Queueing Models Analytical Solutions and Solutions by Simulation

Simple queueing systems are presented as candidates for solution by both analytical and simulation methods. The limitations of the analytical approach are contrasted with the stochastic nature of a simulation solution. A sequence of problems leads from a model which is easily solved analytically to a model which is not amenable to an analytical solution. Simulation output for each problem is compared with known analytical results to disclose some of the pitfalls associated with solutions by simulation. 1. QUEUEING SYSTEMS. A queueing system is a system where entities arrive according to some arrival pattern, stay in the system until a certain set of services have been provided, and then depart. In an open system, entities come from an external calling population and return to that calling population on departure. In a closed system, entities always remain in the system and return periodically for services. We will restrict our attention to open systems in this discussion. Figure 1 below illustrates such a system.