Congestion Volume Rate Calculation In Packet Switching Network

As bandwidth intensive applications, such as online video andstreaming media, become more and more popular, the requirement ofbandwidth is increasing. Such bandwidth intensive applications will starveother light applications, like web browsing and email, by establishing alarge number of TCP flows. Improving the users' experience of lightapplication without affecting bandwidth intensive applications is a criticalproblem in current packet switching networks. Congestion pricing isconsidered to be a good candidate to solve this problem. The basic idea ofcongestion pricing is that users be charged for their amount of traffic thathas actually caused congestion. But there still remains an open question oncongestion volume rate calculation. The significance of this questionconsists of two parts: for Internet Service Providers (ISP), they need todetermine the price based on an estimate of congestion volume caused byusers in a district or a company; for users, it is better for them to know therelationship between the number of TCP flows they establish andcongestion volume before making decisions.This paper calculates congestion volume rate, which is defined as thenumber of marked TCP packets in a network, in both single bottleneck andmulti-bottleneck networks.First, we develop a model of users' behavior and prove that thenumber of applications on the bottleneck may be described as M/M/1 queuing system. Then, we derive a closed-form formula on the relationshipbetween the number of TCP flows and marking probability. Based on thisformula and users' behavior model, we illustrate the relationship betweenusers' behavior and congestion volume rate in single-bottleneck networks.Second, we build a group of equations to describe TCP behaviors in amulti-bottleneck network and calculate congestion volume rate by solvingthese equations. We also investigate the relationship between networkscales and the computing complexity of these equations.Third, in order to analyze multi-bottleneck network moreconveniently, we classify the effect of number of TCP flows on queuelength as direct effect, secondary effect and high-order effects. We define'equivalent flow','inter-flow' and propose a method named 'equivalent flownumber method'. With this method, the multi-bottleneck problem isconverted to multiple single-bottleneck problems. We prove that when thenumber of a TCP flow changes, the direct effect and secondary effect areboth positively related to original queue length. Moreover, direct effect islinear with the number of TCP flows.At last, we verified our model by ns-2simulation.