Poisson Simulation as an Extension of Continuous System Simulation for the Modeling of Queuing Systems

Poisson simulation is an extension of continuous system simulation whereby randomness is modeled as opposed to just adding noise. This article treats how Poisson simulation can be used for modeling queuing systems. The focus is on the implementation of queues in Poisson simulation and the connections to queuing theory. This approach also has theoretical and practical implications. Dynamic and stochastic systems, especially when queues are involved, are often treated by discrete event simulation using a microscopic view in which individual entities are modeled. Poisson simulation makes it possible to handle many such systems on a macroscopic level using aggregated states. It is therefore interesting to compare these approaches. Parallel approaches can then be sketched with discrete event simulation in one branch and Poisson simulation in the other. A fundamental difference between the approaches is whether one prefers to base a model on individual, distinguishable entities or on lumped entities.