Waiting Lists as Systems, Not Metrics

An interactive simulator for exploring demand, capacity, and access trade-offs

What the simulator does

This tool models a healthcare waiting list as a discrete-time queue with stochastic demand, fixed daily capacity, and feedback from non-attendance. Rather than predicting individual outcomes, it shows how access, backlog size, and waiting times evolve over time when those forces interact.

Why this framing

It is built for service planning, policy analysis, and scenario testing — not operational forecasting. By treating the waiting list as a dynamic system rather than a static snapshot, planners can visualize the impact of variability and feedback loops that are often lost in simple linear models.

Model structure

At its core, the model represents a waiting list as a single-server queue with limited daily capacity. The model is intentionally simplified to support transparency and comparison of scenarios. Key variables include Arrival Demand, Service Capacity, and DNA rebooking dynamics.

Aₜ — new referrals arriving on day t
C — daily appointment capacity
Qₜ — queue size at the start of day t
p₍dna₎ — probability of non-attendance
p₍rebook₎ — probability a DNA is rebooked
d — rebooking delay (days)

The four core processes

Arrivals (demand): Modelled as a stochastic Poisson process to reflect real-world fluctuations.
Service capacity: An exogenous constraint reflecting workforce availability.
Attendance and DNAs: Feedback effects generated by rebooking delays.
Departures: Clearance of patients through the system.

Queue dynamics

The model updates the queue size daily based on new arrivals and departures. The rebooking of non-attending patients after a set delay creates a secondary inflow that interacts with the primary demand stream, essentially making the backlog self-re-entrant.

Reproducibility and uncertainty

The simulator includes a random seed to control stochastic elements. This ensures reproducibility: the same inputs generate the same simulated trajectory, allowing for consistent scenario comparison while acknowledging the inherent variance of service systems.

Stability

The simulation runs over a defined time horizon, including a warm-up period to ensure stable dynamics before summary metrics are calculated. This ensures that transient initial states do not skew the interpretation of steady-state performance.

What this model does not do

This is a strategic tool, not an operational one. It does not predict individual patient wait times, model complex multi-stage clinical pathways, or account for specific workforce shift patterns. Instead, it captures the mechanical properties of a queue.

Interpreting outputs

Focus on patterns, sensitivities, and the relative impact of policy changes (like capacity adjustments) rather than single-point numerical forecasts. Outputs identify the trade-offs between speed of access and system resilience.