Abstract
With the increasing demand for mobile Internet access, WLAN virtualization is becoming a promising solution for sharing wireless infrastructure among multiple service providers. Unfortunately, few mechanisms have been devised to tackle this problem and the existing approaches fail in optimizing the limited bandwidth and providing virtual networks with fairness guarantees. In this paper, we propose a novel algorithm based on control theory to configure the virtual WLANs with the goal of ensuring fairness in the resource distribution, while maximizing the total throughput. Our algorithm works by adapting the contention window configuration of each virtual WLAN to the channel activity in order to ensure optimal operation. We conduct a control-theoretic analysis of our system to appropriately design the parameters of the controller and prove system stability, and undertake an extensive simulation study to show that our proposal optimizes performance under different types of traffic. The results show that the mechanism provides a fair resource distribution independent of the number of stations and their level of activity, and is able to react promptly to changes in the network conditions while ensuring stable operation.
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Notes
In case of overlapping BSS scenarios, our mechanism can be independently implemented on each AP, as long as they employ appropriate dynamic channel assignment schemes such as, e.g., [11].
Later on we relax this assumption and demonstrate that performance is optimized even when some stations are not saturated.
Although for simplicity reasons we assume throughout the paper a fixed frame length, this assumption could be relaxed following our previous work [13].
Note that this assumption is reasonable, as large values of the transmission probability would lead to high collision probability and hence to an inefficient utilization of the WLAN.
Although in the figure we represent each VAP as a different block, they all run o the same physical device and therefore they can easily share operation parameters, e.g., sniffed frames.
The source code of the simulator used in [13, 16] is available at http://enjambre.it.uc3m.es/~ppatras/owsim/.
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Acknowledgements
This work has been partly supported by the European Community’s Seventh Framework Programme (FP7-ICT-2009-5) under grant agreement n. 257263 (FLAVIA project), and by the Spanish Government, MICINN, under research grant TIN2010-20136-C03.
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Appendix
Appendix
Theorem 1
Given the definition of e i in Eq. 14 , there exists an unique solution to the system defined by e i = 0 ∀ i that satisfies e opt = 0 and e fair,i = 0 ∀ i.
Proof
By subtracting e j from e i we obtain
and therefore, given that e i = 0 ∀ i,j, the above results in S i = S j ∀ i, j, and therefore we have that e fair,i = 0 ∀ i. Furthermore, this results in the following relation (as already expressed in Eq. 6),
which specifies, for a given (n i , n j ) pair, a one-to-one relationship between τ j and τ i ∀ i,j, and therefore we can take e.g. τ 1 as reference. In this way, if we express e opt = 0 as
we have that the rhs of the above equation is a constant between 0 and 1, while the lhs is a decreasing function of τ 1 from 1 to 0. Therefore there exists a unique solution that solves the above equation, thus ensuring also that e opt = 0. □
Theorem 2
The K P and K I relationship specified by Eq. 34 guarantees stability.
Proof
According to [33], we need to check that the following transfer function is stable
Computing the above yields
which can be expressed as
where P(z) is a polynomial and
According to [33], a sufficient condition for stability is that the zeros of the pole polynomial fall within the unit circle. This can be ensured by choosing the coefficients {a 1,a 2} that belong to the stability triangle [17]:
Equation 46 is satisfied as long as K P > K I , while Eq. 48 is satisfied if K I > 0. By operating in Eq. 47 we obtain the relationship \(K_P < -K_H^{-1} + K_I/2\), which combined with the previous relations results in the conditions expressed by Eq. 34. □
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Banchs, A., Serrano, P., Patras, P. et al. Providing Throughput and Fairness Guarantees in Virtualized WLANs Through Control Theory. Mobile Netw Appl 17, 435–446 (2012). https://doi.org/10.1007/s11036-012-0382-2
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DOI: https://doi.org/10.1007/s11036-012-0382-2