Controlling arrival and service rates to reduce sensitivity of queueing systems with customer abandonment

TL;DR

This paper introduces a congestion-based control scheme for the Erlang A queueing model, reducing the sensitivity of large systems to parameter variations by dynamically adjusting arrival and service rates.

Contribution

It proposes a novel congestion-based control scheme and analyzes its effectiveness in reducing system sensitivity compared to traditional models.

Findings

CBC scheme reduces sensitivity of large systems

Derived performance indicators using Markov chain decomposition

Confirmed robustness of the CBC scheme through analysis

Abstract

The Erlang A model--an M/M/s queue with exponential abandonment--is often used to represent a service system with impatient customers. For this system, the popular square-root staffing rule determines the necessary staffing level to achieve the desirable QED (quality-and-efficiency-driven) service regime; however, the rule also implies that properties of large systems are highly sensitive to parameters. We reveal that the origin of this high sensitivity is due to the operation of large systems at a point of singularity in a phase diagram of service regimes. We can avoid this singularity by implementing a congestion-based control (CBC) scheme--a scheme that allows the system to change its arrival and service rates under congestion. We analyze a modified Erlang A model under the CBC scheme using a Markov chain decomposition method, derive non-asymptotic and asymptotic normal representations of performance indicators, and confirm that the CBC scheme makes large systems less sensitive than the original Erlang A model.