Random Number Generation in the Parallel Environment

By randomly seeding individual processors in a parallel environment with unique random number generators it is possible to take full advantage of the economies of scale present in the parallel environment to achieve more accurate simulations. While a single random number generator is sufficient for a serial computer, the same is not true for a parallel computer. Multiple copies of the same generator do not improve the quality of the simulation as the period may be insufficient to prevent exhaustion or ’banding’ of the variates. Our approach is to provide each processor with its own unique random number generator and use a common seed value. This ensures each simulation is unique as each generator is different due to random assignment by the front-end computer. The linear congruential method was chosen due to widespread familiarity and acceptance of the technique. By using a sequence of random numbers generated on the front-end computer, prime numbers are selected from a predefined array of 2048 primes and assigned to processors. To provide maximum possible period to the generators, all 2048 primes in the array are six digits in size. This gives the researcher the ability to run simulations involving up to a million random numbers with a high degree of certainty that each processor is running a different simulation. By taking advantage of the large periods, the economies of scale available on a parallel machine can then be expolited to run large scale simulations involving millions of numbers which would be prohibitive on a serial machine.