Related papers: A combinatorial model for lane merging
We study effects of lane changing rules on multilane highway traffic using the Nagel-Schreckenberg cellular automaton model with different schemes for combining driving lanes (lanes used by default) and overtaking lanes. Three schemes are…
Motion prediction for intelligent vehicles typically focuses on estimating the most probable future evolutions of a traffic scenario. Estimating the gap acceptance, i.e., whether a vehicle merges or crosses before another vehicle with the…
A combinatorial rectangle may be viewed as a matrix whose entries are all +-1. The discrepancy of an m by n matrix is the maximum among the absolute values of its m row sums and n column sums. In this paper, we investigate combinatorial…
We consider an intersection zone where autonomous vehicles (AVs) and human-driven vehicles (HDVs) can be present. As a new vehicle arrives, the traffic controller needs to decide and impose an optimal sequence of the vehicles that will exit…
An $r$-matching in a graph $G$ is a collection of edges in $G$ such that the distance between any two edges is at least $r$. A $2$-matching is also called an induced matching. In this paper, we estimate the maximum number of $r$-matchings…
Reinforcement learning techniques can provide substantial insights into the desired behaviors of future autonomous driving systems. By optimizing for societal metrics of traffic such as increased throughput and reduced energy consumption,…
We present progress on three old conjectures about longest paths and cycles in graphs. The first pair of conjectures, due to Lov\'{a}sz from 1969 and Thomassen from 1978, respectively, states that all connected vertex-transitive graphs…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
Road network is a critical infrastructure powering many applications including transportation, mobility and logistics in real life. To leverage the input of a road network across these different applications, it is necessary to learn the…
Oppositely driven binary particles with repulsive interactions on the square lattice are investigated at the zero-temperature limit. Two classes of steady states related to stuck configurations and lane formations have been constructed in…
A two--dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of…
We show that every pair of longest paths in a $k$-connected graph on $n$ vertices intersect each other in at least $(8k-n+2)/5$ vertices. We also show that, in a 4-connected graph, every pair of longest paths intersect each other in at…
We give a rigorous solution of an optimisation problem of minimizing the expected delay caused by encountering a red traffic light on a road journey. The problem incorporates simple constraints on maximum speed, acceleration and braking…
Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges…
Given the aging infrastructure and the anticipated growing number of highway work zones in the United States, it is important to investigate work zone merge control, which is critical for improving work zone safety and capacity. This paper…
We introduce the class of bilateral parking procedures on the integer line. While cars try to park in the nearest available spot to their right in the classical case, we consider more general parking rules that allow cars to use the nearest…
On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed.…
The traffic modelling often keeps the mesoscopic scale in the theoretical sphere because the integro-differential nature of its equations. In the present work we suggest to use the lattice Boltzmann method to overcome these difficulties. In…
We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers'…
A fundamental problem in traffic networks is driving under safety and limited physical space constraints. In this paper, we design longitudinal vehicle controllers and study the dynamics of a system of homogeneous vehicles on a single-lane…