 
Summary: 1
On Load Balancing in Erlang Networks
Murat Alanyali and Bruce Hajek
University of Illinois at Urbana Champaign1
Abstract
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 online. 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.
1 Introduction
The dynamic resource allocation problem arises in a variety of applications with
loadsharing features (see Ganger et al.(1993), and WillebeckLeMairand Reeves
(1993) for some examples). The generic resource allocation setting involves a
number of locations containing resources. The dynamic aspect of the problem is
the arrivalsof consumers, each of which requires a certain amountof 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
