Queuing systems of any domain oftentimes exhibit correlated arrivals that considerably influence system behavior. Unfortunately, the vast majority of simulation modeling applications and programming languages do not provide the means to properly model the corresponding input processes. In order to obtain valid models, there is a substantial need for tools capable of modeling autocorrelated input processes. Accordingly, this paper provides a review of available tools to fit and model these processes. In addition to a brief theoretical discussion of the approaches, we provide tool evaluation from a practitioners perspective. The assessment of the tools is based on their ability to model input processes that are either fitted to a trace or defined explicitly by their characteristics, i.e., the marginal distribution and autocorrelation coefficients. In our experiments we found that tools relying on autoregressive models performed the best.
Discrete event simulation (DES) is considered to be an appropriate approach to predict the behavior of queuing systems (Law and Kelton 2000). This is especially true for complex systems characterized by dynamic and stochastic behavior with a high level of interferences. DES is employed in a wide range of domains like manufacturing/intralogistics, telecommunications, and transportation (see references in Section 2.1).
The result quality (in the sense of accurately predicting/capturing the system behavior) strongly depends on the employed model which, of course, should capture the relevant characteristics of the real system. The corresponding model roughly consists of static elements as well as parameters and processes. This paper focuses on modeling stochastic input processes. In the ideal case there is some historical trace data for doing so. In all other cases parameters of the processes have to be estimated. Random number generators (RNG, see Section 2.2) are used to create particular events accordingly.
Usually, RNGs create numbers which are stochastically independent. Indeed, it is regarded as a quality feature if randomly generated numbers show as little correlation as possible (L’Ecuyer 2006). However, consider for example some batch building or priority rules in queueing systems, obviously, these factors will lead to dependencies and we cannot assume an input process based on independent random numbers is still appropriate. There is a considerable amount of literature supporting this hypothesis and the existence of autocorrelation in processes should generally be considered (see Section 2.1). Consequently, appropriate generators for random variates are a necessity to model these systems.
Unfortunately, there is no DES-tool which allows the generation of autocorrelated random variates out of the box albeit some well researched approaches are available (Section 2.2). In order to model autocorrelated input processes, some stand alone tools have to be adopted. This paper discusses the available tools and evaluates their capabilities of creating autocorrelated processes.