Staffing queueing systems with cyclical demand and unreliable servers

Abstract

Unplanned staff absences, referring to scheduled servers being unavailable, pose significant challenges in sectors like healthcare, airlines, and correctional facilities, leading to under-staffing and management reliability issues. This thesis investigates the effectiveness of the Stationary Independent Period by Period (SIPP) method for staffing a multi-server delay queueing system with time-varying demand and server absence. Using the M(t)/M/c(t) queueing model, we systematically examine the SIPP method across various scenarios, including realistic ones, considering cyclical customer arrival rates and multiple servers with uncertain availability. We identify the parameter settings under which the SIPP method is most compromised. We propose two modifications to the SIPP method to account for absence in staffing decisions. We systematically compare these two proposed methods across different scenarios and identify the parameter settings under which each proposed method performs better. We also propose a heuristic to schedule additional servers given a certain budget.