Route Guidance and Signal Control Based on the Back-Pressure Algorithm

Abstract

Bad traffic conditions can be improved by regulating traffic demand and network capacity. Dynamic Traffic Management (DTM) systems allocate temporal and spatial utilization of infrastructures and vehicle fleets by means of dynamic signals. By timely response to changing traffic conditions DTM goals, in terms of effective, safe and reliable use of the infrastructure, can be met. Two important trends in the field of DTM are: a shift from local control measures towards network-wide control; a shift from collective traffic information towards individual advice. Individual advice can be transmitted via in-car technology, however, up until now in-car systems are typically used to improve the (route) choice of the individual road user, whereas DTM aims at improving the network performance as a whole. Network-wide traffic control is complicated by the dynamic nature of traffic itself and the dynamic effects of control measures, especially if the network and DTM structure is complex. Route guidance can make a significant contribution to network-wide DTM. Using in-car navigation to transmit individual directions, it is expected to improve the network performance (better use of the available capacity, higher throughput and stability, and less spill-back), and reduce the travel time for the individual road user as well. Finding the right route guidance configuration is a complex task, that should take potential unfavourable effects and coordination into account. Moreover, integrating traffic signal control at intersections with route guidance is a logical step. Considering the complex nature of the problem and the need for (real-time) responsive control actions, a simplified traffic control model is suggested. The concept of back-pressure control has recently been applied to the problem of controlling a network of signalized intersections. The development of a route guidance algorithm based on back-pressure control, integrated with a back-pressure model for signalized intersections, is to be considered. The main research problem in this thesis is to determine the feasibility and potential benefits of such a system. The main objective of this thesis is to develop a framework that integrates route guidance and signal control based on the back-pressure principle, and determine its feasibility and potential benefit. Conditions that further specify the objective include a focus on network-wide control, on optimizing network conditions (and secondarily find a trade-off with road user benefits), on real-time control, and on a generic approach. The literature review starts with a brief overview route guidance. Applying route guidance has advantages and pitfalls. Route guidance can be modelled as a way to manipulate route choice. Often route guidance is used to minimize the travel time of the individual road user, using route guidance to improve the conditions for the network and road users as a whole isn't often done in operational route guidance. The back-pressure control methodology originated from communication networks, where it is applied to the problem of delivering data packets via a network of nodes and servers. The back-pressure algorithm assigns the servers to be activated and the data they should transfer, based on server capacity and queue differences (queues for specific data groups). The main strengths of back-pressure control are maximization of throughput and network stability. The basic back-pressure algorithm can been extended to cope with finite queues and delay. On the application of traffic signal control back-pressure control has been used in literature. The concept aims to activate the signalling phase that has the highest total weight, a summation of the weights of the allowed traffic streams. The weight is the product of pressure and service rate (saturation flow). The pressure of a traffic stream is the difference between the queues at the incoming link and outgoing links (weighted by proportion). There are several variants to this basic model. In communication networks the use of routes is a result of the algorithm, whereas for traffic signal control the route choice is used as an input from a separate process. The back-pressure concept can however also be used as a method for route guidance. Instead of determining the right phase to be activated, the task is to determine the ratio to direct traffic to following links. Route pressure values can be formulated to expresses how filled up the route is. Route pressure and service rate are less straightforward to define than for the intersection control. A choice model is to be used to determine the ratio of routes, based on the product of route pressure and service rate. The chosen control approach is a traffic control loop in which the traffic process is monitored, controllers for traffic signal control and route guidance calculate new settings which are implemented to the traffic process by means of the traffic signalling system and in-car navigation system. The traffic signal controller can be fed by route guidance information to improve the estimate turn probabilities. The model is a reactive feedback control type. The research approach includes a list of design choices and limitations for traffic signal control and route guidance, as well as requirements related to the experiment to be conducted and the simulation tools. A general back-pressure algorithm for traffic signal control has been designed, with two main variants: one with a fixed cycle time that assigns phase durations for one or more cycles, and one with short time slots that repeatedly activates the dominant phase. Pressure values are based on representative link densities, are normalized to the jam density and can be extended by a power function that increases the relative weight of higher pressures. The necessary turning probabilities are based on measurements or on route guidance settings, which integrates traffic signal control and route guidance. For route guidance a general algorithm has been proposed as well. As a first attempt of service rate, the link capacity of the first outgoing link of the route is used. Furthermore a number of variants for the algorithm have been considered. The first variant is simple but myopic and observes only the first link of each route, which also limits the number of routes that need to be considered. An important limitation of this variant is that congestion on links further downstream is not taken into account. Other variants observe complete routes (from the en-route position). A path size logit choice model is used to determine the proportions for each route. A pressure value that represents the whole route needs to be determined. This can be done by taking the (weighted) average of the link pressures, or by a method that takes outliers specifically into account. Travel time as a measure of user satisfaction, allowing road users to use the shortest routes, can be incorporated into the method. The overall utility function of a route can be written as: $ \text{BP}_r = \alpha_1 P_{\text{route},r} + \alpha_2 P_{\text{firstlink},r} + \alpha_3 P_{\text{user},r}$. The three terms represent the (total) route pressure, the pressure of the first link, and the travel time value. The simulation environment is based on the macroscopic simulation model DSMART. It uses a kinematic wave model, based on the fundamental diagram, space and time discretization. Aggregated flows carry traffic along the links and System Class Dynamics (SCD) ensure the separation of changes in traffic composition and correct handling of traffic dynamics at the nodes. Periodically, traffic controllers are called to update the activated control strategies, based on the proposed traffic control and route guidance algorithms. Traffic signal control objects directly influence the traffic flow and route guidance is enforced by manipulating turn ratios at intersections and diverges. The simulation experiments are divided into three parts: case 1 examines traffic signal control, case 2 focuses on route guidance, and case 3 combines traffic signal control and route guidance. For traffic signal control, back-pressure control is a good way to generate high throughput at the intersections, while keeping the queues evenly distributed and within boundaries. Back-pressure signal control based on time slots is more effective than the cycle time based version. Some aspects of the algorithm and its practical use require special attention. For route guidance an optimal use of back-pressure has not yet been found, as the results are on a most part lacking compared to the standard route choice model. Two main aspects are the definition of a representative route pressure, and the capacity of routes related to the assignment of (destination specific) traffic to each route. The performance is expected to be better if the pressure were (partly) based on the critical links, instead of on average density. Yet the basic algorithm that was formulated works to some extent, and so far the simulated effects can be understood and are up for improvement. It was also found that a `pressure' function that includes not only route densities, but also travel time can give good results. In conclusion, this thesis demonstrates the possibility to create a methodology, based on back-pressure control, that integrates traffic signal control and route guidance. Traffic signal control based on back-pressure control performs well in the simulations, especially the variant with time slots. Throughput is high and queues remain within reasonable boundaries. It is difficult to fully integrate traffic signal control and route guidance, contrary to the straightforward algorithm in the field of wireless communication networks. A modest step of integration is to use route guidance settings to determine the necessary turning probabilities at the intersection. Using back-pressure for route guidance requires (artificial) design choices. The challenge is to define a representative function of route pressure or utility, and to combine this with a service rate value, in order to obtain a high throughput and stability with minimum delays. Several ideas have been presented. The average density has turned out not a good measure for route pressure. It is possible to combine factors of pressure based on density and travel time, in order to use the shortest routes in case of low traffic, and shift to the routes with open capacity if needed.