Congestion control in packet switch networks

[摘要] We consider a congestion control problem in computer networks. The problemis posed as an optimal control problem and reduced to a problem offinding solutions to delay differential equations. Systems involving time delaysin the dynamics are actually very difficult to model and therefore verydifficult to solve. We consider three approaches in our congestion controlproblem: an elastic queue approach leading to an optimal control problemwith a state–dependent delay differential equation; three approaches in flowmodels (also leading to systems containing delay differential equations), preciselythe dual control approach, the primal–dual control approach and thecontrol approach based on queueing delay. The elastic queue approach is notexplored due to the lack of software good enough to solve optimal controlproblems involving delay differential equations.In flow models, we consider the standard case, that is where the feedbackfrom sources to links is exact and the network behaves perfectly well (withoutany unexpected event). We also consider some non–standard cases such asthe case where this feedback contains errors (for example overestimation,underestimation or noise), and the case where one link breaks in the network.We numerically solve the delay differential equations obtained and use theresults we get to determine all the considered dynamics in the network.This is followed by an analysis of the results. We also explore the stabilityof some simple cases in the dual control approach, with weaker conditionson some network parameters, and discuss some fairness conditions in somesimple cases in all the flow model approaches. Non–standard cases are alsosolved numerically and the results can be compared with those obtained inthe standard case.

[发布机构] University of the Witwatersrand