Analysis and optimum performance of two message-passing parallel processors synchronized by rollback

Abstract

We analyze a probabilistic model of two processors sharing a common task, such as distributed simulation, proceeding at possibly different rates and with each allowed its own clock and ‘virtual time’. When the task requires it, the processors communicate by messages which are stamped with the local time at the point of origination. This feature is also used to synchronize the processors by ‘rollback’, in which technique a processor receiving a message in its past is required to set its clock and state back as necessary to guarantee correctness. The probabilistic model incorporates for each processor: (i) a distribution for the amount by which the local clock is incremented at each state transition, and (ii) a probability indicating the likelihood of generating a message at each state transition.

For the case of exponential distributions we obtain by the method of Wiener-Hopf factorization explicit formulas for the steady-state distribution of the difference in virtual times, the average rate of progress and the average amount of rollback per state transition. We introduce a performance measure which reflects both the average rate of progress and the cost of implementing rollback. This performance measure is optimized with respect to the system parameters and an explicit solution is obtained. This result provides remarkably explicit insights into optimal operations.