## 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.

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## Notes

The reader is referred to [18] for a detailed justification of these configuration choices.

Following [2], by saturation we mean that a station always has a packet ready for transmission.

Although the 802.11e parameters are configurable, the standard includes a default setting for these parameters [16].

A similar approach was used in [19] to analyze RED from a control theoretical standpoint.

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## Acknowledgements

The work described in this article has been partially supported by the European Community’s Seventh Framework Programme under the ICT FP7 Integrated Project CARMEN (INFSO-ICT-214994) and by the Spanish Government under the POSEIDON project (TSI2006-12507-C03). Apart from this, the European Commission and the Spanish Government have no responsibility for the content of this paper. The authors would like to thank the reviewers for their valuable comments which helped improving this paper.

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## Appendix

### 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

where

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]:

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

and from Eqs. 43 and 45 we have

from which

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.

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Patras, P., Banchs, A. & Serrano, P. A Control Theoretic Approach for Throughput Optimization in IEEE 802.11e EDCA WLANs.
*Mobile Netw Appl* **14**, 697–708 (2009). https://doi.org/10.1007/s11036-008-0121-x

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DOI: https://doi.org/10.1007/s11036-008-0121-x