Unboundedly parallel simulations via recurrence relations for network and reliability problems

Novel methods are presented for parallel simulation of discrete event systems that, when applicable, can use a number of processors much larger than the number of objects in the system being simulated. The simulation problem is posed using recurrence relations, and three algorithmic ideas are brought to bear on its solution: parallel prefix computation, parallel merging, and iterative folding. Efficient parallel simulations are given for the G/G/1 queue, a variety of queuing networks having a global first come first served structure (e.g., a series of queues with finite buffers), acyclic networks of queues, and networks of queues with feedbacks and cycles. In particular, the problem of simulating the arrival and departure times for the first N jobs to a single G/G/1 queue is solved in time proportional to N/P+log P using P processors