Inhomogeneous CTMC Model of a Call Center with Balking and Abandonment

TL;DR

This paper develops a nonstationary CTMC model for inbound call centers that incorporates abandonment and balking, providing a numerical solution for transient state probabilities to better understand call center dynamics.

Contribution

It introduces a novel nonstationary CTMC model for call centers with abandonment and balking, solved via uniformization with steady-state detection.

Findings

Accurately models call center behavior with abandonment and balking

Provides numerical solutions for transient state probabilities

Enhances understanding of nonstationary call center dynamics

Abstract

This paper considers a nonstationary multiserver queuing model with abandonment and balking for inbound call centers. We present a continuous time Markov chain (CTMC) model which captures the important characteristics of an inbound call center and obtain a numerical solution for its transient state probabilities using uniformization method with steady-state detection. Keywords: call center, transient, Markov processes, numerical methods, uniformization, abandonment, balking