Queueing Network — Emergency Department
Five-stage emergency pathway at 11 arrivals an hour, with a finite-capacity imaging suite and a senior-review loop back to assessment, solving to an 87% doctor utilisation and a 2.2-hour end-to-end stay.
Make it your own.
title "Emergency department — Monday evening"
target 85%
arrivals Triage 11/h
# Triage is fast and predictable, so its service variability is BELOW
# exponential — cv 0.6 shortens the queue the M/M/c formula would predict.
station Triage { servers: 2; service: 8m; cv: 0.6 }
station "Doctor assessment" { servers: 5; service: 22m }
station Imaging { servers: 3; service: 26m; capacity: 12 }
station "Senior review" { servers: 3; service: 12m; cv: 1.3 }
station Discharge { servers: 3; service: 9m }
route Triage -> "Doctor assessment" 0.94
route Triage -> "Senior review" 0.06 # obvious admissions skip the SHO
route "Doctor assessment" -> Imaging 0.42
route "Doctor assessment" -> "Senior review" 0.58
route Imaging -> "Senior review" 1.0
route "Senior review" -> "Doctor assessment" 0.12 # sent back for more work-up
route "Senior review" -> Discharge 0.88
route Discharge -> exit 1.0