A time-varying Poisson arrival process generator

Abstract

Frequently an arrival process is acceptably Poisson, but the ar rival rate varies with time. This note uses inversion to derive a time-varying Poisson generator whose rate function is continuous and piecewise-linear. The piecewise-linear function includes the piecewise constant arrival rate while involving only slightly more computations and represents a reasonable compromise between flexibility and practicality. In this case, inversion is efficient while being highly compatible with correlation induction variance reduction methods. The generator has been implemented for routine use in the INSIGHT simulation language providing a useful new input process while promoting variance reduction through common and antithetic variates.

Keywords

arrival generation discrete simulation industrial engineering nonhomogeneous Poisson process,queuing

Get full access to this article

View all access options for this article.

References

Albin, S.L. "On the Poisson approximations for superposition arrival processes in queues." Management Science 28 (1982), 126-137.

Bratley, P. ; Fox, B.L. ; and Schrage, L.E. A guide to simulation. Springer-Verlag, New York, New York (1983).

Cinlar, E. "Superposition of point processes." In Stochastic point processes. statistical analysis, theory, and applications ( P.A.W. Lewis , ed.). Wiley, New York, New York (1972), 549-606.

Kaminsky, F.L. and Rumpf, D.L. "Simulating nonstationary Poisson processes: a comparison of alternatives including the correct approach." Simulation 29:1 (1977), 17-20.

Lewis, P.A.W. and Shedler, G.S. "Simulation of nonhomogeneous processes by thinning." Naval Research Logistics Quarterly 26 (1979), 403-414.

Marse, K. and Roberts, S.D. "Implementing a portable FORTRAN Uniform (0, 1) generator." Simulation 41:4 (1983), 135-139.

Roberts, S.D. Simulation modeling and analysis with INSIGHT . Regenstrief Institute (1983).

Schmeiser, B.W. "Random variate generation: a survey." In SIMULATION WITH DISCRETE MODELS: A State-of-the-Art View (T. Ören, C. Shub , and P Roth, eds.) From the 1980 Winter Simulation Conference Institute of Electrical and Electronics Engineers, Inc., New York, New York (1980), 79-104.