Optimization of WLAN associations considering handover costs
 Peter Dely^{1}Email author,
 Andreas Kassler^{1},
 Nico Bayer^{2},
 Hans Einsiedler^{2} and
 Christoph Peylo^{2}
https://doi.org/10.1186/168714992012255
© Dely et al.; licensee Springer. 2012
Received: 14 February 2012
Accepted: 25 July 2012
Published: 16 August 2012
Abstract
In wireless local area network (WLAN) hotspots the coverage areas of access points (APs) often overlap considerably. Current state of the art optimization models find the optimal AP for each user station by balancing the load across the network. Recent studies have shown that in typical commercial WLAN hotspots the median connection duration is short. In such dynamic network settings the mentioned optimization models might cause many handovers between APs to accommodate for user arrivals or mobility. We introduce a new mixed integer linear optimization problem that allows to optimize handovers but takes into account the costs of handovers such as signaling and communication interruption. Using our model and extensive numeric simulations we show that disregarding the handover costs leads to low performance. Based on this insight we design a new optimization scheme that uses estimates of future station arrivals and mobility patterns. We show that our scheme outperforms current optimization mechanisms and is robust against estimation errors.
Keywords
Introduction
Many commercial wireless local area networks (WLANs) are deployed with a considerable overlap between the coverage areas of two adjacent access points (APs). Consequently, users often can choose which AP to connect to. In current systems, end users select an AP to associate with typically using the received signal strength indicator (RSSI). This leads to unequal resource usage and poor performance. Recently, especially in enterprize WLAN deployments, centralized management schemes became more and more interesting as they allow to exercise more control on the STA/AP associations. However, finding the best AP for a user station (STA) is nontrivial, as it depends on many factors such as signal strength, interference and load of the AP. Furthermore, the best AP for an STA might change over time, for example due to mobility or timevariant interference of other users.
Finding the best STA/AP selection has been studied extensively[1–6]. However, those optimization models do not consider the cost of reconfiguring the network: If an STA needs to handover from one AP to another AP, the user might experience a temporary disruption of service during the handover. In addition, signaling messages required for the handover create overhead. In networks with high dynamicity, reoptimizing the network at every change might lead to high costs through network reconfiguration and to low long term user download rates. Recent measurements have shown that in particular public WLAN hotspots exhibit a high dynamicity due to short user interarrival times and short session durations[7]. User mobility is another cause of changes in the network.
This example demonstrates that the optimal handover policy (when to handover to which AP) depends on many factors, such as the service disruption duration, the network topology, the distance and throughput between APs and STAs and the connection opportunities. Clearly, one difficulty of finding the optimal handover policy is that the best decision in the present depends on the unknown future state of the network (e.g., which AP is in reach at what time).
Related study
Optimizing STA/AP associations has been investigated in a number of works. For example,[4] attempts to characterize the capacity region of multichannel WLANs under different association policies. The authors conclude that the PHY rate and the load dependent throughput must be considered to achieve high performance.[3] presents a usercentric framework to select an AP and its operational channel. STAs exchange information with APs, which then periodically compute the optimal channel and associations. The authors remark that too frequent reoptimziation results in frequent reassociation which influences the user experience due to the hard breakdown in the reassociation process.[3] however does not aim to derive how often to reoptimize. For their simulations they reoptimize every 600 s, which seems to be very long in dynamic networks.[9] proposes a constantfactor approximation scheme for maxmin fair bandwidth allocation in WLANs. For the online optimization of networks with STAs joining and leaving the authors adopt a Hysteresis approach.[2] applies an approach, in which a reoptimization is only performed when a time or a load threshold is exceeded.[1] proposes an NPhard, nonlinear optimization problem and heuristic solution algorithm for computing proportional fair AP association in multirate WLANs.[10] presents a MILP formulation of the STA/AP association problem and implements an optimization system adapting cellbreathing concepts known from cellular networks.[11–15] propose systems for controlling STA/AP associations using simple heuristics.[16] proposes a multiobjective optimization problem that tries to avoid unnecessary handovers. However, all those approaches do not consider the costs for handovers in their optimization models.
