Using Restart Sequences to Determine Beneficial First Passage Under Restart

TL;DR

This paper investigates how restart mechanisms can reduce the mean hitting time in First Passage processes by analyzing a construct called the restart sequence, which depends solely on the process distribution.

Contribution

It introduces the restart sequence as a new tool to characterize when restart can beneficially reduce mean hitting times in discrete First Passage processes.

Findings

Restart sequences can determine when restart reduces mean hitting time.

The analysis applies to a broad class of discrete FP processes.

The approach provides a new perspective on optimizing restart strategies.

Abstract

First Passage (FP) processes are utilized widely to model phenomena in many areas of mathematical applications, from biology to computer science. Introducing a mechanism to restart the parent process can alter the first passage characteristics, and the properties of the resulting First Passage Under Restart (FPUR) process have been subject to much recent investigation. Here we seek to more fully characterize whether a discrete FP process can have its mean hitting time reduced through the implementation of restart by analyzing a construct we call the restart sequence, which is determined solely by the distribution of the FP process.