Optimality properties of proportional capacity assignment in message and packet-switched networks

The problem of capacity assignment in message and packet-switched networks is addressed from the standpoint of either (1) minimizing the variance of the delay subject to a constraint on the average delay or (2) minimizing the average delay subject to a constraint on the variance. This is of importance in applications involving voice, real-time data, and/or interactive computing where it is essential that fluctuations in the response time be either minimized or limited. It is shown that the corresponding optimal capacity assignments are proportional ones, and a number of properties of these assignments, including performance vs. capacity tradeoffs and average delay vs. coefficient of variation limitations, are developed. The results are also compared with those for the classical minimum average delay-fixed capacity and minimum capacity-fixed average delay formulations in terms of capacity requirements, average delay, and coefficients of variation. Conditions under which the two sets of capacity assignments may approach each other in optimality are presented.