Besides deciding when to handover to which AP, optimizing the actual handover procedure has been the focus of several works and technical standards. For example,[17] investigates how to optimize the scanning procedure for new APs. IEEE 802.11r[18] reduces the number of MAC layer frames required to perform a handover and thereby allows faster handovers. IEEE 802.21[19] specifies procedures for horizontal and vertical handovers. In this standard, a controller that resides either in the network or the client decides when to execute handovers. Handover policies (when to handover to what AP) are not part of IEEE 802.21. IEEE 802.11h[20] describes how WLANs can coexist with radars in 5 GHz band. This standard specifies frames to instruct an STA to switch AP and channels. IEEE 802.11r, IEEE 802.11h, and IEEE 802.21 still require a controller to decide when to do a handover. Nevertheless, as we will outline in the Section ‘Implementation in real networks’ those standards can support the implementation of an optimization scheme and to reduce the cost associated with each handover.
Contributions
 1.
We develop a new model to derive the optimal association strategy for STAs. The system consists of a collection of APs and STAs. The system state is described by service requests, link capacities and link interference conditions. We start by formulating a Mixed Integer Linear model, which allows to maximize the throughput of users for a given network state (later referred as “Static network model”). Based on this static network model we discuss three simple and commonly found myopic optimization schemes (variants of [14] and [2]). Myopic here means that the schemes do not consider costs of future handovers and only try to optimize the present network state. The first algorithm reoptimizes the network at every state change. The second scheme additionally allows to restrict the number of handovers at each reoptimization step. The third algorithm implements a classical hysteresis scheme, where a reoptimization is only applied if the throughput is improved by a configurable amount.
 2.
Furthermore we formulate a model (later referred as “Dynamic model”) that assumes that the future network state is known. By violating the nonanticipativity constraint (i.e., using future state information), too frequent handovers, or handovers to APs that will soon be used by other STAs can be avoided. In a practical setting, it is of course not possible to know the future network state exactly, as the state depends on random user activity. However, in simulations, where the user activity is determined apriory, the model provides an upper bound on the solution quality of the three simple schemes that do not require exact information about the future. With extensive numerical simulations we show that with respect to the upper bound the simple schemes perform reasonably well if there is little dynamicity in the network. However, if the network state changes often, e.g., due to user mobility, the schemes all exhibit low performance.
 3.
Therefore we propose an optimization scheme that uses network state estimates of the immediate future. We show that a simple interpolation from the present network state already greatly improves the performance compared to the above mentioned schemes. Our optimization model thus provides valuable insights for the design of centralized WLAN management systems. The aim of this article is not to show how such estimates of the future can be obtained (for example by using mobility predication), but to show that even if those predictions are inaccurate they can help to improve performance.
The rest of this article is organized as follows: In the Section ‘Static network model’, we model the problem of finding optimal associations and download rates in a static network setting. In the Section ‘Dynamic network model’, we extend this model to incorporate temporal network state changes, such as reassociations cause by user mobility. In the Section ‘Static optimization’, we discuss in detail the impact of disregarding handover costs in the optimization model. The Section ‘Sliding windowbased dynamic optimization’ uses the insights of the Section ‘Static optimization’ to devise a new sliding window based optimization model. Finally, we conclude the article with the Section ‘Conclusion’.
Static network model
In this section, we develop an optimization model of the network, which considers the network state at a given point of time, but not the dynamicity of changes. In the Section ‘Dynamic network model’, we extend this model to a dynamic model to incorporate changes over time.
System model and notation
The network consists of STAs and APs which are connected to the Internet. STAs download data from the Internet via the APs. Accordingly, we model the network as a set of STAs$\mathcal{S}$ and a set of APs$\mathcal{A}$. Each AP$a\in \mathcal{A}$ is connected to the Internet with a connection of capacity b_{ a }. A wireless link between AP$a\in \mathcal{A}$ and STA$s\in \mathcal{S}$ is denoted as (a,s). As typical for WLAN devices, we assume that a rate adaption scheme is in place, which chooses the best Modulation and Coding Scheme (MCS) for each link. The corresponding PHY rate of the chosen MCS on link (a,s) is denoted as p_{(a,s)}.
