A QUEUING SYSTEM SIMULATION
In our previous chapters, we have presented various analytical methods for studying the performance of queues and queueing networks. As would be evident from our discussions in those chapters, analytical models of such systems are tractable only if one makes suitable simplifiting assumptions. For example, in the study of individual queues, we usually have to resort to such assumptions regarding the nature ofthe arrival and service processes in order to provide analytical results on the performance of the system. The situation becomes worse for queueing networks where the simple product form solution holds exactly only under very restrictive assumptions. In some of the methods described for analysing queueing networks, the entire analysis was based on the assumption that even though the product-form expression may not be exactly applicable to the particular network, it still holds as a good approximation. Even with such an assumption (and some even more drastic ones), the analysis of reasonably complicated systems of individual queues or queueing networks becomes rapidly impossible to tackle. In situations where studies of such systems are nevertheless required to be clone, there is usually very little choice other than to use simulations and simulation tools to examine the system.
Simulations provide a convenient tool to study complex systems, which cannot be accurately modelled for exact or approximate mathematical analysis. A simulation scenario for a complex system may be set up with as much detail as required – essentially as much detail as it would feasible to handle within the limits of the simulation time that can be spent and the simulation complexity one is prepared to code for. Since analytical modeling usually requires simplifying assumptions of its own, simulations are also useful to provide crosschecks on the results obtained by analysis.
We introduce some of the basic terminology of simulation techniques and review some of the relevant concepts of simulations. We consider in detail how simulators may be constructed to study queues and queueing networks and discuss how one can generate confidence in the results obtained through simulations.
Given the choice between studying a system through simulations or
through analytical modelling, the best idea usually is to use a combination of both the approaches. A system can be simulated to behave very closely to what would actually happen in a real system whereas exact or approximate analysis of the system may only be feasible under very drastic (and sometimes inappropriate) assumptions. However, simulations would generally take a long time to run if one wants to generate results with a high enough degree of confidence. Sensitivity of the various system performance parameters to variations in the valucs of various input paramcters is also easier to study using analytical methods than with simulations.
