Load balancing with migration penalties

Many practical systems perform load balancing. The main aim of load balancing is to utilize the capacity of a system of parallel processors efficiently and to reduce the delay of processing jobs. This paper is concerned with load balancing, or process migration, when there is a penalty associated with migration. We consider the following model: jobs arrive at each of n parallel servers. An arriving job can either be processed in a unit of time, on average, at the server where it arrives, or it can migrate to another server where it creates K ges 1 independent jobs. When K = 1, migrating jobs impose no extra cost and this problem is considered extensively in the literature. We are interested in the situation K > 1. The problem is to decide whether a job should migrate or not. On the one hand migration leads to load balancing and hence reduces backlogs. However, it also leads to the creation of extra work and, hence, to a potential loss of throughput. We ask: do there exist simple migration policies that can reduce backlogs while providing the highest throughput? Somewhat surprisingly, we find that policies like "migrate to the least loaded server" are unstable: they cause a loss of throughput. However, we find that a simple variant of this rule is stable and leads to a reduction of backlogs