Queue Depth Calculator
Size an interface queue for a target latency and check the M/M/1 wait time at your utilisation.
About Queue Depth Calculator
A queue's depth is best expressed in time: bytes divided by the drain rate. Sizing it from a latency target keeps worst-case delay bounded, while the M/M/1 result shows the average queue that random arrivals actually build at your utilisation. Queue length grows without bound as utilisation approaches 1 — at 90% load the average queue is nine times what it is at 50% — which is why latency-sensitive links are engineered well below capacity.
Formulas
Queue Depth
queue bytes = link rate × target latency ÷ 8, and queue packets = queue bytes ÷ average packet size.
- target latency
- Maximum queuing delay you will tolerate, in seconds
- link rate
- Interface speed in bits per second
M/M/1 average queue
M/M/1 queue length = ρ² ÷ (1 − ρ)
- ρ
- Offered load as a fraction of capacity
- queue length
- Mean packets waiting, excluding the one in service
Worked example
With the default values below, Queue Depth Calculator returns Queue Depth of 417. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Link speedminimum 0.1 Mbit/s
- 1,000 Mbit/s
- Target queuing latencyminimum 0.01 ms
- 5 ms
- Average packet sizeaccepts 64–9,216 bytes
- 1,500 bytes
- Link utilisation (0–0.99)accepts 0.01–0.99
- 0.8
Results
- Queue Depth
- 417 packets
- Queue Size
- 610 KiB
- M/M/1 Average Queue Length
- 3.20 packets
- Serialisation Time Per Packet
- 0.0120 ms
- Average Queuing Delay
- 0.0384 ms
Step by step
- 1Values used
- 2Queue Depth
- 3M/M/1 average queue
- 4Queue Depth= 417 packets
- 5Queue Size= 625,000
- 6M/M/1 Average Queue Length= 3.20 packets
- 7Serialisation Time Per Packet= 0.0120 ms
- 8Average Queuing Delay= 0.0384 ms
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Queue Depth calculated?
queue bytes = link rate × target latency ÷ 8, and queue packets = queue bytes ÷ average packet size. A queue's depth is best expressed in time: bytes divided by the drain rate. Sizing it from a latency target keeps worst-case delay bounded, while the M/M/1 result shows the average queue that random arrivals actually build at your utilisation.
Why does Queue Depth matter?
Queue length grows without bound as utilisation approaches 1 — at 90% load the average queue is nine times what it is at 50% — which is why latency-sensitive links are engineered well below capacity.
What values do I need to enter?
This calculator takes 4 inputs: Link speed, Target queuing latency, Average packet size, Link utilisation (0–0.99). The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.