Queue Depth Calculator
Size an interface queue for a target latency and check the M/M/1 wait time at your utilisation.
Inputs
Queue Depth
417packets
Queue Size
610 KiB
M/M/1 Average Queue Length
3.20packets
Serialisation Time Per Packet
0.0120ms
Average Queuing Delay
0.0384ms
Step by step
Values used
Link speed = 1,000 Mbit/s; Target queuing latency = 5 ms; Average packet size = 1,500 bytes; Link utilisation (0–0.99) = 0.8000
Queue Depth
queue bytes = link rate × target latency ÷ 8, and queue packets = queue bytes ÷ average packet size.
M/M/1 average queue
M/M/1 queue length = ρ² ÷ (1 − ρ)
Queue Depth
= 417 packets
Queue Size
= 625,000
M/M/1 Average Queue Length
= 3.20 packets
Serialisation Time Per Packet
= 0.0120 ms
Average Queuing Delay
= 0.0384 ms
How it works
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
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.