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Queueing network templates

Queueing Network — Warehouse Picking

Pick-to-despatch flow for 620 orders an hour with a mis-pick rework loop from quality check back to the pick face, identifying pack — not picking — as the station that breaks the 85% target.

Template previewQueueing network
Fulfilment centre — pick to despatchOpen queueing network · 5 stations · 7 routes · arrivals 620/h · target ρ 85%10.180.820.09 back0.911620/harrivals1exitInductλ 620/h · ρ 80.4%Wq 15.5s · Lq 2.67W 29.5s · L 5.09M/M/3 · P(wait) 65.3%Pick face×22λ 630/h · ρ 83.6%Wq 13.2s · Lq 2.32W 2m · L 20.7G/G/22 · P(wait) 32.3%Quality checkλ 113/h · ρ 63%Wq 26.4s · Lq 0.83W 66.4s · L 2.09M/M/2 · P(wait) 48.7%Packbottleneck×13λ 620/h · ρ 90.1%Wq 33.2s · Lq 5.72W 1.7m · L 17.43M/M/13 · P(wait) 63%Despatch×5λ 620/h · ρ 75.8%Wq 8.64s · Lq 1.49W 30.6s · L 5.28M/M/5/60 · blocked 0%StationModelcK1/μλλ effaρP(wait)P(block)LqWqLWInductM/M/33∞14s620/h620/h2.4180.4%65.3%0%2.6715.5s5.0929.5sPick faceG/G/2222∞1.8m630/h630/h18.3883.6%32.3%0%2.3213.2s20.72mQuality checkM/M/22∞40s113/h113/h1.2663%48.7%0%0.8326.4s2.0966.4sPackM/M/1313∞68s620/h620/h11.7190.1%63%0%5.7233.2s17.431.7mDespatchM/M/5/6056022s620/h620/h3.7975.8%47.6%0%1.498.64s5.2830.6sBottleneck: Pack at ρ = 90.1% on 13 servers — 14 servers (1 more) would bring it under the 85% target.Offered 620/h · throughput 620/h · blocked 0/h (0%) · L 50.58 in system · W 4.9m end to end · 5 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 "Fulfilment centre — pick to despatch"
target 85%
arrivals Induct 620/h

station Induct          { servers: 3;  service: 14s }
# Pick walk distance varies enormously across the building, so cv 1.35.
station "Pick face"     { servers: 22; service: 105s; cv: 1.35 }
station "Quality check" { servers: 2;  service: 40s }
station Pack            { servers: 13; service: 68s }
station Despatch        { servers: 5;  service: 22s; capacity: 60 }

route Induct -> "Pick face" 1.0
route "Pick face" -> "Quality check" 0.18
route "Pick face" -> Pack 0.82
route "Quality check" -> "Pick face" 0.09   # wrong item — re-pick
route "Quality check" -> Pack 0.91
route Pack -> Despatch 1.0
route Despatch -> exit 1.0