Learning From Queues: Operational Analysis and Performance Evaluation of Dialysis Duration in a Paired Kidney...

The allocation and timing for kidney matching and transplantation among incompatible donor-recipient pairs in the Paired Kidney Exchange face significant operational challenges of managing an uncertain waitlist. The time for dialysis of patients waiting for biologically compatible kidneys follows the concept of a stochastic queueing system. This study embodies the Learning Health System approach by integrating real-world data and mathematical modeling to generate actionable insights that guide decision-making.

This work employs an $M/M/1$ model with Poisson arrivals and exponentially distributed service times for incompatible donor-recipient pairs in a single transplant facility. Inter-arrival and service times are used to derive queue length and waiting-time measures to characterize system congestion and instability, with performance measures evaluated as indicative approximations analyzing the corresponding metrics.

The system is persistently overloaded, with arrival rates exceeding service rates ( $\lambda$ $>$ $\mu$ ; $\rho >$ 1), causing prolonged waiting times. Analytical and Hutson-B bootstrap confidence interval analysis shows congestion persists across plausible variations, and sensitivity analysis indicates moderate perturbations do not alleviate overload. Regression and correlation analyses indicate that delays are associated with arrival pressure and biologically imposed constraints, supporting compatibility-constrained matching as the primary operational challenge. Patients experience uncertain, extended waiting periods, reflecting stochastic instability in biologically constrained queueing systems.

Transplant service management requires systematic reforms, as clinical matching and allocation delays hinder timely care. Establishing a national transplant registry, integrated real-time queue monitoring, decentralized planning with expansion of transplant centers and improved inter-center coordination for paired exchange and increasing its cycle lengths are essential to ensure efficient service delivery and informed healthcare policy. These interventions create a continuous feedback loop where operational data informs queueing-theoretic analysis, informs policy, system redesign, and ultimately improves patient access and outcomes, demonstrating how data-driven learning optimizes complex healthcare services.