Statistical Modelling of Internet Traffic Presenter: Moshe Zukerman ARC Centre for Ultra Broadband Information Networks Electrical and Electronic Engineering.

Statistical Modelling of Internet Traffic

Presenter: Moshe Zukerman ARC Centre for Ultra Broadband Information

NetworksElectrical and Electronic Engineering Dept.,

The University of Melbourne

Outline

Comparison with road traffic

Macroscopic traffic information

Microscopic traffic modelling

Single server queue insights – link utilization

Implications for future developments

Disclaimer• I will represent views and conclusions from an

academic traffic modelling point of view.• The conclusions are optimistic and rosy from the traffic

perspective.• They do not consider: cyber terrorism, Denial of

Service attacks, viruses, disasters, hardware or software failures, or any other practical possible event(s) that may lead to network bottlenecks or congestion.

• All these are issues related to important telecommunications research topics but are beyond the scope of this talk.

New Jersey Traffic and Teletrafficists

Similarity between road and Internet traffic

• Network should be designed to meet the traffic demands.

• Congestion leads to delays and unsatisfied customers with impact on the economy.

• Infrastructure is expensive especially for a large country like Australia.

Some differences between road and Internet traffic

• Loss and collisions are not viable options in road traffic. Internet messages are lost and retransmitted all the time.

• Vehicles move in different speeds leading to inefficiencies.

• To increase capacity in roads there is a need to widen or add roads. For Internet this can be done without touching the fiber in the ground.

• Size of Internet messages are significantly more variable than those of vehicles.

• Internet traffic growth has been much much stronger than road traffic growth.

Moore’s Law

• Moore's Law: power and speed of computers will double every 18-24 months.

• Internet backbone traffic grew from 1 Tbit/sec = 1 million million bits per second in 1990 to 3,000 Tbit/sec in 1997.

• Number of Internet hosts more than doubled every year for the last 20 years.

Macroscopic Approach:

Multi Hour Traffic Matrixgives you, for every origin-destination pair,

the total traffic within every relevant time

interval (e.g. every hour).

Physical versus Logical Network

B

A

M

S

Physical Network

A M

B S

Logical Network

Example for the use of multi hour traffic data

Physical NetworkLogical Network

L T

NY

C

C

C

L T

NY

2C

2C

2C

Assume each city is asleep in a different 8 hour period, when T is asleep, all the traffic between NY and L goes through T.

Packet Switching versus Circuit Switching

Circuit Switching: exclusive capacity end-to- endexample: telephone network (organize ) Packet Switching: store and forwardexample: Internet (very massy, but has its benefits)

Internet – A Network of Queues

Microscopic Approach

Focuses on statistical characteristics of traffic streams.

For example, what are the statistical characteristics of arrival times of Internet packets in a certain Internet router on a certain link.

There may be thousands or even millions of these packets arriving within a second.

Single Server Queue

Input Buffer (waiting room) Server Output

Two key contrasting performance measures:1. Utilization2. Queueing delay(Packet loss is translated to delay or to quality.)

Single Server Queue

Input Buffer (waiting room) Server Output

Utilization = Proportion of time the server is Busy, or ratio between work processed and server capacity; measure for system efficiency.

The aim is to maximize utilization subject to meeting queueing delay (and loss) requirements.

Single Server Queue

Input Buffer (waiting room) Server Output

Utilization = Proportion of time the server is Busy, or ratio between work processed and server capacity; measure for system efficiency.

The aim is to maximize utilization subject to meeting queueing delay (and loss) requirements.

I have been waiting for 40 minutes!!

Well, this is because we had too many calls

come in.

An Example

Input Buffer (waiting room) Server Output

Consider an Internet service provider (ISP)with 1000 customers, each transmit at a rate of one million bits per second (1 Mbit/s) a 1/3 of the time and is idle 2/3 of the time. What is the minimal capacity you need so that

no more than 1/1,000,000th of the time queueing delay is more than one second?

1000sources

An Example (cont.)

Input Buffer (waiting room) Server Output

The answer should be between the MEAN (333.33 Mbit/sec) and the PEAK (1000 Mbit/sec). To give a better answer we need traffic modelling.

