Queue length computation of time-dependent queueing networks and its application to blood collection

Service systems often experience time-dependent aspects, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to these situations, but are still used. At the same time a large number of computational papers exist that deal with queue length distributions for time-dependent queues. Most of these are fairly theoretical and based on single queues. Real-life service systems, however, might resemble a queueing network structure. With this paper we aim to bring both worlds together. It presents a computational method for time-dependent queueing networks based on uniformization. Although uniformization is generally perceived to be too computationally prohibitive, we show that our method is very effective for practical instances, as shown with a Dutch blood collection site. The results shown in this paper take a matter of seconds to compute. The objective of the results is twofold: (1) to show that the time-dependent queueing network approach is imperative for some queueing networks, including this application and (2) to evaluate possible improvement scenarios for Dutch blood collection sites that can only be properly assessed with a time-dependent queueing method