Analysis of Error Control and Congestion Control Protocols

This thesis presents an analysis of a class of error control and congestion control protocols used in computer networks. We address two kinds of packet errors: (a) independent errors and (b) congestion-dependent errors. Our performance measure is the expected time and the standard deviation of the time to transmit a large message, consisting of N packets. The analysis of error control protocols. Assuming independent packet errors gives an insight on how the error control protocols should really work if buffer overflows are minimal. Some pertinent results on the performance of go-back-n, selective repeat, blast with full retransmission on error (BFRE) and a variant of BFRE, the Optimal BFRE that we propose, are obtained. We then analyze error control protocols in the presence of congestion-dependent errors. We study the selective repeat and go-back-n protocols and find that irrespective of retransmission strategy, the expected time as well as the standard deviation of the time to transmit N packets increases sharply the face of heavy congestion. However, if the congestion level is low, the two retransmission strategies perform similarly. We conclude that congestion control is a far more important issue when errors are caused by congestion. We next study the performance of a queue with dynamically changing input rates that are based on implicit or explicit feedback. This is motivated by recent proposals for adaptive congestion control algorithms where the sender\u27s window size is adjusted based on perceived congestion level of a bottleneck node. We develop a Fokker-Planck approximation for a simplified system; yet it is powerful enough to answer the important questions regarding stability, convergence (or oscillations), fairness and the significant effect that delayed feedback plays on performance. Specifically, we find that, in the absence of feedback delay, a linear increase/exponential decrease rate control algorithm is provably stable and fair. Delayed feedback, however, introduces cyclic behavior. This last result not only concurs with some recent simulation studies, it also expounds quantitatively on the real causes behind them