Numerical study on the deadline-concerning priority queuing model

TL;DR

This study investigates how deadlines influence response-time distributions in a priority queuing model, revealing that deterministic protocols produce power-law exponents less than one, while nondeterministic ones yield an exponent of one.

Contribution

It introduces a deadline-aware priority queuing model and explores its impact on response-time distributions through numerical simulations.

Findings

Deterministic selection protocol results in power-law exponent < 1.

Nondeterministic selection protocol results in power-law exponent = 1.

Deadlines significantly affect the tail behavior of response times.

Abstract

The Barab\'asi's priority queuing model [A.-L. Barab\'asi, Nature \textbf{435}, 207 (2005)] and its variants have been extensively studied to understand heavy-tailed distributions of the inter-event times and the response times observed in various empirical analyses of human dynamics. In this paper, we focus on the effects of deadlines assigned to the tasks in a queue of fixed size on the response-time distributions. Here, the response time is defined as the time interval between the arrival and the execution of the task. We propose a deadline-concerning priority queuing model, in which as the deadline approaches, the priority is adjusted using the inverse of the remaining time to the deadline. By performing the numerical simulations, we find that the power-law exponent characterizing the response-time distributions is less than $1$ under the deterministic selection protocol while it has the value of $1$ under the nondeterministic selection protocol.