RPA Bot Fleet Queue Simulator

Task Arrivals

Arrival rate λ 12 /min

Bot Fleet

Bot count N 3

Service rate μ (per bot) 10 /min

Exception rate 8%

Live State

System stable

Queue length

Utilization

Throughput

0 /min

Completed / Exceptions

0 / 0

How it works

This is a discrete-event M/M/c queue: tasks arrive one at a time following a Poisson process with rate λ (per minute), and are served by c parallel software bots, each completing a task after an exponentially-distributed service time with mean 1/μ. A finished task is either committed successfully or, with probability p, flagged as an exception and routed to human review — exactly how a real RPA orchestrator (UiPath Orchestrator, Automation Anywhere Control Room) handles brittle steps like a changed UI selector or an unexpected form state.

Offered load:  ρ = λ / (c·μ)
Stability:     the queue only stays bounded if ρ < 1
Little's Law:  L = λ·W   (avg. queue length = arrival rate × avg. wait time)

λ (arrival rate) — how fast new tasks enter the queue.
N (bot count) — how many bots process the queue in parallel (the "c" in M/M/c).
μ (service rate) — how fast a single bot finishes one task.
Exception rate — the fraction of completed tasks a bot cannot resolve automatically and escalates to a human.

When ρ ≥ 1 (arrivals outrun total bot capacity), the queue grows without bound — the exact failure mode that forces real automation teams to add bots or fix slow steps rather than just tuning software.

Queued task Bot (busy) Completed Exception → human review

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