Raw measurement data are too noisy to directly obtain queue and traffic flow estimates usable for feedback control of urban traffic. In this paper, we propose a recursive filter to estimate traffic state by combining the real-time measurements with a reduced model of expected traffic behavior. The latter is based on platoons rather than individual vehicles in order to achieve faster implementations. This new model is used as a predictor for real-time traffic estimation using the particle filtering framework. As it becomes infeasible to let a truly large traffic network be managed by one central computer, with which all the local units would have to communicate, we also propose a distributed version of the particle filter (PF) where the local estimators exchange information on flows at their common boundaries. We assess the quality of our platoon-based PFs, both centralized and distributed, by comparing their queue-size estimates with the true queue sizes in simulated data.

Large-scale traffic systems require techniques that are able to 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, and 4) cope with multimodal conditional probability density functions (pdfs) for the states. Often, centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques that are able to cope with these problems of large traffic network systems. These are parallelized particle filters (PPFs) and a parallelized Gaussian sum particle filter (PGSPF) that are suitable for online traffic management. We show how complex pdfs of the high-dimensional traffic state can be decomposed into functions with simpler forms and how the whole estimation problem solved in an efficient way. The proposed approach is general, with limited interactions, which reduce the computational time and provide high estimation accuracy. The efficiency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity, and communication demands and compared with the case where all processing is centralized.

The development of real-time traffic models is of paramount importance for the purposes of optimizing traffic flow. Inspired by the compositional model (CM) and the METANET model, this paper proposes an interval approach for macroscopic traffic modeling. We develop an interval CM (ICM) and an interval implementation of the METANET model (IMETANET) that provide a natural way of predicting traffic flows without the assumption of uniform distribution of vehicles in a cell. The interval macroscopic models are suitable for real-time applications in road networks and can be part of road traffic surveillance and control systems. The performances of the interval approaches are investigated for both the ICM and the IMETANET models. The efficiency of the interval models is demonstrated over simulated data, and as well as over real traffic data from Motorway Incident Detection and Automatic Signalling (MIDAS) data sets from the United Kingdom.

Traffic systems are often highly populated discrete event systems that exhibit several modes of behavior such as free flow traffic, traffic jams, stop-and-go waves, etc. An appropriate closed loop control of the congested system is crucial in order to avoid undesirable behavior. This paper proposes a macroscopic model based on continuous Petri nets as a tool for designing control laws that improve the behavior of traffic systems. The main reason to use a continuous model is to avoid the state explosion problem inherent to large discrete event systems. The obtained model captures the different operation modes of a traffic system and is highly compositional. In order to handle the variability of the traffic conditions, a model predictive control strategy is proposed and validated.

Discusses controlled timed Petri net models for the formal synthesis of supervisory controllers for real time discrete event systems (e.g. communication protocols, supervisors for FMSs, control of batch processes). We extend the standard Petri net formalism with firing delays between the time a transition becomes state enabled, and the time it is executed. These firing delays are partly controllable between lower and upper bounds. The goal is to guarantee that certain forbidden distributions of tokens will never occur. For this purpose we define the influencing net corresponding to forbidden sets. Deciding whether a maximally permissive controller exists, and if yes, constructing such a controller, requires solving large sets of linear inequalities over firing times in this influencing net. This is generally a very large set. Hence we study some equivalence relations between different subnets of a timed Petri net. An example shows that replacing a subnet by a simpler equivalent subnet can significantly reduce the size of the sets of inequalities to be solved.

Some open-loop and closed-loop control algorithms are discussed for an example of a discrete-event system, namely, the routing of arriving tasks from different arrival streams among several possible service stations. It is shown that it is possible to design open-loop policies that give good performance in a way which is very robust with respect to large changes in the arrival rates. This is possible even though it is assumed that there is no online coordination between the routing algorithms for the different arrival streams. Some further improvements of the performance are possible when a simple feedback policy, namely, overflow routing, is implemented. This also gives reasonable robustness of performance with respect to changes in the service rates.>

A conditional Poisson process is observed, whose rate is a diffusion process of known structure. The problem is to estimate the rate from the observed point process. Recursive equations are given for the conditional moment generating function and for an unnormalized conditional probability density of the rate. By studying these equations separately in between jumps and at the jumps, series expansions are obtained for these generating functions and densities in a number of examples that arise in applications to optical modulation and communications networks.