Analysis of a distributed scheduler for communication networks

Abstract

Let G=(V,E) be a given network, and d a positive integer. A d-scheduling of G is an infinite sequence of rounds [r ₁,r ₂, ...], such that for each i, r _i is a non-empty subset of V, and the distance between any two nodes in r _i is greater than d. A d-scheduler is a protocol that determines a d-scheduling of G. Of special interest is the case d=1, which corresponds to a proper communication schedule of the half-duplex model, where information can move in either direction of a communication line, but not simultaneously. This case corresponds also to a proper scheduling of processes in a resource sharing system, where an edge represents a resource shared by two processes, and every process needs all its resources to operate. Another application of this scheduler is a collision-free protocol for radio-networks (this corresponds to d=2).

In this paper a simple d-scheduler is presented and analyzed. We first show that the resulting scheduling is periodic and fair. Then we give a complete characterization of this scheduling for trees and cycles. We study the period length of that scheduling, and the main result is a worst-case exponential lower bound for this length. We also study other issues concerning these schedulings; optimal rate schedulings are given for some classes of graphs, although the problem of finding optimal schedulings for any d is NP-complete.

The research of this author was supported by the Fund for Research in Electronics, Computers and Communications administered by the Israeli Academy of Sciences and Humanities