Important notation
Symbol  Description  Type 

$\mathcal{S}$  Set of STAs  Parameter 
$\mathcal{A}$  Set of APs  Parameter 
$\mathcal{I}$  Set of interfering links  Parameter 
$\mathcal{T}$  Set of time slots  Parameter 
(a,s)  Link between AP a and STA s  Parameter 
p _{(a,s)}  PHY rate rate on link (a,s)  Parameter 
u_{ s }(t)  Usage indicator, 1 if an STA s would like to download in slot t  Parameter 
$\mathcal{D}$  Handover cost  Parameter 
b _{ a }  Capacity of the wired link of AP a  Parameter 
r _{(a,s)}  Download rate on link (a,s)  Variable 
c _{(a,s)}  Binary selection variable if link (a,s) is used  Variable 
Variables
Furthermore, we denote the download rate that STA s uses when retrieving data from the Internet via AP a as${r}_{(a,s)}\in {\mathbb{R}}^{+}$. With download rate we refer to the rate that a user can download data with (not considering protocol overheads) and not the PHY rate. In practice, such download rates can be enforced by rate shaping at the APs and routers and/or adapting MAC layer parameters[23].
Model constraints
Equation 2 ensures that an STA is connected to at maximum one AP. Equation 3 ensures that a station can only download when it is connected. M is a large number (greater than the download rate of any STA). Equation 4 makes sure that all STAs connected to an AP cannot download more than the connection of the AP to the Internet allows. Equation 5 states that the normalized data rate of a link and the links in its collision domain cannot exceed η and thereby guarantees schedulable rates. η models the efficiency of the MAC layer protocol and is smaller or equal than 1 (we use η = 1 in the remainder of the article). Equations 6 and 7 specify the domain of the decision variables.
Solving the model
Equation 9 states that each STA must receive at least a rate of α. When κ is set to 0, the minimum download rate is maximized. However, by the definition of equation 8 it might occur that some download rates are not maximized beyond α, even if they could be increased without decreasing α. By increasing κ, more focus is put on overall network performance and less on fairness. Hence, α might be lower then. In the rest of the paper we set κ = 10^{−8} to enforce a high level of fairness and to make sure that download rates are maximized beyond α.
Equations 29 constitute a Mixed Integer Linear Program (MILP) which can be solved with MILP solvers such as CPLEX[25]. We have implemented the model in CPLEX and seen that even for a relatively large network (13 APs and 40 STAs) the problem can be solved within seconds on a normal PC (2.26 GHz Intel Core2 Duo, 4 GB RAM).
Dynamic network model
We proceed by extending the static network model to a dynamic model. The main difference between the static and the dynamic model is that the dynamic model incorporates a temporal view on the network. For example, the dynamic model considers when an STA joins the network, how the link speed changes over time and when the STA leaves the network again.
Parameters and variables
We assume that the time of interest is divided into slots of arbitrary, but equal length. Changes in the model parameters and variables only occur at the boundary between two slots. The set of slots is denoted with$\mathcal{T}$. Given a slot$t\in \mathcal{T}$, t + 1 refers to the slot following t.
Furthermore, the parameters p and$\mathcal{I}$ are now time dependent. We write p_{(a,s)}(t) to describe the PHY on link (a,s) in slot t. Similarly,$\mathcal{I}\left(t\right)$ now specifies the set of interfering links in slot t.
A STA s can only download data when it is in the connected state. A STA can only enter the connected state after it has been in the connecting state for${\mathcal{D}}_{a}^{\left(s\right)}$ time slots. In other words,${\mathcal{D}}_{a}^{\left(s\right)}$ models the service interruption duration (in time slots) when an STA s performs a handover to AP a.
Model constraints
Equation 21 ensures that the capacity of the Internet link is not exceeded. Equation 22 ensures that only connected STAs can download. Equation 23 is the capacity constraint of the wireless channel. Equations 24 and 25 state that an STA can only be associated and connected to at maximum one AP in each slot. Furthermore, an STA can only attempt to connect to an AP, if the user is requesting a service (Equation 26). Finally, Equations 27 and 28 describe the domain of the decision variables.
