Khintchine-Pollaczek formula for random walks whose steps have one geometric tail

TL;DR

This paper derives a Khinchine-Pollaczek formula for certain random walks with geometric tail steps, utilizing the memory-less property, and applies it to a microtubule queue model.

Contribution

It introduces a new formula for random walks with geometric tail steps, expanding theoretical understanding and providing a practical example in biological modeling.

Findings

Derived a Khinchine-Pollaczek formula for geometric tail steps

Utilized the memory-less property of geometric distribution

Applied the formula to a microtubule queue model

Abstract

We derive a Khinchine-Pollaczek formula for random walks whose steps have a geometric left tail. The construction rests on the memory-less property of the geometric distribution. An example from a tandem queue modeling dynamic instability in microtubules is given.