Waitlist Capacity Simulator

Avg referrals per day

Appointments per day (capacity)

DNA rate (%)

DNA rebook rate (%)

Rebook delay (days)

Patient dropout (%/day)

Simulation horizon (days)

Warm-up (days)

Replications (Monte Carlo)

Random seed (base)

£ cost per WTE per year

Extra slots/day per +1 WTE

Assumptions

Auto-generated from current inputs (for transparency and reporting).

Example scenarios

Auto-fill inputs and run comparable scenarios.

Key metrics

Queue size over time

Solid line is the median across replications; shaded band is 5th–95th percentile.

Wait time distribution (days)

Pooled across all replications.

What this simulator does

This tool models how a healthcare waitlist evolves over time based on demand, appointment capacity, non-attendance (DNA) behaviour, and patient-side dropout.

It runs a stochastic discrete-time queueing model and reports results across multiple Monte Carlo replications, so outputs reflect a distribution of plausible outcomes rather than a single trajectory.

Designed for service planning, policy analysis, and scenario testing. All calculations use synthetic data only.

How the model works

Daily referrals arrive as a Poisson process (mean = avg referrals/day).
Capacity is a fixed number of appointment slots per day, set by staffing.
Each booked patient leaves the queue. With probability p_DNA they did-not-attend; with probability p_rebook they re-enter the queue after the rebook delay. Otherwise they leave the system.
Patients waiting in the queue can drop out independently each day at a small per-day hazard, reflecting people who move, recover, or disengage.
Each replication uses a deterministic seed offset from the base seed, so results are reproducible.

Interpreting outputs

Stable system: queue trajectory flattens; wait-time metrics are meaningful.
Unstable system: queue keeps growing across the horizon. Steady-state metrics are not meaningful — the system needs more capacity, lower demand, or higher attrition.
Confidence band: shows variation across replications, not real-world uncertainty about parameters.
£ / week saved: illustrative only — incremental annual cost (from extra slots/day inferred to extra WTEs) divided by the median reduction in median wait, expressed in weeks.

Limitations

Single-server queue: no priority tiers, no multiple clinician streams, no heterogeneous appointment lengths.
Poisson arrivals assume independence between days and may understate over-dispersion seen in real referral data.
Capacity is exogenous and constant; real capacity flexes with leave, sickness, and case-mix.
This is a teaching and scenario-comparison tool, not a forecasting system.