From Queues to Decisions: Analytical Models for Capacity, Congestion, and Service Systems

This seminar presents Service systems often appear to have enough capacity on paper, yet still experience long queues and delays. My research uses queueing models to understand this gap between nominal capacity and the capacity that a system can effectively deliver. In this talk, a hospital service system will be discussed in which first-time and referred patients share a common service facility but follow different diagnostic and treatment pathways. A phase-type queueing model is developed to capture this heterogeneity while retaining analytical tractability, enabling the derivation of key system performance measures. For the two-treatment case, the stationary behaviour can be obtained in closed form, while a matrix-analytic approach extends the model to an arbitrary number of treatment modes. The analysis also shows how patient mix and service requirements influence congestion and helps identify the service stage contributing most to the overall workload. The queueing analysis is then used for decision-making: determining where additional capacity should be introduced, how much capacity is required to achieve a desired utilisation level, and how service capacity should be selected when both congestion and operating costs matter. This analytical perspective also motivates further research in bidirectional EV charging and home healthcare, where interruptions, uncertainty, and competing demands create new challenges for capacity planning and quality of service..