Massively parallel SIMD simulation of markovian DEDS: Event and time synchronous methods

We examine two schemes for parametric parallel simulation on SIMD supercomputers. In SIMD machines, the parallel processors execute a common instruction stream using local data-under the control of a front-end processor. In contrast to most parallel simulation approaches-which simulate a single system using multiple processors-we simulate distinct parametric variants at each processor. We extract some of the common computation embedded in these simulations and perform it on the front-end, leaving the rest to the parallel processors.The first simulation approach, which we call time synchronous, is essentially Vakili's standard clock. This approach generates a uniformized event process on the front-end processor which is thinned at each back-end processor based on local state information. The second scheme, which we call event synchronous, generates a standard Poisson process on the front-end, which is time-scaled and marked on the back-end processors.We develop a framawork for comparing these methods based on their simulated event rate (number of simulated events per real time unit). We show that the time synchronous method can be tuned to optimize the event rate for a given family of systems and we solve this optimal standard clock problem for several test cases. Finally we describe implementation issues peculiar to the SIMD architecture. Our focus is primarily on the M/M/1/K queue, but the methods extend to more general Jackson networks.