Semester , 2003 / 4 Lecture 9 : Dynamics in Load Balancing

In this lecture we consider dynamics of a load balancing system. We study the number of steps required to reach pure Nash equilibrium in a system of ”selfish” and greedy players (jobs). We are interested in the convergence time to Nash equilibrium, rather than the quality of the allocation. We consider a variety of load balancing models including identical, restricted, related and unrelated machines. We compare different scheduling strategies such as allowing the largest job to move first (or smallest weight first) and compare their effect on the convergence time. Note that the discussion can be easily extended to the domain of routing problems. The lecture is divided into two major sections. In the first we deal with migration policies that allow a single user to migrate at a time. In the second part we discuss the case where users migrate concurrently. For the former part we consider two settings: