# A Revenue-Maximizing Scheme for Radio Access Technology Selection in Heterogeneous Wireless Networks with User Profile Differentiation

Elissar Khloussy, Xavier Gelabert, Yuming Jiang

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Elissar Khloussy, Xavier Gelabert, Yuming Jiang. A Revenue-Maximizing Scheme for Radio Access Technology Selection in Heterogeneous Wireless Networks with User Profile Differentiation. 19th Open European Summer School (EUNICE), Aug 2013, Chemnitz, Germany. pp.66-77, 10.1007/978-3-642-40552-5_7. hal-01497038

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# A Revenue-Maximizing Scheme for Radio Access Technology Selection in Heterogeneous Wireless Networks with User Profile Differentiation

Elissar Khloussy¹, Xavier Gelabert², and Yuming Jiang¹

¹ Department of Telematics, NTNU, Norway

² Huawei Technologies Sweden AB, 16440 Kista, Sweden

`{khloussy@item.ntnu.no, xavier.gelabert@huawei.com,`
`jiang@item.ntnu.no}`

**Abstract.** In this paper, the problem of radio access technology (RAT) selection in heterogeneous wireless networks (HWNs) is tackled from an operator's perspective, with the objective of maximizing the generated revenue. Two user profiles are considered with different priority levels. An integrated 3GPP Long Term Evolution (LTE) and Wireless Fidelity (WiFi) network is considered as an example of HWN, where LTE is used mainly for the high-priority class, while a portion of its resources, defined by a load threshold, can be shared by the low-priority class. A Markovian model is defined and validated by simulation. Subsequently, the value of the load threshold for resource sharing in LTE is investigated, and an optimization problem is formulated to find the optimal threshold for which the revenue is maximized.

**Keywords:** Heterogeneous Wireless Networks, Resource Management, Revenue Maximization.

## 1 Introduction

With the tremendous evolution of wireless network technologies and the ever increasing demand from users to be always best connected, various radio access technologies (RATs) have been standardized and deployed. It has become very likely to encounter geographical areas covered by more than one RAT, each with different characteristics in terms of latency, coverage, and link capacity. By providing more connection options than a single-RAT network, a heterogeneous wireless network (HWN) offers the operator additional tuning knobs to meet the users' needs and at the same time generate higher revenues.

In this paper, we consider the scenario of a HWN that is run by a single operator and where two RATs are integrated, namely 3rd Generation Partnership Project (3GPP) Long Term Evolution (called LTE hereafter) and Wireless Fidelity (WiFi). This network scenario is rather practical and can be found from real networks. Moreover, mobile devices and smartphones supporting both technologies are now available in the market. With these factors combined, it
becomes of interest to investigate mechanisms that allocate users' connections effectively, allowing an efficient utilization of the system resources.

In order to take advantage of the combined features of the different coexisting RATs in a HWN, a good coordination among these RATs is required. This involves the adoption of common radio resource management (CRRM) strategies, a critical factor for the success of HWNs. Among the various CRRM functionalities [1], RAT selection is known to be most fundamental. It can be *user-centric* or *operator-centric*. Typically, a user-centric RAT selection scheme considers the user's preferences as objective, such as signal strength and access cost. An operator-centric one is oriented towards maximizing the operator's interests, e.g. the overall HWN capacity, and takes into consideration the network-related parameters such as RATs' loads and capabilities as well as the existing service types [1]. In this paper, we address an *operator-centric* RAT selection with specific objective of maximizing the operator's revenue.

A thorough analysis and classification of the recently proposed radio resource management procedures in HWNs can be found in [1, 2]. In [1], the authors provided a case study that illustrated the potential gain offered by CRRM especially in terms of capacity enhancement. In [3], a CRRM scheme that minimizes the vertical handover rate and service cost while achieving the desired quality of service (QoS) was proposed. In CRRM, RAT selection functionality has gained a particular attention in the literature. For example, Gelabert et al. provided in [4] a framework to allocate services in HWNs with the help of Markov chain. The model was used to compare and evaluate the performance of various RAT selection policies that fall into three categories: service-based, load-balancing based and multi-mode terminal driven strategies. However, the users' perceived QoS was the main focus of most of the proposed RAT selection algorithms e.g., [5-7].

