Deadlock detection and resolution in queueing networks with blocking

Queueing networks with after-service blocking and limited or no buffer space are prone to deadlocks, a situation in which jobs become directly or indirectly blocked by themselves. Such networks are frequently used to model real-world scenarios, particularly in healthcare. This paper addresses deadlock detection and resolution in queueing networks with blocking, as a resolution mechanism is essential to prevent permanent deadlocks. We derive closed-form expressions for the number of customers in a single-node network to illustrate the effect of resolution frequency. For more complex settings, we propose a dynamic deadlock resolution strategy based on Integer Linear Programming (ILP), which adaptively determines job transitions. The effectiveness of the ILP is demonstrated using a system dynamics model, and its impact on blocking probabilities is evaluated through simulation. This approach substantially improves system performance: increasing the resolution frequency reduces job rejections and blocked servers, especially in systems with few servers or coarse time discretization. A case study on elderly care in Amsterdam shows that coordinated deadlock resolution can reduce patient rejections by up to 10% and wrong-bed days by up to 20% over a ten-year horizon, improving patient flow without expanding capacity.

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