A queueing model with servers disguised as customers

TL;DR

This paper introduces a novel queueing model where servers arrive disguised as customers, capturing phenomena like pseudoprogression in cancer, and provides analytical equations and simulations to understand its behavior.

Contribution

It presents a new queueing model with disguised servers, deriving analytical solutions and demonstrating its behavior through simulations.

Findings

Queue length initially increases then stabilizes.

Model captures pseudoprogression phenomena.

Analytical equations derived for the new model.

Abstract

We propose a new queueing model, motivated by the phenomenon of pseudoprogression in cancer, in which the length of a queue appears to increase initially, before reducing to a steady state. We assume that servers arrive to the queue alongside the customers, i.e. `disguised' as customers. We derive the general equations for this model using matrix analytic methods, and demonstrate its behaviour with numerical simulations.