Very few *operator-centric* approaches with the objective of maximizing the operator's revenue can be found. In [8], a fuzzy neural-based CRRM strategy was presented. Both techno-economic cognitive mechanisms and user differentiation concepts were investigated, with the aim of guaranteeing the user satisfaction maintained at a certain target level, while also considering the network's generated revenue. However, the proposed CRRM strategy, based on a fuzzy neural network, is complex for implementation in real networks. In our early work [9], CRRM strategies based on call admission control and vertical handover were presented and compared. It was shown that a significant increase of revenue could be incurred by the adoption of CRRM policies. However, the evaluation in [9] was only based on simulation. Other admission control where decisions are taken dynamically to maximize the operator's revenue can also be found in the literature [10, 11].

In this paper, we propose a new scheme for RAT selection that is intuitive and easy to implement. In addition, the proposed approach is devised to work at a different level in the sense of providing the operator with the initial setting of an important parameter i.e., the load threshold in LTE, at the early planning phase of the system. With an appropriate setting of the load threshold, system resources can be used efficiently and the revenue be maximized. To demonstrate
its use, a specific example of HWN, which is an integrated LTE/WiFi network,
is considered. Also, for practical reasons, only two user profiles with different
priority levels are offered and a load threshold is defined in LTE to reserve
resources to the high-priority users. Importantly, an analytical model for the
proposed scheme is presented and validated by simulation. In addition, we in-
vestigate the impact of the choice of the load threshold on the revenue and solve
the corresponding optimization problem.

The paper is organized as follows. Sec. 2 describes the system model and
the proposed RAT selection scheme. In Sec. 3, the different elements of the
Markovian model are introduced. Sec. 4 presents the results obtained by the
model and the simulation. In Sec. 5 we introduce and solve the optimization
problem for finding the optimal threshold value, and Sec. 6 concludes the paper.

## 2 The System Model and User Profile-Based RAT Selection

We consider an integrated LTE/WiFi heterogeneous network. While WiFi offers
broadband data transmission for a limited coverage area at low cost and simple
control plane, LTE provides more efficient services and better QoS with wider
coverage area, at bandwidth and cost comparable to that of the WLAN [12, 13].

In the considered scenario, a user can be either residing in an area covered
by LTE only, or in a dual coverage area with a probability $P_{dual}$. Two user
profiles $C_1$ and $C_2$ are provided. Class $C_1$ has higher priority than class $C_2$.
Practically, the prioritized class $C_1$ targets the business sector, known to be
more sensitive to the perceived QoS than the charged price. The low-priority
class $C_2$ targets the individual users who care mainly about the access cost, and
don't have strict requirements with respect to the QoS. Naturally, $C_1$ users get
faster connection speed by paying higher connection fees as compared to users
belonging to $C_2$ class. In terms of admission to LTE, $C_1$ users have a privilege in
using LTE resources over $C_2$. For this purpose, a load threshold $\theta$ is defined as
the percentage of LTE capacity that the low-priority users are allowed to share
with $C_1$ users.

The RAT selection block, as illustrated in Fig. 1, requires mainly two types of
inputs: network parameters (LTE and WiFi loads and the value of $\theta$), and user
parameters (the user's class of service, and whether the user is in a dual-coverage
area or not). It generates as output the decision of admitting or blocking the
arriving session, as well as the selected RAT in the case where the admission of
the session is successful.

