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Queueing network templates

Queueing Network — Mass Vaccination Centre

Saturday clinic taking 240 arrivals an hour through registration, clinical screening, twelve vaccination booths and a seventy-seat observation bay, solving to a 20-minute stay with screening, not the booths, as the constraint.

Template previewQueueing network
Mass vaccination centre — Saturday morning …Open queueing network · 4 stations · 5 routes · arrivals 240/h · target ρ 85%10.931240/harrivalsexit 0.071exitRegistration×6λ 240/h · ρ 77.8%Wq 18.5s · Lq 1.24W 88.5s · L 5.9G/G/6 · P(wait) 47.4%Clinical screeningbottleneck×9λ 240/h · ρ 81.5%Wq 39.4s · Lq 2.62W 2.5m · L 9.96G/G/9 · P(wait) 46.6%Vaccination booth×12λ 223/h · ρ 77.5%Wq 17.5s · Lq 1.08W 2.8m · L 10.38M/M/12 · P(wait) 31.5%Observation bay×70λ 223/h · ρ 79.7%Wq 2.78s · Lq 0.17W 15m · L 55.97M/M/70 · P(wait) 4.4%StationModelc1/μλaρP(wait)LqWqLWRegistrationG/G/6670s240/h4.6777.8%47.4%1.2418.5s5.988.5sClinical screeningG/G/991.8m240/h7.3381.5%46.6%2.6239.4s9.962.5mVaccination boothM/M/12122.5m223/h9.377.5%31.5%1.0817.5s10.382.8mObservation bayM/M/707015m223/h55.879.7%4.4%0.172.78s55.9715mBottleneck: Clinical screening at ρ = 81.5% on 9 servers — already inside the 85% target; the network is balanced.Offered 240/h · throughput 240/h · L 82.22 in system · W 20.6m end to end · 4 stationsStable — every station holds ρ below 1. Network response time is Little's law on the solved flows: W = L / throughput.

Make it your own.

title "Mass vaccination centre — Saturday morning clinic"
target 85%
arrivals Registration 240/h

# Registration is a scripted check-in, so its service time is tighter than
# exponential; screening is not, because one in twenty people has a question
# that turns into a consultation.
station Registration          { servers: 6;  service: 70s; cv: 0.7 }
station "Clinical screening"  { servers: 9;  service: 110s; cv: 1.25 }
station "Vaccination booth"   { servers: 12; service: 150s }
station "Observation bay"     { servers: 70; service: 15m }

route Registration -> "Clinical screening" 1.0
route "Clinical screening" -> "Vaccination booth" 0.93
route "Clinical screening" -> exit 0.07          # deferred or declined
route "Vaccination booth" -> "Observation bay" 1.0
route "Observation bay" -> exit 1.0