Performance Scalability in Communication Networks.

Abstract

Performance scalability is an essential problem in modern communication networks that expand rapidly. In this dissertation, we consider three models of large-scale communication networks with limited local resources and investigate their asymptotic characteristics as the number of users or the size of the network increases. First, the effectiveness of application-layer coding in a network with a large number of users is considered. The end users encode data packets before transmitting them. The effect of additional packets on the network performance is twofold: (i) additional packets increase offered load, which results in higher drop probability, and (ii) some of dropped packets can be recovered at the receivers after decoding. It is argued that the space of all networks can be partitioned into two regions where coding is beneficial and detrimental, respectively. In particular, we establish an asymptotic regime that contains the boundary between these two regions. On the boundary, networks with and without coding have the same performance. Informally, application-layer coding improves the performance only in networks with low loss probabilities (without coding), and employing such coding in networks with high loss probabilities only degrades the performance. Next, we consider a k-node linear network consisting of bufferless nodes. The asymptotic behavior of the departure process is investigated, as the size of the network increases. Our result provides a complete characterization of a properly scaled limiting departure process, i.e., the joint probability density function of any finite number of consecutive inter-departure times, as the size of the network increases. Finally, linear networks consisting of finite-buffer nodes are considered, and properties of the throughput are investigated, as the size of the network increases. Using an approximation, we establish an asymptotic critical loading regime in which the ratio of the throughput to the input arrival rate is strictly within (0, 1). Such a regime is desirable from the point of view of both the throughput and network cost. Our results indicate that the qualitative behavior of the achievable throughput under the critical regime depends on whether the buffer size is greater than 1.