Knowledge vs. Experience: Asymptotic Limits of Impatience in Edge Tenants

TL;DR

This paper analyzes how different information feeds influence customer reneging and jockeying in queue systems, revealing that despite finite differences, both models converge to the same long-term behavior under certain conditions.

Contribution

It introduces a theoretical framework comparing analytic and learned information feeds in queue dynamics, demonstrating their asymptotic equivalence and practical differences.

Findings

Total wait time grows linearly with backlog, leading to inevitable abandonment.

Both information models converge to the same asymptotic limits under mild conditions.

Finite backlog differences significantly affect delays and reneging rates in practice.

Abstract

We study how two information feeds, a closed-form Markov estimator of residual sojourn and an online trained actor-critic, affect reneging and jockeying in a dual M/M/1 system. Analytically, for unequal service rates and total-time patience, we show that total wait grows linearly so abandonment is inevitable and the probability of a successful jockey vanishes as the backlog approaches towards infinity. Furthermore, under a mild sub-linear error condition both information models yield the same asymptotic limits (robustness). We empirically validate these limits and quantify finite backlog differences. Our findings show that learned and analytic feeds produce different delays, reneging rates and transient jockeying behavior at practical sizes, but converge to the same asymptotic outcome implied by our theory. The results characterize when value-of-information matters (finite regimes) and when it does not (asymptotics), informing lightweight telemetry and decision-logic design for low-cost, jockeying-aware systems.