computer.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4066593
zbMATH Keywords: disk systems
zbMATH Keywords: disk SCAN policy
zbMATH Keywords: shortest-seek-time-first disk scheduling
zbMATH Keywords: moving-server systems
zbMATH Keywords: polling server
zbMATH Keywords: greedy server
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01158396
OpenAlex ID: W2078906366
description: scientific article; zbMATH DE number 4066593