,Abstrmt-We analjxe the effects of price estimatinn ermr in n dual-E:rddient optimization flou contml scheme, and Characterize the perhrmance of the algorithm in this case. By treating estimation error as inexactness of the gradient, we utilize sufficient conditions for cnnvergence subject to hounded error to characterize the Inng-term dynamics of the link utilization in ternis of a region which the trajectory enters in finite time. a congestion-based queue-management protocol which. in the above context. amounts to an implicit price-notification scheme. Although this mechanism is more practical than the explicit uansmission of price information. it suffers from various errors inherent in the implicit price-notification. Our aim in this paper is to examine the effects of such errors on the performance of the algorithm presented in P I . One particular source of error inherent to any physical implementation is the limited information available to individual sources. i.e.. the receipt of acknowledgments and the round-trip-time (RTT) for each packet transmitted. The prices (congestion measures) in these two cases are. respectively. loss probability and queueing delay. The exact price is either very hard to estimate (loss probability) or very noisy (queueing delay). (zS). We also will make use of the smallest minimum rate. and largest maximum rate. which we denote by m = min, i n s and A i = mas, A&. Our nbjective is to chbose source rates z. to solve the following optimization problem: C1: --subject to  A unique maximizer. called the primal optimal solution. exists since the objective function is scrictly concave. and hence continuous. and the feasible solution set is compact. The dual function can he calculated to be (see PI): 0-7803-8355-9M20.00 02004 BEE. 984
In REF , the authors added an estimation error into the link price and then treated the estimation error as inaccuracy of the gradient in the distributed NUM algorithm.
Optimization flow control with estimation error
IEEE INFOCOM 2004
IEEE INFOCOM 2004
Computer Science