Queuing systems in a feedback environment: Continuous versus discrete-event simulation

The discrete stochastic nature of typical queuing problems calls for discrete-event simulation, rather than continuous simulation that would ignore the discrete details that may be important in queuing dynamics. However, continuous simulation can perhaps be suitable for certain large queuing systems that involve feedback interactions and time delays. This study examines this question by a series of simulation experiments with queuing systems. We start with an M/M/2 system with state-dependent arrivals. Since continuous simulation represents the system states by continuous variables, when these variables (number of entities) revolve around small integer values, discrete and continuous simulation approaches exhibit significant differences in their output dynamics. However, when the system scale is increased (many servers, many entities), errors caused by continuity assumption drop significantly and the two simulation approaches yield much closer outputs. Finally, when a delay is introduced before the state of the system influences the arrival rates, the system behaviour becomes oscillatory, involving even sustained oscillations when the delay is discrete. We show that in such settings, continuous simulation can be superior to discrete simulation, since the system exhibits far-from-equilibrium dynamics driven by the endogenous system structure, rather than by discrete stochastic events. Our results have various real-life modelling implications.