Objective function
Equation 16–28 and 31 are now constraints to a standard MILP with Equation 30 as objective function. By solving this MILP we can compute the optimal download rates and handover patterns in each time slot, given we know the PHY rates, collision domains and service requests for the whole system runtime.
Depending on the application scenario, other objective functions could be chosen. For example, for multimedia streaming one could try to avoid too long periods with low or zero download rate to minimize video stall times due to buffer underrun. Using a piecewise linear function, time slots with a rate smaller than a threshold can get negative, those larger than a threshold can have positive weight. Evaluating the impact of different objective functions on the solution is however out of the scope of this article.
Static optimization
As the optimization models and goals of[1, 3, 4, 9, 10] differ considerable, our goal is here not to compare those approaches directly. We will instead describe three approaches of when to invoke the optimization and reconfigure the network. We apply our static model with those approaches and compare the performance to the upper bound provided by the dynamic model (which assumes perfect knowledge of the future).
Invocation strategies
Greedy
The Greedy scheme computes the solution to the static model in every time slot. It does not consider the current state of an STA (connected or not). It greedily tries to optimize the network configuration in the present state, not considering any implications on the future performance of the network. If the computed optimal network configuration differs from the current configuration, the required changes to implement the optimal configuration are applied accordingly. This invocation strategy is for example proposed in[14].
In the example network depicted in Figure1 the greedy scheme produces the same results as “Scheme A”. No interference from other STAs is present and therefore according to the Greedy Scheme it is best to download from the AP with the highest PHY rate.
kHandover
The kHandover scheme extends the Greedy scheme by adding an additional constraint that specifies that at maximum k handovers can be performed using one slot. As handovers induce service disruption it might be beneficial to limit the number of handovers.
Hysteresis
The Hysteresis scheme aims to avoid flapping of configurations and reconfigurations that might only yield minor improvements. In this scheme, the solution quality of the current network configuration$\widehat{\alpha}$ (without changing associations) and the optimal solution α^{∗} are computed. The optimal solution is then applied if${\alpha}^{\ast}>\widehat{\alpha}/f$. Typically, f is chosen between 0 and 1. A value close to 0 requires a large improvement over the current solution in order to be applied. This might lead to a small number of handovers, but might operate the network in a suboptimal configuration. In contrast, a value close to 1 might cause a larger number of handovers. This variant of this invocation strategy is for example used in[2].
In the example network of Figure1, if the user starts walking from the 18 Mbit/s zone of AP1 to the intersection of the 6 Mbit/s zone of AP1 and the 18 Mbit/s zone of AP2, the solutions are α^{∗} = 18 and$\widehat{\alpha}=6$. For f < 1/3, a handover to AP2 would be triggered.
Evaluation
Next we evaluate the performance of the invocation strategies presented above and the impact of different parameters such as user mobility considering reconfiguration cost. Our key findings are that

User mobility has a significant impact on the performance of the invocation strategies.

With low mobility, a Hysteresis based scheme performs well.

The impact of the handover cost on performance depends on the user mobility.
Evaluation settings
We used CPLEX[25] and a set of custommade simulation scripts^{a} to numerically evaluate the performance of the different schemes. In each time slot the static optimization problem is solved and the solution is applied according to the invocation strategy under investigation. The size of dynamic model grows proportionally with number of time slots. In order to solve the model fast and to be able to run a large set of different scenarios, the number of time slots should not be too large. A short slot length is a more accurate representation of the reality, in which the network state changes continuously and not only at slot boundaries. However, short slot lengths lead to a large number of slots when simulating a long time period. In our simulations, time slots are 1 second long and the network is simulated for 120 slots. During this time, each user randomly generates one traffic request within the first 30 s and aims to download data from the Internet via an AP for at least 50 s. Each simulation was repeated 30× with different random STA positions and mobility patterns.
