Optimal design of windows for high speed data networks

Abstract

The basic mechanism of sliding windows for the congestion control of virtual circuits is examined. A problem of optimal design of windows is formulated and solved, and formulas are obtained for basic quantities of interest, such as throughput, delay, and moments of packet queues, in the optimal operating regime as well as in other regimes. All results are asymptotic in which the large parameter is lambda , the mean number of packets of the virtual circuit which may be processed and transmitted at a single node in an interval equal to the mean propagation delay. It is shown that K* approximately lambda +O( square root lambda ), where K* is the optimal window size. Also, in the optimal operating condition, the steady-state mean and standard deviation of the queue packets at individual nodes are O( square root K*). The constants associated with these asymptotic solutions are oblivious to the minutiae of the physical model and therefore universal; these constants have been computed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>