1000sources

An Example (cont.)

Input Buffer (waiting room) Server Output

If Server capacity = MEAN (333.33 Mbit/sec) then Utilization = 1. If Server capacity = PEAK (1000 Mbit/sec) then Utilization = 1/3.

1000sources

An Example (cont.)

Input Buffer (waiting room) Server Output

It is unlikely that we need the peak – right?It is unlikely that all 1000 sources will need their

1 Mb at a random point in time – the probability of this event is 1/(31000), so to guarantee that no more than 1 out of 1,000,000 will be lost or suffer delay of more than a second we can do with probably way less than service capacity of 1000 Mbit/sec.

1000sources

Another Example

Input Buffer (waiting room) Server Output

Now we know we need the peak – right?It is more likely that all 3 sources will need their 1

Mb at a random point in time – the probability of this event is 1/27, so to guarantee that no more than 1 out of 1,000,000 will be lost or suffer delay of more than a second, we must have service capacity of 3 Mbit/sec. In this case, the utilization is 1/3.

3sources

Multiplexing Gain

Input Buffer (waiting room) Server Output

nsources

From these examples, we see that the more sources we have, the higher is the utilization we can achieve. This is called “Multiplexing Gain” and it is similar to Economy of Scale.

Multiplexing Gain (continued)

Input Buffer (waiting room) Server Output

nsources

We have developed a traffic model using AT&T Internet traffic measurements taken in 1998. And we computed the required capacity for queueing probability of 1/1000000. This gives us the Utilization. We consider growth predictions and data, and we obtained the following graphs.

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More efficient Internet in the future

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More efficient Internet in the future

2005 2006 2007 Year

“Bell Labs Internet traffic discovery could point the way to more efficient networks”

FOR RELEASE WEDNESDAY JUNE 06, 2001

http://www.lucent.com/press/0601/010606.bla.html

MURRAY HILL, N.J. - A recent discovery by researchers at Bell Labs, the R&D arm of Lucent Technologies (NYSE: LU), sheds new light on the nature of Internet traffic and could lead to more efficient routers and other network components. Using sophisticated new software programs to analyze and simulate data traffic in unprecedented detail, the researchers found that the "burstiness" seen in traffic at the edges of the Internet disappears at the core.

Their surprising discovery - that traffic on heavily loaded, high-capacity network links is unexpectedly regular - may point the way to more efficient system and network designs with better performance at lower cost.

At the edge of this desert of bursty traffic which we have been traversing, while the communication infrastructure of the third millennium is put in place, there sits, just on the horizon, a land of milk and honey – the realm of integrated multi-service networks, in which all services receive good service, despite the high utilization levels on all links … and the reason things are so good in this realm is that the traffic there is Gaussian!

(Gaussian = bell shaped = smooth)

R. Addie, M. Zukerman, T. Neame, Broadband Traffic modeling: simple solutions to hard problems, IEEE Comm. Magazine, August 1998.

150 Mbit/sec

frequency

Bit rate

1000 Mbit/sec

Bursty traffic

850 Mbit/sec

frequency

Bit rate1000 Mbit/sec

Smooth traffic

It’s all about using the scraps!

Bursty traffic = low utilization and bad service

Smooth traffic = high utilization and good service

time

time

Test for consideration of new switching technologies

If your network already runs on high utilization, and provides good quality of service, do not “fix” it!!

Things get even better!

• Input rate Average delay = Average queue size Or • Average delay = Average queue size/ Input rate• Average queue size depends on the ratio of: Input rate/ output rate Thus, • Scaling upwards improves the delay!!!!

Input Buffer (waiting room) Server Output

The New Technological Concept:Optical Packet Switching

• Packet Switching but without buffers;• Packets cannot be delayed along the way.• Delay is possible at the edges. • Something between packet switching and

circuit switching.• Can it use significantly more of the scraps

than circuit switching?

Conclusion:

Two reasons for Performance improvement:

1. More sources - traffic becomes smoother.2. Scaling reduces delay.