Evaluation metric and statistical analysis
Recall that α denotes the minimum throughput of all stations and the optimal value of α computed with the dynamic network model is called α^{∗}. Hence, the normalized performance ranges between 0 and 1, where a value of 1 means that the respective heuristic is as good as the optimum solution. The plots below show the average (errorbars are standard deviation) of the 30 repetitions.
Impact of user mobility and network size
Handovers of STAs are typically necessary due to user mobility and due to newly arriving STA. To evaluate the impact of both effects, we first simulated a network with 40 STA, of which 0, 10, 20, 30, or 40 STAs are moving at a speed of 1 m/s and the rest are static. The handover cost$\mathcal{D}$ is 3 for all handovers, i.e., a handover results in 3 time slots where no data can be downloaded.
With no STA mobility, the gap between the heuristics and the optimum is caused by two effects: first, even in absence of mobility, handovers might be required when STAs join or leave the network. The heuristics do not find the best points in time for those handovers. Second, the heuristics maximize the fair throughput in each time slot. In order to maximize the long term average fair throughput, the dynamic model allows temporary unfairness. As mobility increases the timing of handovers gets more important and hence the performance of the heuristics drops.
The performance of the Greedy and the kHandover scheme is identical. We found that the kHandover scheme does not really avoid handovers, it just delays them to the next time slot (if there are already k handovers in the current time slot).
Figure4 furthermore shows that for a fixed speed (e.g., 0 m/s), the performance decreases if the number of STAs in the network is increased. A larger number of STAs causes more dynamicity in the network, e.g., through new STA arrivals. Each time the state of the network changes, the discussed invocation strategies might trigger a handover, even if it might be better to remain in the current network configuration for a while and only change the STA/AP associations later.
Impact of handover cost$\mathcal{D}$
The interruption due to handovers depends on many factors, such as the used hardware and encryption scheme. For commercial enterprize WLANs or hotspots the interruption is in the order of a few hundred milliseconds to a few seconds[27–29]. When further taking into account the interruption due to TCP timeouts and packet losses, 2–4 s are a realistic range[30].
We would like to note that a constant normalized performance as seen with the Hysteresis scheme does not necessarily reflect a constant absolute throughput. For example, in the case of 1.5 m/s station speed, the normalized throughput remains almost constant regardless of the handover cost. The absolute throughput however drops from 2.2 to 1.5 Mbit/s.
Impact of hysteresis parameter f
If there is no mobility in the network (speed 0 m/s), only a few handovers are required due to station arrivals. So, even a small improvements due to a handover (which are infrequent in this setting) should be exploited as the network state is stable for a longer time afterwards. Hence a large f is better in such a situation. With higher mobility the opposite is true: smaller values for f are better. For example, when nodes move with 1.5 m/s, f = 0.7 gives best performance and chooses the optimal amount of handovers. However, the normalized performance then does not exceed 0.2, showing that not only the number of handovers matters. The rate allocation and the actual choice of the STA/AP associations are more important.
Impact of handover limit k
Discussion
The numerical evaluation has shown that the proposed invocation strategies work well as long as there is no user mobility. In that case, 70–80% of the bound given by the dynamic model are achievable. However, when the users are mobile, the performance quickly drops below 20%. A detailed analysis of the handover patterns has revealed that indeed the reasons for this low performance are too frequent handovers (as illustrated in the motivating example of the Section ‘Introduction’) or handovers to APs that will soon be used by other STA. Sometimes it is better, if an STA does not immediately handover to the AP with the highest signal strength, but remains at the current one (even if the signal strength and the resulting MCS are lower). We apply this insight in the following section, where we develop a sliding window scheme that estimates the immediate future networks states and incorporates this in the handover decisions.
Sliding windowbased dynamic optimization
In this section, we develop and evaluate a sliding windowbased scheme. They key ideas of this scheme are to use predictions of the immediate future and to consider amount of data a STA has already downloaded in the past. This allows to avoid too frequent handovers and to compute a better the rate allocation. The scheme does not include or depend on any specific method to predict the future network state. We show that already a simple prediction method of the future network state is useful, even if the predictions are erroneous. Developing more sophisticated estimation methods are out of the scope of this article.
