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Queueing network templates

Queueing Network — Container Terminal Night Shift

Ninety-six trucks an hour through gate, yard crane, a three-desk customs inspection bay with only ten places and four quay cranes, showing the gate rather than the quayside sitting at the 80% ceiling.

Template previewQueueing network
Container terminal — berth 8, night shiftOpen queueing network · 4 stations · 5 routes · arrivals 96/h · target ρ 80%10.060.94196/harrivals1exitGate inbottleneck×6λ 96/h · ρ 80%Wq 57.9s · Lq 1.54W 4m · L 6.34G/G/6 · P(wait) 51.8%Yard crane×8λ 96/h · ρ 80%Wq 1.6m · Lq 2.58W 5.6m · L 8.98G/G/8 · P(wait) 45.8%Customs inspectionλ 5.76/h · ρ 77.6%Wq 15.5m · Lq 1.44W 40.5m · L 3.77M/M/3/10 · blocked 3%Quay crane×4λ 95.8/h · ρ 79.9%Wq 88.4s · Lq 2.35W 3.5m · L 5.55M/M/4 · P(wait) 59.4%StationModelcK1/μλλ effaρP(wait)P(block)LqWqLWGate inG/G/66∞3m96/h96/h4.880%51.8%0%1.5457.9s6.344mYard craneG/G/88∞4m96/h96/h6.480%45.8%0%2.581.6m8.985.6mCustoms inspectionM/M/3/1031025m5.76/h5.58/h2.477.6%59.2%3%1.4415.5m3.7740.5mQuay craneM/M/44∞2m95.8/h95.8/h3.1979.9%59.4%0%2.3588.4s5.553.5mBottleneck: Gate in at ρ = 80% on 6 servers — already inside the 80% target; the network is balanced.Offered 96/h · throughput 95.8/h · blocked 0.18/h (0.2%) · L 24.64 in system · W 15.4m 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 "Container terminal — berth 8, night shift"
target 80%
arrivals "Gate in" 96/h

station "Gate in"            { servers: 6; service: 3m; cv: 0.7 }
# Yard crane cycle time depends entirely on how deep the box is buried.
station "Yard crane"         { servers: 8; service: 4m; cv: 1.35 }
# The inspection bay physically holds ten boxes; past that the lane is held.
station "Customs inspection" { servers: 3; service: 25m; capacity: 10 }
station "Quay crane"         { servers: 4; service: 2m }

route "Gate in" -> "Yard crane" 1.0
route "Yard crane" -> "Customs inspection" 0.06
route "Yard crane" -> "Quay crane" 0.94
route "Customs inspection" -> "Quay crane" 1.0
route "Quay crane" -> exit 1.0