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Queueing network templates

Queueing Network — High-Street Coffee Shop

The 08:00 rush at 210 customers an hour across till, espresso bar, food warming and collection, showing how a near-minute barista queue emerges from an espresso bar that is only 80% loaded.

Template previewQueueing network
High-street coffee shop — 08:00 rushOpen queueing network · 4 stations · 6 routes · arrivals 210/h · target ρ 80%0.880.120.310.691210/harrivals1exitOrderbottleneckλ 210/h · ρ 81.7%Wq 38.4s · Lq 2.24W 80.4s · L 4.69G/G/3 · P(wait) 67.5%Espresso bar×5λ 185/h · ρ 80.1%Wq 55.8s · Lq 2.86W 2.2m · L 6.87G/G/5 · P(wait) 55.6%Food warmingλ 82.5/h · ρ 62.3%Wq 29.8s · Lq 0.68W 84.8s · L 1.92M/M/2/8 · blocked 1.1%Collectionλ 209/h · ρ 52.3%Wq 6.76s · Lq 0.39W 24.8s · L 1.44M/M/2 · P(wait) 35.9%StationModelcK1/μλλ effaρP(wait)P(block)LqWqLWOrderG/G/33∞42s210/h210/h2.4581.7%67.5%0%2.2438.4s4.6980.4sEspresso barG/G/55∞78s185/h185/h480.1%55.6%0%2.8655.8s6.872.2mFood warmingM/M/2/82855s82.5/h81.5/h1.2662.3%47.1%1.1%0.6829.8s1.9284.8sCollectionM/M/22∞18s209/h209/h1.0552.3%35.9%0%0.396.76s1.4424.8sBottleneck: Order at ρ = 81.7% on 3 servers — 4 servers (1 more) would bring it under the 80% target.Offered 210/h · throughput 209/h · blocked 0.95/h (0.5%) · L 14.91 in system · W 4.3m 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 "High-street coffee shop — 08:00 rush"
target 80%
arrivals Order 210/h

# Order taking is scripted and quick (cv 0.7); the espresso bar is not —
# a flat white and a tray of four is the same server (cv 1.25).
station Order           { servers: 3; service: 42s; cv: 0.7 }
station "Espresso bar"  { servers: 5; service: 78s; cv: 1.25 }
station "Food warming"  { servers: 2; service: 55s; capacity: 8 }
station Collection      { servers: 2; service: 18s }

route Order -> "Espresso bar" 0.88
route Order -> "Food warming" 0.12
route "Espresso bar" -> "Food warming" 0.31
route "Espresso bar" -> Collection 0.69
route "Food warming" -> Collection 1.0
route Collection -> exit 1.0