History of network traffic models

Traffic models are hence, a core component of any performance evaluation of networks and they need to be very accurate.

“Teletraffic theory is the application of mathematics to the measurement, modeling, and control of traffic in telecommunications networks.

Erlang applied the traffic models to estimate the telephone switch capacity needed to achieve a given call blocking probability.

The Erlang blocking formulas had tremendous practical interest for public carriers because telephone facilities (switching and transmission) involved considerable investments.

Over several decades, Erlang’s work stimulated the use of queuing theory, and applied probability in general, to engineer the public switched telephone network.

Teletraffic theory for packet networks has seen considerable progress in recent decades.

At the same time, traffic modeling continues to be challenged by evolving network technologies and new multimedia applications.

One important use of traffic models is to properly dimension network resources for a target level of QoS.

[9] Hence, an understanding of traffic burstiness or variability is needed to determine sufficient buffer sizes at nodes and link capacities.

For example, given a packet scheduling algorithm, it would be possible to evaluate the network performance resulting from different traffic scenarios.

It is critical that any algorithm is stable and allows multiple hosts to share bandwidth fairly, while sustaining a high throughput.

Effective evaluation of the stability, fairness, and throughput of new algorithms would not be possible without realistic source models.

However, that strategy would be overly conservative because a variable bit-rate connection may need significantly less bandwidth than its peak rate.

[8] Traffic modeling consists of three steps: Parameter estimation is based on a set of statistics (e.g. mean, variance, density function or auto covariance function, multifractal characteristics) that are measured or calculated from observed data.

The set of statistics used in the inference process depends on the impact they may have in the main performance metrics of interest.

TCP’s congestion control algorithm complicated the matter of modeling traffic, so solutions needed to be created.

Ilkka Norros devised a stochastic process for a storage model with self-similar input and constant bit-rate output.

SWING uses a surprisingly simple model for the network traffic analysis and generation.

The model examines characteristics of users, Request-Response Exchanges (RREs), connections, individual packets, and the overall network.

Autoregressive model of order p, denoted as AR(p), has the following form: Xt = R1 Xt-1 + R2 Xt-2 + ... + Rp Xt-p + Wt where Wt is the white noise, Ri are real numbers and Xt are prescribed correlated random numbers.

The auto-correlation function of the AR(p) process consists of damped sine waves depending on whether the roots (solutions) of the model are real or imaginary.

Discrete Autoregressive Model of order p, denoted as DAR(p), generates a stationary sequence of discrete random variables with a probability distribution and with an auto-correlation structure similar to that of the Autoregressive model of order p.[3] Regression models define explicitly the next random variable in the sequence by previous ones within a specified time window and a moving average of a white noise.

The memoryless Poisson distribution is the predominant model used for analyzing traffic in traditional telephony networks.

In a Poisson process the inter-arrival times are exponentially distributed with a rate parameter λ: P{An ≤ t} = 1 – exp(-λt).

The reason behind the usage stems from Palm's Theorem which states that under suitable conditions, such large number of independent multiplexed streams approach a Poisson process as the number of processes grows, but the individual rates decrease in order to keep the aggregate rate constant.

[17] This model was principally designed to recognize that address locality applies to routing decisions; that is, packets that arrive near each other in time are frequently going to the same destination.

Traffic quantity is then a superposition of packet trains, which generates substantial bursty behavior.

[14] NS-2 is a popular network simulator;[18] PackMimeHTTP is a web traffic generator for NS-2, published in 2004.

Over most time scales, the effort is a success; only a long-running simulation would allow a distinction to be drawn.