Theoretical analysis of high-speed multiple TCP connections through multiple routers

We study a system of multiple routers traversed by multiple TCP connections using TCP New Reno, CUBIC and Compound. More than one router may be congested. To analyze this system we will use earlier theoretical models of TCP New Reno and CUBIC but develop a new model of TCP Compound experiencing random packet losses and queuing delays. We model the router queues as M/GI/1 queues with arrival rates controlled by TCP window flow control. We also look at an alternate approach assuming proportional fairness of TCP to find the throughputs of the multiple TCP connections. These approximations are validated through comparison with ns-2 simulations.