Revenue Management in the Presence of Self-Similar Alpha-Stable Distributions

Abstract

We consider the problem of maximizing network revenue from the perspective of bandwidth allocation and route selection. The objective is to perform offline maximization of revenue from served demands in the context of self-similar (long range dependent) traffic. We use an alpha-stable distribution for the aggregate demand volume to capture the appropriate level of traffic burstiness. We take a centralized view of the network topology, link capacity and demand. We use a new mean-risk modeling approach to that considers both the mean and the risk of bandwidth allocation. We also propose a risk measure appropriate for infinite variance alpha-stable distribution. IndexTerms: Network Revenue, Mean-Risk Model, Stochastic Dominance, Risk Measure, Traffic engineering I. INTRODUCTION Revenue management is one of the most important issues in traffic engineering [1,2]. There are two main approaches in network revenue management: online and offline processing [2]. Offline optimizers are capable of globally optimizing the network for different traffic and services. The performance of the offline optimization is always used as a reference level for performance evaluation of online optimization [3].This paper concentrates on offline network optimization in terms of the amount of allocated bandwidth and the route selection. We develop a new approach in traffic engineering utilizing decision theory. The approach considers decisions with real-valued outcomes, such as return, net profit, etc. In particular, we investigate the consequences of applying meanrisk analysis to infinite variance traffic. Although our main consideration is revenue management in data networks, the method has broader applicability. We consider the general problem of comparing real valued random variables, assuming that larger outcomes are preferred.With natural extension, the framework of this paper has the potential of contributing to the study of traffic engineering where traffic has burstiness and fractal-like properties.This paper is organized as follows. A brief overview of alpha-stable and LFSN process properties are presented in section II. In section III we discuss modeling of the risk term in the presence of alpha stable distributions. In section IV, we formulate the objective function of the revenue optimization problem and take the network constraints into consideration.