On Load Balancing in Erlang Networks

This chapter summarizes our recent work on the dynamic resource al location problem The question of interest is the performance of simple allocation strategies which can be implemented on line The chapter fo cuses on the least load routing policy The analysis is based on uid limit equations and the theory of large deviations for Markov processes with discontinuous statistics Introduction The dynamic resource allocation problem arises in a variety of applications with load sharing features see Ganger et al and Willebeck LeMair and Reeves for some examples The generic resource allocation setting involves a number of locations containing resources The dynamic aspect of the problem is the arrivals of consumers each of which requires a certain amount of service from the resources and the control variable of the problem is the allocation policy which speci es at which location each consumer is to be served Oftentimes in applications locations contain nitely many resources hence the main objective of the allocation policy is to guarantee low blocking probability On the other hand in some applications such as spread spectrum mobile radio networks there are no sharp capacity constraints and the goal becomes to dynamically balance the load In either case one wants the allocation policy to have low complexity require little information about the system state and be robust to changes in the tra c parameters An instance of resource allocation arises in the wireless network pictured in Fig The network consists of a number of base stations and users The users require communication channels that are available at the base stations whereas each station may serve the users within its geographical range The resource allocation problem in this setting concerns the question of station selection Our mathematical abstraction of a load sharing network is a triple U V N where U is a nite set of consumer types V is a nite set of locations and N u V u U is a set of neighborhoods see Fig for examples A The work in this chapter was sponsored in part by the National Science Foundation under Contract NSF NCR and by a TUBITAK NATO Fellowship