Exact results for the Barabasi queuing model

TL;DR

This paper derives exact analytical results for the Barabási queuing model with arbitrary list length and randomness, revealing new scaling behaviors and extending previous extremal and two-item analyses.

Contribution

It provides the first exact solutions for the general case of the Barabási queuing model with variable list length and randomness levels.

Findings

Uncovered new scaling features of the model.

Derived exact solutions from master equations.

Extended understanding beyond extremal and two-item cases.

Abstract

Previous works on the queuing model introduced by Barab\'asi to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items. Here we obtain exact results for the general case with arbitrary values of the list length $L$ and of the degree of randomness that interpolates between the deterministic and purely random limits. The statistically fundamental quantities are extracted from the solution of master equations. From this analysis, new scaling features of the model are uncovered.