Groupe d’études et de recherche en analyse des décisions

Continuous Flow Models: Modeling, Simulation, IPA and Telecommunications Applications

Benjamin Melamed

Fluid-flow systems are being considered as alternative queueing models in manufacturing systems bulk material transport and handling, and telecommunications networks with packet traffic. Such systems often lead to infeasible simulation models for traditional discrete queueing systems due to the excessive number of events that need to be processed. In this talk, we introduce a simple class of fluid-flow models, called Continuous Flow Models (CFMs), which have several important advantages over discrete queueing models. First, CMFs often have simpler dynamics leading to simpler sample path representation. Second, CFMs can often be simulated at a fraction of the computational effort and memory called for by their discrete queueing counterparts (e.g., high-speed telecommunications networks). And third, unlike traditional queueing systems, CFMs admit unbiased and nonparametric IPA (Infinitesimal Perturbation Analysis) gradient estimators of low computational complexity, so that IPA gradients can be computed either from a simulation run or from observations of a real-life system. Consequently, CFMs can be used in performance evaluation and prediction via discrete-event simulation and real-life networks, and their nonparametric nature holds out the promise of applications to network design, provisioning and control of networks that model workload flow. The talk will show how to combine basic CMFs into CFM networks, and will highlight a peculiar problem with modeling propagation delay, resulting in event storms that can bog down simulation runs to a crawl. It will then describe workload-related performance measures, such as loss and buffer contents, and will exhibit their IPA derivative estimates with respect to various design parameters, such as buffer size, arrival rate and service rate. The talk will conclude with remarks on the potential application of CFM IPA derivatives as a design and analysis tool for CFM networks, and their possible use in real-time control of systems that can be modeled as CFM networks.