A Continuous Petri Net Approach for Model Predictive Control of Traffic Systems

Júlvez, Jorge; Boel, René

doi:10.1109/tsmca.2010.2041448

Cited by 79 publications

(27 citation statements)

References 19 publications

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“…According to some existing works, the modelling of the systems by using Petri nets formalisms can be considered from either a discrete and/or a continuous point of view. Continuous Petri nets for the macroscopic and microscopic traffic flow control are used in [15]- [34], while hybrid Petri nets are used in [11] to provide a valuable model of urban networks of signalized intersections. Recently, batch Petri nets with controllable batch speed are used [10] to study a portion of the A12 highway in The Netherlands.…”

Section: A Review Of the Literaturementioning

confidence: 99%

“…These are a few works that demonstrate the high potential of Petri nets as a tool for modelling and performance analysis of urban transportation systems, but also on the other hand, it is shown that the application of Petri nets is still in its early stage and particularly limited to intersection traffic control [11]- [14]- [15]- [25]- [35]- [34] and to some studies dealing with the modelling of urban transportation systems for planning purposes [28]- [29]- [33]. In addition, according to our knowledge, unlike traditional urban transportation systems, no work has been undertaken on PBS systems modelling and performances analysis by using Petri net models.…”

Section: A Review Of the Literaturementioning

confidence: 99%

See 1 more Smart Citation

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems

Labadi¹,

Benarbia²,

Hamaci³

et al. 2012

Petri Nets - Manufacturing and Computer Science

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Section: A Review Of the Literaturementioning

confidence: 99%

Section: A Review Of the Literaturementioning

confidence: 99%

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems

Labadi¹,

Benarbia²,

Hamaci³

et al. 2012

Petri Nets - Manufacturing and Computer Science

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“…In this case, it is important to approximate the fundamental diagram expressing the relationship between the density of cars and the flow of cars in a given section of the road. Using some additional places, the flow of a transition can be modeled as a piecewise linear function of the marking of a given place (Júlvez and Boel 2010). For example, a three phases flow can be easily represented: with an ascending phase, a constant phase (using self-loop places around transitions) and a descending phase (using complementary places) (Fig.…”

Section: Figmentioning

confidence: 99%

On fluidization of discrete event models: observation and control of continuous Petri nets

Silva

Júlvez

Mahulea

et al. 2011

Discrete Event Dyn Syst

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As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

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“… (in order to avoid working with large integers we fluidize our traffic variables, approximating integer numbers of vehicles by real number, see [7] …”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

Sutarto

Boel

Joelianto

2015

IET Control Theory & Applications

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This paper proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described in this paper using a mode-dependent first order autoregressive (AR) stochastic process. The parameters of the AR-process take different values depending on the mode of traffic operation -free flowing, congested, or faulty -making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain, and hence we call this hybrid process a jump Markov process. This paper proposes an expectationmaximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied in this paper to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inferences algorithms and an online particle filter (PF). We also develop an EM parameter estimation that, in combination with a time window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator. The proposed parameter estimation technique can thus be used as part of an adaptive model-based filter for feedback control of traffic lights.Keywords: Hybrid system, parameter estimation, particle filter, stochastic system, fault detection, urban traffic networks. 2 IntroductionUrban traffic congestion is a problem that significantly affects many aspects of the quality of life. A more efficient use of the existing road infrastructure, using advanced traffic control strategies, can lead to reduced congestion, reduced emissions, reduced fuel consumption, and improved safety. The model based control strategies that are needed in order to achieve such an improvement depend strongly on the quality and the accuracy of the dynamic model of the system, on the availability of reliable online data and also on the ease of implementation of the control strategy. The model must describe the variability over time of the traffic flow, allowing model based estimation of the current state, fusing noisy traffic data from various traffic sensors. This estimation together with the model in turn allows probabilistic prediction of future traffic flows, so that control actions -selecting switching times of traffic lights in the application we have in mind -can properly anticipate future traffic flow. In this paper we use a stochastic hybrid model to effectively describe the evolution over time of the arrival and flow rates of vehicles in an urban traffic network as stochastic processes. We define the flow rate as the number of vehicles that pass a location per red/green cycle, divided by the length of this cycle (veh./sec). The random value of the continuous v...

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A Continuous Petri Net Approach for Model Predictive Control of Traffic Systems

Cited by 79 publications

References 19 publications

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems

Petri Nets Models for Analysis and Control of Public Bicycle-Sharing Systems

On fluidization of discrete event models: observation and control of continuous Petri nets

Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

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