Massively Time-Parallel, Approximate Simulation of Loss QueueingSystems

A time-parallel simulation obtains parallelism by partitioning the time domain of the simulation. An approximate time-parallel simulation algorithm named GG1K is developed for acyclic networks of loss FCFS G/G/1/K queues. In the first phase, a similar system (i.e., a G/G/1/infinity queue) is simulated using the GLM algorithm. Then the resultant trajectory is transformed into an approximate G/G/1/K trajectory in the second phase. The closeness of the approximation is investigated theoretically and experimentally. Our results show that the approximation is highly accurate except when K is very small (e.g., 5) in certain models. The algorithm exploits unbounded parallelism and can achieve near-linear speedup when the number of arrivals simulated is sufficiently large.