Based on the RATs characteristics and the considered user profile differenti-
ation, we propose the following RAT selection strategy:

- When a new $C_1$ session arrives, it is admitted to LTE as long as LTE has enough available resources. This policy reflects the operator's willingness to offer better QoS for $C_1$ users whose contribution, in terms of generated revenue, is more significant than $C_2$ users.
<figure><img src="image_2.png" /><figcaption>Fig. 1. RAT selection block.</figcaption></figure>

- When a new $C_2$ session arrives, the RAT selection module tries to admit this session into WiFi first. This way, the operator benefits from WiFi capacity to accommodate sessions belonging to the low-priority profile, keeping more resources in LTE available for $C_1$ class. In the case where the admission of the new $C_2$ session to WiFi is not possible (user out of WiFi coverage or WiFi is overloaded), and with traffic load in LTE below the threshold $\theta$, the RAT selection module allows the admission of the new $C_2$ session to LTE.

- When the load in LTE exceeds $\theta$, only $C_1$ sessions are admitted.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Algorithm for RAT selection.</figcaption></figure>
Corresponding to the above strategy, Fig. 2 illustrates the RAT selection algorithm. Note that though the proposed RAT selection scheme gives higher priority to $C_1$ class in using LTE, it also tries to keep the QoS of $C_2$ class from degrading drastically. This is realized by not allowing $C_1$ users to compete with $C_2$ users in using WiFi resources, even when LTE is overloaded.

# 3 The Analysis

The considered scenario can be modeled by the means of a 3D Markov chain. Each state $S(i, j, k)$ represents a state of the network in which $i$ sessions of class $C_1$, and $j$ sessions of class $C_2$ are being served in LTE, and $k$ sessions of class $C_2$ are being served in WiFi.

The transition from one state to another is initiated upon the arrival/departure of a $C_1$ or $C_2$ session to/from any of the two RATs. We assume the traffic generated in both classes $C_1$ and $C_2$ to be inelastic, and arriving according to Poisson processes with rates $\lambda_1$ and $\lambda_2$ respectively. As for the session holding times, they follow exponential distributions with mean values $1/\mu_1$ and $1/\mu_2$ for classes $C_1$ and $C_2$ respectively. We would like to stress that, at the session level, these assumptions are rather realistic [14].

## 3.1 The Set of Feasible States

In the proposed scenario, we assume a fixed total bandwidth for each of the RATs, namely $C_{lte}$ and $C_{wifi}$ for LTE and WiFi respectively, each being partitioned into a fixed set of basic bandwidth units (bbu) as in, e.g. [15, 16].

A state of the network is called feasible if each of its dimensions does not exceed the limit defined by the RATs capacities. Let $I$, $J$ and $K$ denote the maximum values of $i$, $j$ and $k$ that can be accommodated by the system. Since $C_1$ class has the priority in using LTE up to the totality of its resources, and so does $C_2$ in WiFi, The values of $I$ and $K$ can be defined as: $I = \lfloor \frac{C_{lte}}{b_1} \rfloor$, and $K = \lfloor \frac{C_{wifi}}{b_2} \rfloor$, where $b_i$ is the number of bbu required for a $C_i$ session, and $\lfloor x \rfloor$ is the largest integer not greater than $x$. Here, we highlight that while the main interest of network operators is to increase their revenue, it is also critical that the QoS level remains acceptable, which can be ensured with properly chosen $b_i$. There are various techniques for calculating $b_i$, and a promising technique is effective bandwidth [17], but this is out of the scope of the present paper. Here we assume $b_i$ is given.

As for $J$, it can be expressed as the minimum of two quantities, namely the maximum number of $C_2$ sessions allowed to be in LTE assuming that no $C_1$ sessions are being served in the system, and the number of $C_2$ sessions that can be admitted to LTE after serving the $i$ ongoing $C_1$ sessions. Hence, $J$ can be defined as follows:

