ICS Theory Group

ICS 269, Winter 1997: Theory Seminar

31 Jan 1997:
Scheduling with Conflicts and Applications to Traffic Signal Control
Vitus J. Leung, ICS, UC Irvine

We consider the scheduling of jobs that may be competing for mutually exclusive resources. We model the conflicts between jobs with a conflict graph, so that the set of all concurrently running jobs must form an independent set in the graph. This model is natural and general enough to have applications in a variety of settings; however, we are motivated by the following two specific applications: traffic intersection control and session scheduling in high speed local area networks with spatial reuse. Our results focus on two special classes of graphs motivated by our applications: bipartite graphs and interval graphs. In all of the upper bounds, we devise algorithms which maintain a set of invariants which bound the accumulation of jobs on cliques (in the case of bipartite graphs, edges) in the graph. The lower bounds show that the invariants maintained by the algorithms are tight to within a constant factor.

The best competitive ratio achievable by any online algorithm for the maximum completion time on interval or bipartite graphs is Omega(n), where n is the number of nodes in the conflict graph. As a result, we study scheduling with conflicts under probabilistic assumptions about the input. Each node i has a value pi such that a job arrives at node i in any given time unit with probability pi. Arrivals at different nodes and during different time periods are independent. We focus on distributions where the expected time to complete the jobs that arrive in a single time unit is less than 1. Under these assumptions, we are able to obtain a bounded competitive ratio for an arbitrary conflict graph. In addition, if the conflict graph is a perfect graph, we give an algorithm whose competitive ratio converges to 1.

For the specific application of traffic signal control, we simulate our simple K2,2 algorithm on a traffic network with Poisson arrivals at the edges of the network and Robertson's platoon dispersion model within the network. In some cases, our simple algorithm achieves significant improvements over actuated control.

(Practice job interview talk.)