Related papers: A combinatorial model for lane merging

Each connected component of a mapping $\{1,2,...,n\}\rightarrow\{1,2,...,n\}$ contains a unique cycle. The largest such component can be studied probabilistically via either a delay differential equation or an inverse Laplace transform. The…

We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of…

In the random geometric graph $G(n,r_n)$, $n$ vertices are placed randomly in Euclidean $d$-space and edges are added between any pair of vertices distant at most $r_n$ from each other. We establish strong laws of large numbers (LLNs) for a…

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…

We present in this paper a method to estimate urban traffic state with communicating vehicles. Vehicles moving on the links of the urban road network form queues at the traffic lights. We assume that a proportion of vehicles are equipped…

Autonomous vehicles hold great promise in improving the future of transportation. The driving models used in these vehicles are based on neural networks, which can be difficult to validate. However, ensuring the safety of these models is…

The vision of automated driving is to increase both road safety and efficiency, while offering passengers a convenient travel experience. This requires that autonomous systems correctly estimate the current traffic scene and its likely…

With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…

This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with…

Answering a question raised by Dudek and Pra\l{}at, we show that if $pn\rightarrow \infty$, w.h.p.,~whenever $G=G(n,p)$ is $2$-coloured, there exists a monochromatic path of length $n(2/3+o(1))$. This result is optimal in the sense that…

Interaction between vehicles and pedestrians is seen in many areas such as crosswalks and intersections. In this paper, we study a totally asymmetric simple exclusion process with a bottleneck at a boundary caused by an interaction. Due to…

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…

Vehicle trajectories can offer the most precise and detailed depiction of traffic flow and serve as a critical component in traffic management and control applications. Various technologies have been applied to reconstruct vehicle…

Accurate lane topology is essential for autonomous driving, yet traditional methods struggle to model the complex, non-linear structures-such as loops and bidirectional lanes-prevalent in real-world road structure. We present SeqGrowGraph,…

Let $P,Q$ be longest paths in a simple graph. We analyze the possible connections between the components of $P\cup Q\setminus (V(P)\cap V(Q))$ and introduce the notion of a bi-traceable graph. We use the results for all the possible…

This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the CRITICAL gap, and reject gaps below this threshold, where the…

Traffic congestion remains a significant challenge in modern urban networks. Autonomous driving technologies have emerged as a potential solution. Among traffic control methods, reinforcement learning has shown superior performance over…

Let $a,b$ be fixed positive coprime integers. For a positive integer $g$, write $W_k(g)$ for the set of lattice paths from the startpoint $(0,0)$ to the endpoint $(ga,gb)$ with steps restricted to $\{(1,0), (0,1)\}$, having exactly $k$…

Predicting the future trajectory of a surrounding vehicle in congested traffic is one of the basic abilities of an autonomous vehicle. In congestion, a vehicle's future movement is the result of its interaction with surrounding vehicles. A…

A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…