Incorporating Uncertainties into Traffic Simulators
It is possible to incorporate uncertainty in model inputs into analyses of traffic simulators, and incorporating this uncertainty can significantly improve the predictions made with these simulators.
CORSIM is a microsimulator for vehicular traffic, and is being studied with respect to its ability to successfully model and predict the behavior of traffic in a large vehicular network. However, the developments described herein will also be useful in dealing with general discrete network structures, such as traffic in telecommunications networks. In these types of networks, ‘vehicles’ are analogous to packets or ATM cells or messages, ‘streets’ to communications channels or links, ‘highways’ to high capacity trunks, and ‘turning proportions’ to routing and switching decision probabilities made within network elements – routers, switches, etc.
Inputs to the simulator include information about network topology, traffic behavior, turning probabilities at each point of intersection, and distributions of traffic ingress into the system. Data are available concerning the turning proportions in a sub-network, as well as counts of vehicular ingress into the sub-network and internal system counts, during a day in May 2000. Some of the data are based on direct measurements and are quite accurate, while some other data are quite inaccurate. Traffic data from telecommunications networks also varies from accurate (when high-performance line-rate monitors are used) to coarse estimates – e.g., in wireless networks, and in all-optical networks in which monitoring is typically done only at endpoints and in the optoelectronic control plane.
Previous utilization of the full data set was to ‘tune’ the parameters of CORSIM – in an ad hoc fashion – until CORSIM output was reasonably close to the actual data. This common approach, of simply tuning a complex computer model to real data, can result in poor parameter choices and will completely ignore the often considerable uncertainty remaining in the parameters.
To overcome these problems, we adopt a Bayesian approach, together with a measurement error model for the inaccurate data, to derive the posterior distribution of turning probabilities and of the parameters of the CORSIM input distribution. This posterior distribution can then be used to initialize runs of CORSIM, yielding outputs that reflect that actual uncertainty in the analysis. Determining the posterior via Markov Chain Monte Carlo methodology is not directly feasible because of the runningtime of CORSIM. Fortunately, the turning probabilities and parameters of the input distribution enter CORSIM through a probability structure that can almost exactly be described by a stochastic network that does allow an MCMC analysis.
KeywordsPosterior Distribution Telecommunication Network Demand Rate Stochastic Network Measurement Error Model
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