Queuing Delay Calculator & Traffic Intensity Simulation

Q: What is traffic intensity?

Traffic intensity is (L a)/(R): the average packet arrival rate a times the packet length L, divided by the link rate R. When it is below 1 the queue stays bounded; at or above 1 the queue grows without bound.

Q: How do you calculate queuing delay for N packets arriving at once?

The k-th packet waits (k-1) (L)/(R). The average over N packets is ((N-1) L)/(2R).

About this simulator

Queuing delay is the time a packet waits in a router's buffer before it can be transmitted. Unlike the other delays it changes from packet to packet and depends on traffic. This simulation runs a real first-in-first-out queue so you can compare a burst of packets with steady and random arrivals and see how traffic intensity decides everything.

How it works

Packets arrive at the router and join a FIFO queue if the link is busy transmitting another packet.
Each packet waits for every packet ahead of it to finish transmitting ( $L / R$ each).
If the arrival rate times the packet length exceeds the link rate ( $La/R > 1$ ) the queue grows without bound.

Formulas used

$\text{Traffic intensity} = \dfrac{L\,a}{R}$
$\text{Burst of } N \text{ packets: average wait} = \dfrac{(N-1)\,L}{2R}$
$d_{\text{queue}}(k) = \max(0,\ \text{link free time} - \text{arrival time})$

Worked example

Five 1,500-byte packets arrive together at a 10 Mbps link (each takes $1.2\ \text{ms}$ to transmit). The first waits $0$ , the second $1.2\ \text{ms}$ , then $2.4$ , $3.6$ and $4.8\ \text{ms}$ . The average is $2.4\ \text{ms}$ , exactly $\dfrac{(N-1)\,L}{2R} = \dfrac{4 \times 1.2}{2}\ \text{ms}$ . With traffic intensity $La/R$ above 1 the waits keep growing without limit.

Enter these numbers in the simulator above to see every step.

When to use it

Practising the average queuing delay for a burst of N packets.
Seeing why buffers fill when arrival rate times packet size exceeds the link rate.
Comparing steady traffic with random (Poisson) arrivals.

Frequently asked questions

What is traffic intensity?

Traffic intensity is $\dfrac{L\,a}{R}$ : the average packet arrival rate $a$ times the packet length $L$ , divided by the link rate $R$ . When it is below 1 the queue stays bounded; at or above 1 the queue grows without bound.

How do you calculate queuing delay for N packets arriving at once?

The $k$ -th packet waits $(k-1)\,\dfrac{L}{R}$ . The average over $N$ packets is $\dfrac{(N-1)\,L}{2R}$ .

Why does queuing delay change from packet to packet?

Each packet finds a different number of packets ahead of it, so unlike transmission or propagation delay it depends on traffic, not just on the packet and the link.