IEEE 802.11p Empirical Performance Model from Evaluations on Test Tracks
IEEE 802.11p Empirical Performance Model from Evaluations on Test Tracks
Sébastien Demmel, Alain Lambert, Dominique Gruyer, Grégoire S. Larue, Andry Rakotonirainy
contact: sebastien.demmel@qut.edu.au; dominique.gruyer@ifsttar.fr;
With the data linked to in this page, one can apply the model we developed to simulate the frame loss and range performance of IEEE 802.11p vehicle--to-vehicle communications. The model generates a frame loss profile that gives the frame loss probability at a given distance from the emitter (more information below). We only present here the profile generation mechanism; the management of related tasks, such as deciding when to generate profiles or managing existing profiles must be implemented independently.
Frame loss profile model
A profile represents a single uninterrupted connection between two IEEE 802.11p devices and is used to determine the frame loss probability at any given distance, as long as they are within range (that is, as long as frame loss is under 100%). This mechanism is useful to cover the large performance variations we measured during our evaluation of 802.11p. A single frame loss profile tau is described by equation (1) where d is the distance between the emitter and receptor; and A, B,... F are parameters estimated from empirical data. An instance of an obtained profile compared to a typical individual measurement run (taken at 70 km/h) is shown on Fig.1.
(1) tau=max[ A.expB.(d-C)2, min( max[D.d+E,F], 1 ) ]
Speed Classes
We created four classes of individual frame loss profiles, which are classified according to the relative speed between the emitter and receptor:
{ speed }={ [0;40], [40;60], [60;100], [100;160] }
For each class, the experimental data show that D and E are linearly correlated. The other parameters are assumed to be independent. The relationship between D and E is given by a Generalised Linear Model regression from the observed values of D and E:
(2) E =alpha.D + beta + e --> N(0,sigma)
For each class and each parameter A, B, C, D, F (excluding E), a non-parametric probability density estimate is computed: the continuous distribution A, B, C, D, F of each parameter A, B, C, D, F is computed with a Gaussian kernel smoothing method (the distribution E of the parameter E can be obtained through its linear correlation with D).
Generating a profile
The parameters’ distributions mentionned above are then used to generate realistic random parameters for the frame loss profile model. To generate sets of parameters, the inverse transform sampling method is used. The A, B, C, D, F distributions for each class are transformed into cumulative distribution functions Gx where x={A, B, C, D, F}. These cumulative distributions are then used as follows:
- For each x in {A, B, C, D, F} // x is a parameter and x its distribution
- u <- U(0,1) // a random number u is generated from the uniform distribution U([0,1])
- x <- G-1x(u) // a parameter receives the value from its inverse cumulative distribution
- End For
- E <- alpha.D + beta + e // E is obtained from the linear relationship that links it to D, where alpha and beta are the regression parameters and e is the Gaussian noise e --> N(0,sigma)
- tau=max[ A.expB.(d-C)2, min( max[D.d+E,F], 1 ) ] // Once each parameter has been assigned a value, tau can be processed from the values with Eq.1.
Parameters distributions data
In order to easily generate profile, we provide the cumulative distribution functions Gx for x={A, B, C, D, F} in the attached Excel file DistributionsCorrelationsParameters.xlsx. In the file, there are one tab per each parameter A, B, C, D, F and a additional tab for the correlation between D and E.
Each tab is organised as follows: each speed class (named on top) corresponds to two columns; the column labelled with the name of the parameter provides the x-axis value for the distribution Gx (that is, the actual values that can be taken by parameter x), the column labelled CDF provides the y-axis value for the corresponding x-axis value. This can be used to graph each Gx for x={A, B, C, D, F} or create variables in Matlab and similar software, as shown in Fig.2 for each parameter in the “low speed” class.
The tab describing the correlation between D and E reminds equation (2) at first, then gives the alpha, beta and sigma parameters for each of the four classes.
