Waiting Lists: Distribution, Shape & Simulation

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A queueing-theory toy for waiting lists / backlogs (NHS RTT, MRI, endoscopy, letters, complaints — any queue). Based on the method in Fong, House, Walton et al., Understanding Waiting List Pressures and the NHSRwaitinglist package. Runs in R, in your browser via webR.

Booting R (downloading webR…)

1 · The exponential model & targets

In the M/M/1 steady state, waiting time is exponential. To see a proportion p within y weeks needs mean wait W = −y / ln(1−p), and a steady-state list of λ·W (Little's law).

2 · Same list, different shape

Constraining long waiters necessarily reshapes the list. The exponential (random order) has many short waits and a long tail; the extreme opposite is pure FIFO, where the census is flat at λ until everyone is removed together. Same λ and same mean wait W throughout.

3 · Simulator

A weekly fluid simulation: referrals in, capacity out, under a chosen removal discipline, starting from an initial list. Watch it grow / shrink / hold and read performance at key weeks.