Queueing network
Queueing networks solved, not merely drawn. Declare stations with arrival and service rates and server counts — M/M/1, M/M/c, M/M/c/K and M/G/1 are all supported — wire them with routing probabilities, and the engine solves the traffic equations and reports utilisation, mean queue length, waiting time and sojourn time per station plus the end-to-end response time, flagging any station whose utilisation reaches one as the bottleneck that makes the whole network unstable.
In the same space
Most users come to Queueing network from JMT (Java Modelling Tools), Excel queueing calculators or Simul8 (basic). flowss runs this engine in the browser — no install, shareable via URL, exportable to PNG / SVG / PDF / source.
Syntax at a glance
arrivals Registration 240/h
station Registration { servers: 6; service: 70s }
station "Vaccination booth" { servers: 12; service: 150s }
route Registration -> "Vaccination booth" 1.0Paste this in the Studio code pane to see Queueing network render live. The full grammar is at the upstream-docs link above.
Sample templates
All 13 →Five-stage emergency pathway at 11 arrivals an hour, with a finite-capacity imaging suite and a senior-review loop back to assessment, solving to an 87% doctor utilisation and a 2.2-hour end-to-end stay.
Erlang-C staffing for a 480-call-an-hour contact centre with billing, technical and retention queues, showing why 26 front-line agents at 93% occupancy still leave the average caller queueing over a minute.
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.
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.
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.
An 850-request-a-second checkout path across six services, where the payment adapter's bounded connection pool is the constraint and heavy-tailed pricing latency (cv 1.9) more than doubles the queue an M/M/c model would predict.
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