How good are deterministic models for analyzing congestion control in delayed stochastic networks?

Abstract

We investigate the regime where instability in deterministic fluid flow models for congestion control analysis in data networks corresponds to a significant increase in the variance of the flow in stochastic networks. This is shown to be the case when there are large number of packets in flight with small queue thresholds. The analysis is carried out by modelling an M/M/1 queue with delayed feedback as a stochastic hybrid system and analyzing the transient probability distribution of the states with partial differential equations. We also introduce a deterministic nonlinear dynamic queue model that captures the dynamics of the stochastic feedback system. Most of the literature on congestion control analysis using deterministic models, is currently based on queueing models that are valid in one of the extreme cases of negligible queueing delays relative to propagation delays (these are modelled with static functions) or never emptying queues (modelled as integrators). The proposed model is shown to be valid both in these extreme conditions, as well as intermediate regimes of large delays, emptying queues and significant queue dynamics.