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Queueing network templates

Queueing Network — Airport Security

Departures screening for a 1,450-passenger-an-hour morning bank, with highly variable bag screening and a twelve-place secondary search room whose blocking loss is computed rather than assumed away.

Template previewQueueing network
Airport security — 06:00 departures bankOpen queueing network · 4 stations · 6 routes · arrivals 1450/h · target ρ 88%10.960.040.071450/harrivalsexit 0.931exitDocument checkbottleneck×8λ 1450/h · ρ 90.6%Wq 17.2s · Lq 6.95W 35.2s · L 14.2M/M/8 · P(wait) 71.9%Bag screening×12λ 1450/h · ρ 87.3%Wq 15.4s · Lq 6.21W 41.4s · L 16.68G/G/12 · P(wait) 55.7%Body scanner×10λ 1392/h · ρ 77.3%Wq 3.11s · Lq 1.2W 23.1s · L 8.94M/M/10 · P(wait) 35.2%Secondary search×8λ 155/h · ρ 77.2%Wq 14.4s · Lq 0.59W 2.7m · L 6.77M/M/8/12 · blocked 4.7%StationModelcK1/μλλ effaρP(wait)P(block)LqWqLWDocument checkM/M/88∞18s1450/h1450/h7.2590.6%71.9%0%6.9517.2s14.235.2sBag screeningG/G/1212∞26s1450/h1450/h10.4787.3%55.7%0%6.2115.4s16.6841.4sBody scannerM/M/1010∞20s1392/h1392/h7.7377.3%35.2%0%1.23.11s8.9423.1sSecondary searchM/M/8/128122.5m155/h148/h6.4877.2%34.4%4.7%0.5914.4s6.772.7mBottleneck: Document check at ρ = 90.6% on 8 servers — 9 servers (1 more) would bring it under the 88% target.Offered 1450/h · throughput 1443/h · blocked 7.3/h (0.5%) · L 46.58 in system · W 1.9m 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 "Airport security — 06:00 departures bank"
target 88%
arrivals "Document check" 1450/h

station "Document check"   { servers: 8;  service: 18s }
station "Bag screening"    { servers: 12; service: 26s; cv: 1.5 }
station "Body scanner"     { servers: 10; service: 20s }
# The search room physically holds twelve people; beyond that the lane is
# held and passengers are sent back round, so this is M/M/c/K.
station "Secondary search" { servers: 8;  service: 150s; capacity: 12 }

route "Document check" -> "Bag screening" 1.0
route "Bag screening" -> "Body scanner" 0.96
route "Bag screening" -> "Secondary search" 0.04
route "Body scanner" -> "Secondary search" 0.07
route "Body scanner" -> exit 0.93
route "Secondary search" -> exit 1.0