The Amplitude Dynamics of Impulsive Queues

TL;DR

This paper introduces a novel framework using random impulsive differential equations to analyze multiserver queues with customer abandonment, deriving bounds and optimizing impulse timings for improved system performance.

Contribution

It develops a new analytical approach combining RIDEs with Erlang-A queues, providing closed-form bounds and optimal impulse timing strategies.

Findings

Derived steady-state amplitude bounds and average queue lengths.

Identified impulse timings that optimize system performance.

Applied framework to real-world scenarios like call centers and quantum computing.

Abstract

In this paper, we analyze a multiserver Markovian queue with customer abandonment i.e. the Erlang-A queue uder a novel framework, i.e. the random impulsive differential equations (RIDEs). This framework captures systems that evolve continuously while experiencing sudden, discrete interventions. The combination of such framework with Erlang-A queue give rise to multiple real-life applications, such as improving efficiency at call centers and designing optimal timing to apply quantum error correction in trying to shun away from decoherence in quantum computing. We derive closed-form expressions for steady-state amplitude bounds and average queue lengths under impulse, and we identify the impulse timings that optimize system performance.