IoT Platform: Device Fleet & Message Queue

Device Fleet

Devices 8

Publish rate / device 1.0 msg/s

Hub processing capacity 20 msg/s

Hub & Queue

Queue depth

Avg latency

0 ms

Drop rate

0.0%

Utilization ρ

Connected devices

Processed total

How it works

Each connected device is an independent source that publishes a message with average rate λ_d (a Poisson process — messages arrive at random but with a fixed long-run rate, so the gap between two messages is exponentially distributed). With N devices the hub sees a combined arrival rate:

λ = N × λ_d          (total arrivals per second)

The hub is a single processor that can drain messages from its queue at rate μ (the "Hub processing capacity" slider). This is a textbook M/M/1 queue: one queue, one server, Poisson arrivals, exponential service.

ρ = λ / μ                (utilization — server busy fraction)
L = ρ / (1 − ρ)          (expected messages waiting, ρ < 1)
W = L / λ                (Little's Law → expected time in system)

ρ < 1 — the hub keeps up; the queue stays short and latency stays low.
ρ → 1 — the queue grows without bound in theory; here it is capped at a finite buffer, so once it fills, new arrivals are dropped — exactly what a real broker does under back-pressure.
The stacked cubes above the hub are the live queue; the hub sphere pulses each time it finishes servicing one message (rate μ, one drain event every 1/μ seconds of accumulated capacity).
Traffic Spike multiplies every device's publish rate ×5 for 4 seconds — a burst that pushes ρ over 1 and demonstrates queue buildup, added latency and drops in real time.

Real-world relevance: this is the same queueing model that governs MQTT brokers, Kafka topics and cloud IoT ingestion endpoints (AWS IoT Core, Azure IoT Hub) — provisioning more devices or raising publish rates without scaling the broker's throughput produces exactly this backlog-and-drop behaviour.

Provisioning device Connected device In-flight message Queued message

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