 
Summary: The Annals of Applied Probability
1998, Vol. 8, No. 1, 6797
ON LARGE DEVIATIONS IN LOAD SHARING NETWORKS1
By Murat Alanyali2
and Bruce Hajek
Bell Laboratories and University of Illinois, UrbanaChampaign
Three policies, namely optimal repacking, least load routing, and
Bernoulli splitting, are considered for dynamic resource allocation in load
sharing networks with standard Erlang type statistics. Large deviations
principles are established for the three policies in a simple network of
three consumer types and two resource locations and are used to identify
the network overflow exponents. The overflow exponents for networks with
arbitrary topologies are identified for optimal repacking and Bernoulli
splitting policies and conjectured for the least load routing policy.
1. Introduction. The generic dynamic resource allocation problem in
volves a number of locations containing resources. The dynamic aspect of the
problem is the arrival of consumers, each of which requires a certain amount of
service from the resources, and the control variable of the problem is the allo
cation policy, which specifies at which location each consumer is to be served.
Oftentimes in applications, locations contain finitely many resources, hence
