Large deviations of Jackson networks

Large deviations in queueing networks

In this paper we describe how the joint large deviation properties of traac streams are altered when the traac passes through a shared buuer according to a FCFS service policy with stochastic service capacity. We also consider the stationary case, proving large deviation principles for the state of the system in equilibrium and for departures from an equilibrium system.

Large Deviations and Queueing Networks : Methods for

Sample path large deviations and intree networks

Using the contraction principle, in this paper we derive a set of closure properties for sample path large deviations. These properties include sum, reduction, composition and reeection mapping. Using these properties, we show that the exponential decay rates of the steady state queue length distributions in an intree network with routing can be derived by a set of recursive equations. The solu...

On Large Deviations in Load Sharing Networks

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 o...

Large Deviations of a Modified Jackson Network : Stability and Rough Asymptotics

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion ...