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Queueing network templates

Queueing Network — Bank Branch Counter

Friday-afternoon branch flow at 96 customers an hour across greeter, teller line, a nine-seat advice area and the business desk — a balanced network where every station already sits inside the 80% target.

Template previewQueueing network
Bank branch — Friday afternoonOpen queueing network · 4 stations · 8 routes · arrivals 96/h · target ρ 80%0.710.080.110.0296/harrivalsexit 0.1exit 0.981exitexit 1Greeterλ 96/h · ρ 60%Wq 25.3s · Lq 0.68W 70.3s · L 1.88M/M/2 · P(wait) 45%Teller linebottleneck×6λ 68.2/h · ρ 75.7%Wq 83.3s · Lq 1.58W 5.4m · L 6.12G/G/6 · P(wait) 43.5%Business desk×4λ 10.6/h · ρ 66%Wq 4.1m · Lq 0.72W 19.1m · L 3.36M/M/4 · P(wait) 36.9%Advice desk×5λ 9.04/h · ρ 69.9%Wq 3.4m · Lq 0.5W 27.4m · L 3.99M/M/5/9 · blocked 3.4%StationModelcK1/μλλ effaρP(wait)P(block)LqWqLWGreeterM/M/22∞45s96/h96/h1.260%45%0%0.6825.3s1.8870.3sTeller lineG/G/66∞4m68.2/h68.2/h4.5475.7%43.5%0%1.5883.3s6.125.4mBusiness deskM/M/44∞15m10.6/h10.6/h2.6466%36.9%0%0.724.1m3.3619.1mAdvice deskM/M/5/95924m9.04/h8.73/h3.6269.9%34.1%3.4%0.53.4m3.9927.4mBottleneck: Teller line at ρ = 75.7% on 6 servers — already inside the 80% target; the network is balanced.Offered 96/h · throughput 95.7/h · blocked 0.31/h (0.3%) · L 15.35 in system · W 9.6m 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 "Bank branch — Friday afternoon"
target 80%
arrivals Greeter 96/h

station Greeter          { servers: 2; service: 45s }
station "Teller line"    { servers: 6; service: 4m; cv: 1.15 }
# The advice area seats nine including the two desks — beyond that people
# are asked to come back, which is a loss, not a queue.
station "Advice desk"    { servers: 5; service: 24m; capacity: 9 }
station "Business desk"  { servers: 4; service: 15m }

route Greeter -> "Teller line" 0.71
route Greeter -> "Advice desk" 0.08
route Greeter -> "Business desk" 0.11
route Greeter -> exit 0.10               # cash machine only
route "Teller line" -> "Advice desk" 0.02
route "Teller line" -> exit 0.98
route "Advice desk" -> exit 1.0
route "Business desk" -> exit 1.0