Summary: Convergence Complexity of Optimistic Rate Based
Flow Control Algorithms \Lambda
Yehuda Afek y Yishay Mansour z Zvi Ostfeld x
Computer Science Department,
Tel­Aviv University, Israel 69978.
February 21, 1996
Abstract
This paper studies basic properties of rate based flow­control algorithms and of the max­
min fairness criteria. For the algorithms we suggest a new approach for their modeling
and analysis, which may be considered more ``optimistic'' and realistic than traditional
approaches. Three variations of the approach are presented and their rate of convergence
to an optimal max­min fairness solution is analyzed. In addition, we introduce and analyze
approximate rate based flow control algorithms. We show that under certain conditions
the approximate algorithms may converge faster. However, we show that the resulting
flows may be substantially different than the flows according to the max­min fairness.
We further demonstrate that the max­min fairness solution can be very sensitive to small
changes, i.e., there are configurations in which an addition or deletion of a session with
rate ffi may change the allocation of another session by \Omega\Gamma ffi \Delta 2 n
2 ), but by no more than
O(ffi \Delta 2 n ). This implies that the max­min fairness criteria may provide a bad estimate of

Source: Afek, Yehuda - School of Computer Science, Tel Aviv University
Mansour, Yishay - School of Computer Science, Tel Aviv University

Collections: Computer Technologies and Information Sciences