Improper Poisson line process as SIRSN in any dimension

Coverage Analysis of a Vehicular Network Modeled as Cox Process Driven by Poisson Line Process

In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line process (PLP) and the locations of nodes on each road as a homogeneous 1D Poisson point process (PPP). Assuming that each node transmits independently, the locations of transmitting and recei...

Fractional Poisson Process

For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...

Monotone Subsequences in Any Dimension

We exhibit sequences of n points in d dimensions with no long monotone subsequences, by which we mean when projected in a general direction, our sequence has no monotone subsequences of length n+d or more. Previous work proved that this function of n would lie between n and 2 n; this paper establishes that the coefficient of n is one. This resolves the question of how the Erdo s Szekeres result...

Any-Dimension Algorithms

Continental moisture recycling as a Poisson process

On their journey over large land masses, water molecules experience a number of precipitation–evaporation cycles (recycling events). We derive analytically the frequency distributions of recycling events for the water molecules contained in a given air parcel. Given the validity of certain simplifying assumptions, the frequency distribution of recycling events is shown to develop either into a ...