Types of Delay
In packet-switched networks, a packet starts its journey from a host (the source), then passes through a series of routers, and ends its journey in another host (the destination). While a packet travels from one node to a subsequent node along its path, it may have to suffer from different types of delays at each node. Those delays can be mainly recognized as,
• Nodal processing delay
• Queuing delay
• Transmission delay
• Propagation delay
To analyze the Average queuing delay vs La/R graph, specifically, we need to go through Transmission delay and Queuing delay.
When a packet arrives at a router, it can be transmitted onto a link, only if there are no other packets currently being transmitted on the link and if no other packets are waiting on a queue to be transmitted. If not where the link is currently busy or there are already packets being queued for the link, the newly arrived packets must need to join the queue before transmission.
The transmission delay is the amount of time required to push or transmit all of the packet’s bits into the link whereas the Queuing delay is the amount of time that the packet experiences at the queue as it waits to be transmitted onto the link. The length of queuing delay depends on the below factors.
• Rate at which traffic arrives at the queue
• The transmission rate of the queue
• Nature of the arriving traffic
But the queuing delay cannot say exactly. It can vary from packet to packet. Therefore usually the queuing delay is introduced in terms of ‘average queuing delay’.
Another term that plays an important role in estimating the extent of queuing delay is traffic intensity.
Traffic intensity can be introduced as below.
It’s a measure of the average occupancy of a server or resource during a specified period of time. Therefore one of the golden rules in traffic engineering is to “Design your system so that the traffic intensity is no greater than 1”. Reasons for this rule can be found below.
La/R graph
The dependence of average queuing delay on traffic intensity is plotted in the below graph.
From the above graph, we can analyze cases. Let’s go through each of them one by one.
• When La/R > 1
Here the arriving rate is greater than the transmission rate. So the queue will increase without any bound resulting in the average queuing delay will be infinity since there will be a congestion of transmission rate slower than packets arriving at the buffer.
• When La/R ≤ 1
Here we can analyze the case in two ways.
1. Packets arrive periodically – If each packet arrives at L/R seconds, there will be no queuing delay since each packet arrives in an empty queue.
2. Packets arrive in bursts – If a set of packets arrive at the same time, the first packet queuing delay will be 0 since there is no queue. But the rest of the packets of the set have increasing queuing delays. So the average queuing delay can be defined as,
• When La/R→0
This means the average queuing delay is close to zero and it occurs when packet arrivals are few and arrive in large intervals.
• When La/R→1
This occurs when packets arrive in bursts so the arrival rate exceeds the transmission capacity. Here a queue will form during the periods.
In reality, packets arrive in a random manner and do not follow any pattern. Simply if the arrival rate is less than the transmission delay, the average queuing delay will be zero.
Reference
2. W.A.Ravinath (2021) Behavior of average queing delay vs traffic intensity, Behavior of Average Queing Delay vs Traffic Intensity. Blogger. Available at: https://ravinathwanni.blogspot.com/2021/04/behavior-of-average-queing-delay-vs.html (Accessed: November 7, 2022).
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