A Control Theoretic Approach for Throughput Optimization in IEEE 802.11e EDCA WLANs

Abstract

The MAC layer of the 802.11 standard, based on the CSMA/CA mechanism, specifies a set of parameters to control the aggressiveness of stations when trying to access the channel. However, these parameters are statically set independently of the conditions of the WLAN (e.g. the number of contending stations), leading to poor performance for most scenarios. To overcome this limitation previous work proposes to adapt the value of one of those parameters, namely the CW, based on an estimation of the conditions of the WLAN. However, these approaches suffer from two major drawbacks: i) they require extending the capabilities of standard devices or ii) are based on heuristics. In this paper we propose a control theoretic approach to adapt the CW to the conditions of the WLAN, based on an analytical model of its operation, that is fully compliant with the 802.11e standard. We use a Proportional Integrator controller in order to drive the WLAN to its optimal point of operation and perform a theoretic analysis to determine its configuration. We show by means of an exhaustive performance evaluation that our algorithm maximizes the total throughput of the WLAN and substantially outperforms previous standard-compliant proposals.

Appendix

Theorem 1

The system is stable with the proposed K _p and K _i configuration.

Proof

The closed-loop transfer function of our system is

$$ \begin{array}{lll}\label{eq-tf} S(z) & = & \frac{-C(z)H(z)}{1 - C(z)H(z)} = \\ & = & \frac{- z(z-1) H K_p - z H K_i}{z^2 + (- H K_p -1)z + H (K_p - K_i)} \end{array} $$

(44)

where

$$\label{eq-h} H = - \frac{\tau_{opt} p_{opt} \left(1 + p_{opt}\sum_{i = 0}^{m-1}{(2p_{opt})^i}\right)}{2} $$

(45)

A sufficient condition for stability is that the poles of the above polynomial fall within the unit circle |z| < 1. This can be ensured by choosing coefficients {a ₁, a ₂} of the characteristic polynomial that belong to the stability triangle [24]:

$$\label{eq-cond1} a_2 < 1 $$

(46)

$$\label{eq-cond2} a_1 < a_2 + 1 $$

(47)

$$\label{eq-cond3} a_1 > -1 - a_2 $$

(48)

In the transfer function of Eq. 44 the coefficients of the characteristic polynomial are

$$ a_1 = - H K_p -1 $$

(49)

$$ a_2 = H \big(K_p - K_i\big) $$

(50)

From Eqs. 42 and 45 we have

$$ H K_p = - 0.4 \frac{\tau_{opt}}{p_{opt}} $$

(51)

and from Eqs. 43 and 45 we have

$$ H K_i = - \frac{0.4}{0.85 \cdot 2}\frac{\tau_{opt}}{p_{opt}} $$

(52)

from which

$$ a_1 = 0.4 \frac{\tau_{opt}}{p_{opt}} - 1 $$

(53)

$$ a_2 = -0.16 \frac{\tau_{opt}}{p_{opt}} $$

(54)

Given τ _opt  ≤ p _opt , it can be easily seen that the above {a ₁, a ₂} satisfy the conditions of Eqs. 46, 47 and 48. The proof follows.