Large Deviations for Large Capacity Loss Networks withFixed Routing and Polyhedral Admission Sets

Authors:
Cheng-Shang Chang;Hung-Jen Wang
Affiliations:
Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30043, Taiwan, R.O.C.;Department of Electrical Engineering, National Tsing Hua University, Hsinchu, 30043, Taiwan, R.O.C.
Venue:
Discrete Event Dynamic Systems
Year:
1997

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Abstract

In this paper, we study large deviations of large capacityloss networks with fixed routing. We use two-level modellingfor the loss networks: the call level and the cell level. Atthe call level, a call request is accepted if it succeeds anadmission test. The test is based on a polyhedral set of thenumber of calls in progress when a new call arrives. After beingaccepted, a call then transmits a sequence of cells (random variables)during its holding period. We show that the fluid limits andthe conditional central limit theorems in Kelly (1991) can beextended to the large deviation regime. Moreover, there are correspondingfluid flow explanations for our large deviation results. In particular,we derive the exponential decay rates of the call blocking probabilityand the cell loss probability. These decay rates are obtainedby solving primal and dual convex programming problems.