Exclusion in a priority queue

2014/03/31 by Jan de Gier, Caley Finn · 1 citation
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #cond-mat.stat-mech

paper · pdf · doi:10.1088/1742-5468/2014/07/p07014

published as J. Stat. Mech. (2014) P07014 · 27 pages, 18 figures

openalex publication_date 2014/07/18 · arxiv created 2014/07/22 · arxiv updated 2014/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally asymmetric exclusion process with a dynamically varying lattice length. We calculate exact local density profiles for an unbounded queue by deriving domain wall dynamics from the microscopic transition rules. The structure of the unbounded queue carries over to bounded queues where, although no longer exact, we find the domain wall theory is in very good agreement with simulation results. Within this approximation we calculate average waiting times for queueing customers.

Citations

• Microtubule Length Regulation by Molecular Motors
• An exact solution of a one-dimensional asymmetric exclusion model with open boundaries
• A dynamically extending exclusion process
• Model of hyphal tip growth involving microtubule-based transport

Cited by

• Effective ergodicity breaking in an exclusion process with varying system length

Related

• An Infinite Dimensional Model for A Single Server Priority Queue
• An Infinite Dimensional Model for a Many Server Priority Queue
• Density profiles of the exclusive queueing process
• A queueing theory approach for a multi-speed exclusion process
• A Stochastic Fluid Model Approach to the Stationary Distribution of the Maximum Priority Process