Several popular implementations of linear congruential algorithms allow the generation of pseudo-random numbers from separate streams.
Streams are actually different starting points in the total cycle traveled by the generator.
Thus it is possible to generate enough variates from any given stream to overlap the variates generated from other streams. For a simple system where interarrival and service times are uniform, we obtain analytic expressions for the queue delay, and conclude that the presence of overlapping streams violates the assumption of independence between service and interarrival times.