Timestep stochastic simulation (TSS) is a novel method for generating sample paths of computer networks, with low computation cost independent of packet rates. It has accuracy adequate to evaluate general network and flow configurations, including arbitrary flow start times and durations, drop-tail queuing (i.e., does not require RED), and arbitrary state-dependent control mechanisms for congestion control and routing. TSS generates the evolution of the system state S(t) on a sample path in time steps of size \delta. At each step, S(t+\delta) is randomly chosen according to S(t) and the probability distribution Pr[S(t+\delta|S(t)] obtained using the diffusion approximation. Because packet transmission and reception events are replaced by time steps, TSS generates sample paths at a fraction of the cost of packet-level simulation. Because TSS generates sample paths, control feedback can be based on sample path metrics, rather than ensemble metrics, thereby accurately capturing the effects of state-dependent control mechanisms.