Queueing and Simulation
Queueing and Simulation
Utilisation is nonlinear risk
Orders arrive at 18 per hour. One picker completes 10 per hour on average.
- two pickers provide capacity 20 per hour, utilisation ;
- three provide capacity 30 per hour, .
Average capacity exceeds average demand with two pickers, yet random arrival and service variation create queues. Waiting rises sharply as utilisation approaches one.
Little’s Law
For a stable system over a consistent boundary,
where is average number in system, throughput and average time in system. If throughput is 18 orders/hour and average system time is 20 minutes ( hour), then orders.
Little’s Law does not by itself determine the waiting distribution or required capacity.
Simulate the operating assumptions
Compare two- and three-picker queues
This is an M/M/c-style teaching simulation: exponential interarrival and service times, independent jobs, identical always-available pickers and no priorities. Real data may reject every assumption.
Build a simulation audit
| Component | Evidence needed |
|---|---|
| arrivals | timestamp pattern by hour/day; batches and cancellations |
| service | distribution by basket, picker and interruption |
| routing | first-come, priority or skill matching |
| resources | breaks, failures, shared tasks and shift boundaries |
| warm-up | remove artificial empty-system start when appropriate |
| replications | Monte Carlo error and stable quantiles |
| validation | compare simulated and observed queue measures |
Simulation code implements assumptions; it does not validate them.
Capacity decision
Compare staffing cost with the full distribution of waits, lateness, abandonment and service harm. Test peak and disruption scenarios. A policy can schedule a third picker only in vulnerable windows rather than permanently.
Quick check
Observed average arrivals are 18/hour and two-pick capacity is 20/hour. Why might the queue still be unstable during an evening?