On a Single Server Queue Fed by a Scheduled Traffic with Pareto Perturbations
V.F. Araman, H. Chen, P.W. Glynn, L. Xia

TL;DR
This paper analyzes a single server queue with scheduled arrivals perturbed by Pareto-like heavy-tailed delays, deriving tail approximations for workload distribution in critical and heavy-traffic conditions.
Contribution
It introduces tail behavior analysis for queues with Pareto perturbations, focusing on finite-mean heavy-tailed delays and their impact on workload distribution.
Findings
Tail approximations for steady-state workload under heavy tails
Analysis of Bernoulli sums with power-law success probabilities
Insights into queue behavior with Pareto-like perturbations
Abstract
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of perturbations is assumed to be iid. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbation with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with success probability following a power law with parameter strictly larger than 1.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Queuing Theory Analysis · Healthcare Operations and Scheduling Optimization · Simulation Techniques and Applications
