Related papers: Lonely passengers: a short proof
Transportation Problem is an important aspect which has been widely studied in Operations Research domain. It has been studied to simulate different real life problems. In particular, application of this Problem in NP- Hard Problems has a…
We consider the Schr\"odinger equation with singular position dependent effective mass and prove that it is very weakly well posed. A uniqueness result is proved in an appropriate sense, moreover, we prove the consistency with the classical…
The estimation of the number of passengers with the identical journey is a common problem for public transport authorities. This problem is also known as the Origin- Destination estimation (OD) problem and it has been widely studied for the…
We consider the transport equation on $[0,T]\times \mathbb{R}^n$ in the situation where the vector field is $BV$ off a set $S\subset [0,T]\times \mathbb{R}^n$. We demonstrate that solutions exist and are unique provided that the set of…
One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of the…
We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as…
It is known that a gambler repeating a game with positive expected value has a positive probability to never go broke. We use the mass transport method to prove the generalization of this fact where the gains from the bets form a…
This paper presents a systematic approach for analyzing the departure-time choice equilibrium (DTCE) problem of a single bottleneck with heterogeneous commuters. The approach is based on the fact that the DTCE is equivalently represented as…
We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been…
A 1976 theorem of Chaitin can be used to show that arbitrarily dense sets of lengths n have a paucity of trivial strings (only a bounded number of strings of length n having trivially low plain Kolmogorov complexities). We use the…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main results. Firstly, we introduce a nonsmooth version of the…
It was the problem of finding the minimum value of the sum of the distances of the path through all cities Overview TSP. We propose an authentication with the problem that the deformation sum of the distances of the path to be a constant…
A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…
We consider the extent to which we can learn from a completely randomized experiment whether all individuals have treatment effects that are weakly of the same sign, a condition we call monotonicity. From a classical sampling perspective,…
This paper examines the distinct lack of clear examples of time-travellers and proposes an explanation for their absence without assuming technical barriers to constructing time machines. Instead, it develops and then analyses a model of…
Crowding in train cars is increasingly a major concern for transit agencies. From the perspective of the passengers and the transit agencies, overcrowding of the train cars has several negative consequences such as: (i) extended duration of…
This article deals with the experimental study of pedestrian behaviours in some situations of one-dimensional traffic. Participants were pre-organized in a line, and asked to walk either in a straight line with a fast or slow leader, or to…