Lower Bounds on Average Time for Random Destination Mesh Routing and Their Utility as Performance Predictors for PRAM Simulation
نویسندگان
چکیده
This paper presents lower bounds on the expected time for random destination routing on a mesh, valid for any routing scheme, queueing discipline and queue size. We show that the lower bounds are applicable to probabil-istic simulation of the P processor EREW PRAM with shared memory M on a P processor mesh with distributed memory M = M, M = P ; > 1, and consider two cases: where the number of packets q per processor is one, which corresponds to PRAM simulation with P = P, and where q 1, which corresponds to PRAM simulation with parallel slackness. Experimental results are given showing that the bounds give good analytical predictions of the actual performance of both random destination routing and practical probabilistic PRAM simulation on meshes. The experiments are carried out on a mesh with small xed queues and memory randomized by pseudo-random hash functions. Simulating PRAM memory accesses with random strides show that (ln P=lnlnP)-universal hash functions perform better than linear, 2-universal hash functions.
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