A decomposition scheme for parallelization of system optimal dynamic traffic assignment on urban networks with multiple origins and destinations

Abstract

This paper presents a decomposition scheme to find near‐optimal solutions to a cell transmission model‐based system optimal dynamic traffic assignment problem with multiple origin‐destination pairs. A linear and convex formulation is used to define the problem characteristics. The decomposition is designed based on the Dantzig–Wolfe technique that splits the set of decision variables into subsets through the construction of a master problem and subproblems. Each subproblem includes only a single origin‐destination pair with significantly less computational burden compared to the original problem. The master problem represents the coordination between subproblems through the design of interactive flows between the pairs. The proposed methodology is implemented in two case study networks of 20 and 40 intersections with up to 25 origin‐destination pairs. The numerical results show that the decomposition scheme converges to the optimal solution, within 2.0% gap, in substantially less time compared to a benchmark solution, which confirms the computational efficiency of the proposed algorithm. Various network performance measures have been assessed based on different traffic state scenarios to draw managerial insights.

Cross‐comparison of convergence algorithms to solve trip‐based dynamic traffic assignment problems

“…The analytical approach (e.g., Jiang & Xie, 2014;Mounce & Carey, 2011;Wang, Szeto, Han, & Friesz, 2018) is very accurate but can only be applied in practice to small networks with few ODs. Several studies proposed exact decomposition techniques to reduce the computational complexity of the traffic assignment problems in static (Jafari, Pandey, & Boyles, 2017) and dynamic cases (Mehrabipour, Hajibabai, & Hajbabaie, 2019). However, congestion patterns are almost intractable analytically due to multiple nonlinear interactions inside the network (Taale & Pel, 2015).…”

Evaluation Indexes and Correlation Analysis of Origination–Destination Travel Time of Nanjing Metro Based on Complex Network Method

“…Javani B proposed an OD based on the algorithm for static traffic assignment with fixed OD demand, which is tested in Chicago and Philadelphia [7]. Mehrabipour M proposed a multi OD algorithm based on the cell transmission model, which can optimize the dynamic traffic assignment of the system [8]. Hoang N H proposed a new linear programming framework, which uses the relationship between UE (user equilibrium) and the system optimal solution to solve the dynamic traffic assignment problem [9].…”

“…Direction and stations of Nanjing metro lines 15,14,13,12,11,10,9,8,7,6,5,41,42,43,44,45,46,47,48,49,50,. 51, 52, 53, 54, 55] …”

Multi-Objective Robust Optimization for the Traffic Sensors Location Problem

“…In this game theory approach residual energy of each node plays important role in making game decisions. Mehrabipour et al [44] presented a decomposition scheme to find near-optimal solutions for a cell transmission modelbased system for an optimal dynamic traffic assignment problem with multiple origin-destination pairs. This technique decomposes the original problem into a set of subproblems.…”