On the statistical distributions of substance moving through the nodes of a channel of network

TL;DR

This paper models the movement of substance through network nodes using urns, deriving a class of statistical distributions that include truncated Katz, Ord, and Kemp distributions, with analysis for finite and infinite channels.

Contribution

It introduces a novel model of substance exchange in network channels, deriving new statistical distributions that generalize existing families.

Findings

Derived a class of distributions for substance in network nodes.

Showed the distributions include truncated Katz, Ord, Kemp as special cases.

Analyzed stationary regime of substance flow in finite and infinite channels.

Abstract

We discuss a model of motion of substance through the nodes of a channel of a network. The channel can be modeled by a chain of urns where each urn can exchange substance with the neighboring urns. In addition the urns can exchange substance with the network nodes and the new point is that we include in the model the possibility for exchange of substance among the urns (nodes) and the environment of the network. We consider stationary regime of motion of substance through a finite channel (stationary regime of exchange of substance along the chain of urns) and obtain a class of statistical distributions of substance in the nodes of the channel. Our attention is focused on this class of distributions and we show that for the case of finite channel the obtained class of distributions contains as particular cases truncated versions of the families of distributions of Katz, Ord, Kemp, etc. The theory for the case of infinite chain of urns is presented in the Appendix.