A multi-class urban traffic model considering heterogeneous vehicle composition: An extension of the S model

Highlights

• The multi-class S model describes the heterogeneous flow of vehicles.

• The performance of multi-class S model is compared with the single-class S model using microsimulation as a reference.

• The computation time of the macroscopic models does not depend on the number of vehicles.

Abstract

In this paper a new multi-class urban traffic model is proposed based on the features of a single-class urban traffic model and the characteristics of a multi-class freeway traffic model. The heterogeneous traffic flow is represented using the concept of Passenger Car Equivalent (PCE) for congestion and free-flow regimes separately. The proposed multi-class urban traffic model is intended for model-based control applications. The single-class model and the proposed multi-class traffic model are compared with microscopic simulation data obtained using the SUMO (Simulation of Urban MObility) open-source simulator. The two models are calibrated through optimal parameter estimation and their performance is evaluated and compared by taking into account the error index between the models and the simulation data. Simulation results show that the multi-class model gives a significantly better fit.

Introduction

Nowadays, modern major cities have problems resulting from their accelerated and often uncontrolled growth. One of these are traffic jams, which affect mobility and have adverse environmental, social, and economic impacts. Efficient management of the traffic network can reduce congestion and its associated consequences such as emission of polluting gases, fuel consumption, noise, accident rates, and waiting times.

In order to solve these mobility problems, it is important to implement efficient and effective online (monitoring and control) and offline (planning of new roads, government policy measures) management strategies for the urban traffic network. Usually, these strategies require an urban traffic representation, i.e., a dynamic mathematical model that describes the evolution of the traffic flows in the system. However, urban traffic is not homogeneous as there are several types of vehicles on the road: cars, sport utility vehicles (SUVs), vans, buses, trucks, and motorcycles, with their own characteristics such as engine power, weight, and size. As a result, the vehicle flow is a composition of different types of vehicles interacting with each other and their characteristics should be represented by the mathematical model. In addition, this model should have a high accuracy and, as it is used for on-line model-based applications, a low computational burden.

In general, the urban traffic models used in model-based controllers (Diakaki et al., 2000, Tettamanti et al., 2008, de Oliveira and Camponogara, 2010, Geroliminis et al., 2013, Tettamanti et al., 2014, Diakaki et al., 2002, Viti and van Zuylen, 2004, Keyvan-Ekbatani et al., 2015, Lu et al., 2017, van den Berg et al., 2003) and monitoring applications (Tiriolo et al., 2014, Adacher and Tiriolo, 2015) describe the vehicles using one generic class (average class) of vehicles, which does not allow to identify the particular dynamics of the different vehicle types. Nevertheless, multiple classes of vehicles have been included in some macroscopic models based on the generalization of the cell transmission model (Tiaprasert et al., 2017, Tuerprasert and Aswakul, 2010), in continuous models based on gas-kinetic and fluid dynamics modelling principles (Hoogendoorn and Bovy, 2000, Gashaw et al., 2018), and in cellular automata models (Meng et al., 2007, Zhao et al., 2008, Chen et al., 2013, Meng and Weng, 2011). However, these models are not adequate for real-time implementation of optimal control strategies due to their high computational burden. On the other hand, most papers about multi-class traffic modelling focus on highways (Pasquale et al., 2017, van Lint et al., 2008, Dhamaniya and Chandra, 2013, Liu et al., 2017, Wong and Wong, 2002, Logghe and Immers, 2008). Particularly, van Lint et al., 2008, Liu et al., 2017 describe the relation between vehicles for different congestion regimes on highways. On the other hand, different vehicle classes have been represented based on the Passenger Car Equivalent/Unit (PCE) concept which relates any vehicle class with a standard vehicle. Since the first definition of PCE given in the Highway Capacity Manual (TRB, 1950) that explains the effect of buses and heavy traffic with respect to other vehicles. Several studies have been carried out on adjusting the values of different classes of vehicles in PCE for different road geometries, congestion levels, and control conditions (traffic signals). The calculation methods for the PCE values mainly depend on the variables that are considered (Giuffrè et al., 2015, Shalini and Kumar, 2014), i.e., the measured or estimated variables such as flow, density, headway, queue discharge flow, speed, delay, capacity ratio, and travel time. However, taking into account that variables such as maximum acceleration, maximum speed, emissions, noise, fuel consumption, vehicle occupancy, etc. are related to the vehicle class, the equivalences given in the PCE values do not always are correct, e.g., $1\text{motorcycle}=0.3\times \text{PCE}$ could be a good approximation for traffic models but not for noise models. Since explicit models of various classes have been developed for highways, our contribution in this paper is the development of a macroscopic urban traffic model that considers different classes of vehicles separately. Based on van Lint et al., 2008, Liu et al., 2017 and on a macroscopic urban traffic model for single-class vehicles (the S model) (Lin et al., 2012), we will propose in this paper a new multi-class urban traffic model that is also suited for model-based optimization-based control applications.

This paper is organized as follows: in Section 2 the single-class S model is presented. Next, in Section 3 the new multi-class S model is proposed. Then, in Section 4 parameter estimation for the single-class and the multi-class S model is discussed. After that, in Section 5 a case study is presented that compares the performance of the multi-class and the single-class S model using a microscopic simulator (SUMO) as reference. Finally, in Section 6 conclusions and future research are presented.