Related papers: Walk versus Wait: The Lazy Mathematician Wins
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…
Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As…
A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time \tau the random walk reaches a given level. Specifically, the p-moment…
This paper considers the problem of designing the user trajectory in a device-to-device communications setting. We consider a pair of pedestrians connected through a D2D link. The pedestrians seek to reach their respective destinations…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
For a transition between two stable states, the committor is the probability that the dynamics leads to one stable state before the other. It can be estimated from trajectory data by minimizing an expression for the transition rate that…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…
Two mobile agents (robots) have to meet in an a priori unknown bounded terrain modeled as a polygon, possibly with polygonal obstacles. Agents are modeled as points, and each of them is equipped with a compass. Compasses of agents may be…
In this study, we present a comparative analysis of bus routes servicing the University of Pittsburgh to identify the most efficient options for students. We examine factors such as ridership, on-time performance, and travel distance to…
Providing transport users and operators with accurate forecasts on travel times is challenging due to a highly stochastic traffic environment. Public transport users are particularly sensitive to unexpected waiting times, which negatively…
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…
Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely…
The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
Consider a customer who needs to fulfill a shopping list, and also a personal shopper who is willing to buy and resell to customers the goods in their shopping lists. It is in the personal shopper's best interest to find (shopping) routes…
A temporally abstract action, or an option, is specified by a policy and a termination condition: the policy guides option behavior, and the termination condition roughly determines its length. Generally, learning with longer options (like…
The greedy walk is a deterministic walk that always moves from its current position to the nearest not yet visited point. In this paper we consider the greedy walk on an inhomogeneous Poisson point process on the real line. Our primary…
The subject of this paper is the simple random walk on $\mathbb{Z}$. We give a very simple answer to the following problem: under the condition that a random walk has already spent $\alpha$-percent of the traveling time on the positive side…
It has been well established that wireless network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment some of the packets might not have coding pairs, which limits the number…