Perimeter and boundary flow control in multi-reservoir heterogeneous networks

Abstract

a b s t r a c tIn this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system's throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a singlereservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.

Multi-gated perimeter flow control of transport networks

“…4(b) and 4(c) depict the control and state trajectories for the perimeter control problem without queue dynamics [12], i.e. for the single-input single output control problem with only (1).…”

“…Capacity (around 30·10 4 veh/h) is observed at n(t) of about 6000 veh. The shape of the NFD was reproduced under different demand scenarios with Dynamic Traffic Assignment activated to capture adaptive drivers in microsimulation via AIMSUN [12]. The shape of O c in Fig.…”

“…E-mail: R.Mat-Jusoh.1@research.gla.ac.uk and Konstantinos.Ampountolas@glasgow.ac.uk improve mobility in single-region homogeneous [4], [9], [10] or multi-region heterogeneous networks [11], [12], [13], [14], [15]. A perimeter flow control policy "meters" the input flow to the system and hold vehicles outside a protected network area if necessary, so as to maximise the throughput.…”

Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing

“…Stability analysis has shown the global convergence of the controllers: "For all choices of parameters, the strategy preserves closed-loop stability and forces the actual control variables to reach the desired one" (Kosmatopoulos and Papageorgiou, 2003). Recently, similar strategies have been introduced for MFD perimeter control for multiple regions (Aboudolas and Geroliminis, 2013 ;Keyvan-Ekbatani et al, 2015;. The purpose of these strategies is to retain accumulation of vehicles at a desired level that maximizes system outflow, without the direct need for demand information or prediction.…”

A Two-Layer Network Dynamic Congestion Pricing Based on Macroscopic Fundamental Diagram

“…Keyvan-Ekbatani et al [22] studied the feedback gate control method using the simulation network with perimeter gate control and obtained satisfying results with lower total travel time. Aboudolas and Geroliminis [23] used multireservoir networks with well-defined MFDs to design the perimeter and boundary flow control schemes that aimed at distributing the accumulation of vehicles in each reservoir as homogeneously as possible. However, deficiencies are also existed in these control schemes: (i) the change of signal at the cordon may have an influence on the shape of MFD, but the influence was largely ignored; (ii) the common perimeter control needs sufficient road space for stopping and queuing [24,25], which may not be always allowed.…”