A Single Source
Network data sources alternate between:
- Sending data at 100% of their network speed and...
- Doing nothing!
The periods of each depend on the communication task at hand.
The average data rate U is somewhere between 0% and 100%.
The "Burstiness" of the traffic is given by the reciprocal of the average rate, ie:
B = Peak rate (100%) / Average rate = 1 / U
The "Burstiness" figure varies widely from just above 1 for large file transfers to over 10 or 20 for random web surfing.
Aggregated Sources
In most of the Internet, traffic on a data link originates from a large number of these sources (operating at a variety of basic data rates).
Individually, the sources may behave like the four below:
When summed together, the resulting traffic looks something like:
Packets awaiting routing are stored in a queue:
When the inflow rate exceeds the outflow, the queue fills.
When the inputs are quiet, the queue empties.
Peak inflow rate < outgoing channel data rate:
- The data is sent out in packets with gaps between them.
- No packets suffer undue delay - the delivery time is reasonably constant.
Peak inflow rate > outgoing channel data rate:
- The data is sent out in packets with minimal or no gaps between them.
- Some packets suffer undue delay.
- Router queues fill. Overflow is possible, causing packets to be discarded.
The end result of sending data through the Internet is that:
- Delivery delay is not constant (inter-packet times suffer timing jitter) which gets worse as the network load increases.
- Under heavy load, some packets are lost (TCP solves this problem using retransmission, but the penalty is even slower data delivery).
Pure Chance Traffic
This sort of traffic arises when each data packet is unrelated to any other data packet and just arrives at some random time. Even so, it is possible to characterise this traffic and therefore to make estimates regarding its effect on the data network.
Let's have a closer look at the "random" traffic:
The average arrival rate in packets per second
The interpacket interval is the reciprocal of this.
The "service rate" is actually derived from the Utilisation.
The average packet duration is the reciprocal of this.
The channel utilisation.
The "busy" period (when the data link is sending a packet) lasts for a random time conforming to a "negative exponential distribution".
P(t) is the probability that a packet duration is greater than time "t".
- Small packets are most likely.
- The average packet duration is 1/μ
Similarly, the "period" (time from start of one packet to start of the next) is "negatively exponentially distributed".
- Small periods are most likely.
- The average period is 1/λ
Queueing of Random Data
When a number of streams of "pure chance" traffic" leave a router via one path, they are queued awaiting transmission. If data enters the queue at a greater average rate than it leaves, the queue will fill until it overflows (regardless of how much memory is allocated).
When the aggregate input rate is less than the outgoing channel capacity, the quantity queued will depend on the outgoing utilisation figure.
Because the packets are of random size and arrive randomly on a number of input channels, it is possible to have some data in the queue even though the aggregate traffic is insufficient to fill the outgoing data channel (simultaneous arrivals).
The behaviour of the queue is predicted by "Erlang's Queue Formula", familiar to teletraffic engineers, but well beyond the scope of this subject:
Application of this formula to a router with one queued outgoing channel produces a simple result:
| Queue Size |
|
U is the outgoing utilisation B is the channel bit rate. |
| Average Delay |
|
For example, consider a router where a number of data streams all try to leave via one queued output. Suppose the average packet size is 512 bytes:
As the outgoing channel rises toward 100% Utilisation, the average queue size grows rapidly.
In theory, with 100% utilisation the queue length is infinite and the average time to get a packet through the queue is infinite:
The average queue size is small for average utilisations below 90%.
The peak queue size is, in theory, always infinite. If a small rate of packet loss is tolerable, a somewhat smaller queue will be sufficient.
In practice, the queue needs to be much larger than the average size, typically 10 times, to accommodate the occasional run of frequent and/or large packets.
If the aggregate traffic tries to exceed 100% (a number of incoming channels all want to send to the same outgoing channel simultaneously), the router will quickly fill its buffer and start dropping random packets.
Real Internet Traffic?
TCP traffic doesn't follow the "pure chance model"!
- The packets are not launched independently.
- TCP tries to push the network as hard as possible.
As discussed in the previous lecture, the congestion control algorithms implemented by TCP result in a "sawtooth" traffic profile:
When several streams of this sort of traffic overload a router, they tend to synchronise.
A peak in traffic overflows a router queue, random packets are dropped, resetting one or more TCP sessions at about the same time.
The end result is that aggregated TCP traffic is very "peaky".
Fractal Traffic
When observed over a short period, typical data traffic appears to be classically randomly distributed:
As the observation period is extended, and the traffic averaged over a longer period, the traffic does not "average" to a smoother value as expected with pure chance traffic - see later.
Classical Pure Chance Traffic
When pure chance traffic is observed over the same time periods, the effect of extended averaging is to reduce the variability of the traffic:
Extended averaging period, smoother traffic.
Even longer period, even smoother traffic.
