Queueing delay

Queueing delay is a term in computer engineering.

It refers to a job that is put into a queue, and has to wait there until it can be executed. The time it waits there before being executed is called the queueing delay.

This term is most often used in reference to routers. When packets arrive at a router, they have to be processed and transmitted. A router can only process one packet at a time. If packets arrive faster than the router can process them (such as in a burst transmission) the router puts them into the queue (also called the buffer) until it can get around to transmitting them.

Queuing delay is proportional to buffer size. The longer the line of packets waiting to be transmitted, the longer the average waiting time is. However, this is much preferable to a shorter buffer, which would result in ignored ("dropped") packets, which in turn would result in much longer overall transmission times.

Calculation of Time

For a router

With transmission delay of $D_{t}$
At 100% utilization
With a buffer capable of holding N packets
Not counting dropped packets

the average queuing delay $D_{q}$ is:

D_{q}={(0\times D_{t}+1\times D_{t}+2\times D_{t}...(N-1)\times D_{t}) \over N}

Using sum-of-series simplification, this simplifies to:

D_{q}={{D_{t} \over 2}\times (N-1)}