Asymptotic analysis of communication networks

Ozcan Ozturk, Purdue University

Abstract

The performance of networks and their ability to offer Quality of Service (QoS) depend on accurately capturing the parametric dependence of the QoS measures such as the delay or loss distributions. This involves an appropriate model and analyzing it through simulation or analytical methods. Queueing models have been used extensively for this purpose but it has been observed that the traditional models used for telephone networks are generally not applicable in high-speed networks. The bursty nature and also the recently demonstrated self-similar, long range dependence properties of data traffic create complex correlations in the arrival process and thus invalidate the Markovian assumptions. The analysis of non-Markovian queueing systems is not easy and exact solutions can not be generally obtained. But the stringent QoS requirements imply that the estimations are associated with the tails of the buffer occupancy distribution which naturally leads to a study of the asymptotics. There are basically two approaches (1) The large buffer asymptotics, and (2) The many sources asymptotics. Both cases for a single node have been investigated quite thoroughly. However, there has been limited success at identifying the asymptotics for network models. In this thesis, we obtain asymptotic packet loss and delay approximations for a general network and discuss the implications of the results on performance and control of networks. We first present results on the large buffer asymptotics of a multiplexer accessed by heterogeneous traffic modeled as an M/G/∞ process with Weibullian session lengths. These results extend and improve the results reported in the literature. Then we investigate a network accessed by mutually independent classes of traffic. The network considered is assumed to be loop-free with respect to source-destination pairs. For M/G/∞ type inputs with Pareto session lengths O-asymptotics for the tail of queue lengths are derived. This extends the similar results obtained for a single node. We introduce a new network model with many sources and small buffers. We obtain the buffer overflow and packet loss asymptotics and analyze the implications of these results for admission control. The derivation is carried out for both First-In First-Out (FIFO) and Generalized Processor Sharing (GPS) scheduling disciplines. GPS is used extensively in current networks for QoS purposes.

Degree

Ph.D.

Advisors

Mazumdar, Purdue University.

Subject Area

Electrical engineering

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