13 templates
Queueing network templates
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.
Queueing Network — Emergency Department
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.
Operations & OpsQueueing Network — Contact Centre
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.
Operations & OpsQueueing Network — Airport Security
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.
Operations & OpsQueueing 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.
Lean & FlowQueueing 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.
Lean & FlowQueueing Network — Checkout API Call Chain
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.
Data & SchemaQueueing 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.
Operations & OpsQueueing Network — Car Service Centre
A main-dealer workshop taking 4.2 vehicles an hour, with a parts-window loop that sends bays back into the queue and a road-test pair that turns out to be the real constraint rather than the ten workshop bays.
Lean & FlowQueueing Network — Passport Office Counter
Public counter handling 74 applicants an hour, where a two-desk supervisor referral room with only six places blocks more than a quarter of the people sent to it and quietly sheds them from the network.
Operations & OpsQueueing Network — CI Build Farm
Merge-queue pipeline at six jobs a minute with flaky-test retry loops from both suites, showing how a 90-slot integration executor pool, not the forty compile workers, is the station that touches the 80% target.
Data & SchemaQueueing Network — Mass Vaccination Centre
Saturday clinic taking 240 arrivals an hour through registration, clinical screening, twelve vaccination booths and a seventy-seat observation bay, solving to a 20-minute stay with screening, not the booths, as the constraint.
Operations & OpsQueueing 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.
Operations & OpsQueueing Network — Fleet Telemetry Ingest
A 4,000-message-a-second vehicle telemetry pipeline across gateway, decoder, enrichment, a bounded rule engine pool and column storage, with a replay loop from the dead-letter path back into decoding.
Architecture