On the minimization of traffic congestion in road networks with tolls

Abstract

Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise- 123Ann Oper Res linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.

Model and methods to address urban road network problems with disruptions

“…These methods were chosen based on their successful results for a significant number of applications, such as Resende (), Stefanello et al. (), Reis et al. (), and Morán‐Mirabal et al.…”

A Method for Traffic Congestion Clustering Judgment Based on Grey Relational Analysis

“…Traffic flows are characterized by three properties [11]: traffic flow velocity, traffic flow density and traffic volume. Traffic flow velocity indicates the average speed of vehicles on the road, in units of km/h.…”

New Complexity Results and Algorithms for the Minimum Tollbooth Problem

“…We verify that it is indeed an optimal flow using technique similar to the one used in Theorem 1. Specifically, under the optimal flow and with respect to the new cost functions, e (x) + x e (x): (i) h will cost 11B, (ii) for each i, a i and b i will cost 3 2 α i , c 1,i and c 2,i will cost 5 2 α i , and q i and g i will cost 4α i , which makes each path in G i costing 11 2 α i , and (iii) the cost of any path through the G i 's has cost n i=1 11 2 α i = 11B.…”

“…A comprehensive explanation is presented under Lemma 5. Fix cost on the right sub-tree, 2 ← lst (r,opt) ·p2· ; 8 Fix cost on the left sub-tree, 1 ← in − 2 ; 9 else 10 Fix cost on the sub-trees, 1 ← in , 2 ← in ; 11 Recur on root r 1 of first children T ·1, PLACETOLL (T ·1, 1 ) ; 12 Recur on root r 2 of second children T ·2, PLACETOLL (T ·2, 2 ) ; Algorithm 5: COMBINESERIES Input: Lists: lst 1 , lst 2 , lst. Output: Processed List: lst.…”

“…Output: Processed List: lst. 1 Let l and r be the size of lst 1 and lst 2 respectively; 2 Length of maximum used path in the combined graph 3 max ← max{lst (1,0) · , lst (2,0) · }; 4 Min number of edges to induce max in G p for p ∈ {1, 2}, 5 s p ← min{lst (p,j) ·η : lst (p,j) · ≥ max } ; 6 Min number of edges in lst, s ← s 1 + s 2 ; 7 Max number of edges in lst, f ← lst (1,l) ·η + lst (2,r) ·η; 8 for i ← s to f do 9 Find the possible edge divisions for i, I = (j 1 , j 2 ) : lst (1,j1) ·η + lst (2,j2) ·η = i ; 10 Find the cost maximizing division; 11 (opt 1 , opt 2 ) = arg max (j1,j2)∈I min lst (1,j1) · , lst (2,j2) · ; 12 i ← min{lst (1,opt1) · , lst (2,opt2) · } ; 13 Create the new element α, (α·η, α· , α·p1, α·p2) ← i, i , lst (1,opt1) , lst (2,opt2) ; 14 Insert α in list lst;…”