A Queueing Model With Servers Disguised as Customers

Queueing theory has been used to model and optimize customer service in numerous real life applications. In this paper, we propose a new model, motivated by the phenomenon of pseudoprogression in cancer, in which the length of a queue appears to increase for a period of time, before reducing at a faster rate. We assume that servers arrive in the queue alongside the customers, that is, ’disguised’ as customers. We derive the general equations for this model using matrix analytic methods, and demonstrate its working with numerical simulations.