Sliding window method
With${r}_{(a,s)}^{\ast}\left(t\right)$ (where$t\in {\mathcal{T}}_{m})$ we denote the download rate of STA s from AP a during time slots prior to the current time slot. Hence, it is not a variable (since we cannot change the past), but a parameter. The parameters p_{(a,s)}(t) and u_{ s }(t) for times t_{ c } + W_{ p } + 1 > t > t_{ c }are not known and need to be estimated. Different techniques are available to estimate those parameters. Each one comes at different cost and achieves different accuracy. For example, one could utilize mobility prediction techniques[33] or machine learning techniques such as Support Vector Machines[34] for the parameter estimation. We would like to point out that our approach is independent of the prediction technique.
Evaluation
We evaluated the sliding window method using the setup of the Section ‘Evaluation’ in a network with 10 STA moving at 1.5 m/s. Under those settings the invocation strategies of the Section ‘Evaluation’ reach at maximum 35% of the upper bound. We compare the performance of the sliding window method with different prediction window sizes W_{ p }(W_{ m } is set to 120 for all simulations) and prediction errors. We assume that parameters can be estimated with higher accuracy in the immediate future than in distant future. Hence, the probability that a predicted parameter at slot t ≥ t_{ c } is not equal to the actual parameter can be described as$1{(1e)}^{t{t}_{c}}$, where e∈[0…1] models the accuracy of the prediction. Furthermore, we implement a simple prediction method, where we set p_{(a,s)}(t) = p_{(a,s)}(t_{ c }) and u_{ s }(t) = u_{ s }(t_{ c }), i.e., we assume that using the present network state will remain unchanged during whole prediction window. We call this estimation “Simple Estimation”.
Surprisingly, a larger window is not always better. For example on average W_{ p }= 10 is better than W_{ p }= 20. A larger window sometimes results in handovers to accommodate for a change in the network state in future (e.g., after 17 slots), which is not nonoptimal compared to a very large window. However, the smaller window cannot “see” that network state change, as it is outside the prediction window.
Introducing errors to the prediction makes the performance worse. However, even with a large error probability in the prediction (e = 0.20 means that at 5 slots in the future the state is wrongly estimated with 67% likelihood) good performance gains can be achieved. However, it seems not to be beneficial to extend the prediction window to more than 5 slots, as the error probability gets too high then.
The simple estimation method works relatively well for small prediction windows. With W_{ p }= 5 approximately 65% of the normalized performance can be achieved. This is an increase of 15% compared to W_{ p }= 0 and 30% compared to the Hysteresis scheme.
Implementation in real networks
The aim of this article is not to present any practical implementation of the proposed schemes. However, we would like to emphasize that the sliding window scheme can be implemented in enterprise WLANs and public hotspots. For example,[35],[13] or[14] present management architecture proposals for implementing an AP selection scheme in WLANs or mesh connected WLANs. They include central control servers, which collect monitoring information and could in principle execute our optimization scheme. IEEE 802.11k[36], a recent IEEE standard that describes the exchange of monitoring information between APs and STAs, can be used to obtain information about available connection opportunities and interference from the STA. IEEE 802.21 or IEEE 802.11h could be used to trigger handovers.
Conclusion
In this article, we have investigated the AP/STA association selection and rate control problem under dynamic network conditions. We have demonstrated that disregarding the costs of handovers and network reconfiguration results in performance degradations of up to 80%. In particular short session durations and user mobility contribute to this performance degradation. As devices with instant on feature, such as smartphones and tablet PCs, get more common, short sessions and mobility play a more important role.
We have developed an optimization scheme that takes into account estimates of the future network state. By predicting future states and using this information during the optimization better decisions can be done which translate into higher performance, even if the predictions are not accurate. Our scheme is independent of the estimation method and can therefore be applied in scenarios that favor different estimation methods. The window based model can be adapted for other static optimization models that currently do not take into account the cost of handovers (for example[3] or[1]). Thereby those models can deliver improved performance in networks with high dynamicity.
Endnote
^{a}Available for download athttp://www.cs.kau.se/~pdely/downloads/
Declarations
Authors’ Affiliations
References
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