Desynchronization and Speedup in an Asynchronous Conservative Parallel Update Protocol

(Dated: February 1, 2008)ABSTRACTIn a state-update protocol for a system of L asynchronous parallel processes thatcommunicate only with nearest neighbors, global desynchronization in operationtimes can be deduced from kinetic roughening of the corresponding virtual-timehorizon (VTH). The utilization of the parallel processing environment can be de-duced by analyzing the microscopic structure of the VTH. In this chapter we give anoverview of how the methods of non-equilibrium surface growth (physics of complexsystems) can be applied to uncover some properties of state update algorithms usedin distributed parallel discrete-event simulations (PDES). In particular, we focus onthe asynchronous conservative PDES algorithm in a ring communication topology.The time evolution of its VTH is simulated numerically as asynchronous cellularautomaton whose update rule corresponds to the update rule followed by this algo-rithm. There are two cases of a balanced load considered: (1) the case of the minimalload per processor, which is expected to produce the lowest utilization (the so-calledworst-case performance scenario); and, (2) the case of a general finite load per pro-cessor. In both cases, we give theoretical estimates of the performance as a functionof L and the load per processor, i.e., approximate formulas for the utilization (thus,the mean speedup) and for the desynchronization (thus, the mean memory requestper processor). It is established that the memory request per processor, required forstate savings, does not grow without limit for a finite number of processors and afinite load per processor but varies as the conservative PDES evolve. For a givensimulation size, there is a theoretical upper bound for the desynchronization and atheoretical non-zero lower bound for the utilization. We show that the conservativePDES are generally scalable in the ring communication topology. The new approachto performance studies, outlined in this chapter, is particularly useful in the searchfor the design of a new-generation of algorithms that would efficiently carry out anautonomous or tunable synchronization.

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