$$J(i) = \min(\lfloor \theta \frac{C_{lte}}{b_2} \rfloor, \lfloor \frac{C_{lte} - b_1 \cdot i}{b_2} \rfloor). \quad (1)$$
<table><caption>**Table 1.** Transition rates from generic state $S(i, j, k)$.</caption><thead><tr><th>To State</th><th>Rate</th><th>Condition</th></tr></thead><tbody><tr><td>$S(i+1, j, k)$</td><td>$\lambda_1$</td><td>$i < I$</td></tr><tr><td>$S(i-1, j, k)$</td><td>$i \cdot \mu_1$</td><td>$i > 0$</td></tr><tr><td>$S(i, j, k+1)$</td><td>$\lambda_2 \cdot P_{dual}$</td><td>$k < K$</td></tr><tr><td>$S(i, j, k-1)$</td><td>$k \cdot \mu_2$</td><td>$k > 0$</td></tr><tr><td>$S(i, j+1, k)$</td><td>$\lambda_2 \cdot (1 - P_{dual})$</td><td>$j < J(i) \land k < K$</td></tr><tr><td>$S(i, j-1, k)$</td><td>$\lambda_2$</td><td>$j < J(i) \land k = K$</td></tr><tr><td>$S(i, j-1, k)$</td><td>$j \cdot \mu_2$</td><td>$j > 0$</td></tr></tbody></table>

Hence, the set of feasible states in the proposed system can be written as:

$$S = \{S(i, j, k) | 0 \le i \le I, 0 \le j \le J(i), 0 \le k \le K\}. \quad (2)$$

## 3.2 State Transitions

Having defined the set of feasible states, we need to specify the transitions between the different states in order to build the transition rate matrix **Q**. The transition rates from a given state $S(i, j, k)$ to any of its neighboring states are provided in Table 1. After creating **Q** matrix, the next step is to find the stationary probability vector. This can be obtained with the help of numerical methods, and specifically we use the Successive Overrelaxation Method (SOR) [18]. The steady state probability allows us to derive the needed performance metrics as shown in the following subsection.

## 3.3 Performance Metrics

**Average Number of Sessions** The average number of sessions admitted in the system for both classes is defined as follows:

$$E[x] = \sum_{S(i,j,k) \in S} x \cdot P_{(i,j,k)}, x \in \{i,j,k\}. \quad (3)$$

where $E[x]$ is the average value of $x$, and $P_{(i,j,k)}$ is the steady state probability for the state $S(i, j, k)$.

**Blocking Probability** By (3), the average number of users is found, which also represents the carried traffic in the system. This latter can be computed as the portion of the offered traffic $A$ ($A = \lambda/\mu$) that has been admitted successfully to the system as follows:

$$E[x] = A_{\gamma} \cdot (1 - P_{b,\gamma}), \gamma \in \{1, 2\}. \quad (4)$$

where $P_{b,\gamma}$ is the blocking probability of class $C_{\gamma}$, $x = i$ for $\gamma = 1$, and $x = j+k$ (with $E[j+k] = E[j] + E[k]$) for $\gamma = 2$. Therefore, the blocking probability of
<table><caption>**Table 2.** System Parameters.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th></tr></thead><tbody><tr><td>Capacity of LTE</td><td>C<sub>lte</sub></td><td>10</td></tr><tr><td>Capacity of WiFi</td><td>C<sub>wifi</sub></td><td>5</td></tr><tr><td>Number of bbu required per C<sub>1</sub> session</td><td>b<sub>1</sub></td><td>2</td></tr><tr><td>Number of bbu required per C<sub>2</sub> session</td><td>b<sub>2</sub></td><td>1</td></tr><tr><td>Throughput per bbu in LTE</td><td>r<sub>lte</sub></td><td>1Mbps</td></tr><tr><td>Throughput per bbu in WiFi</td><td>r<sub>wifi</sub></td><td>1Mbps</td></tr><tr><td>Arrival rate of C<sub>1</sub> class</td><td>λ<sub>1</sub></td><td>1/60 s<sup>-1</sup></td></tr><tr><td>Arrival rate of C<sub>2</sub> class</td><td>λ<sub>2</sub></td><td>1/30 s<sup>-1</sup></td></tr><tr><td>Session holding time of C<sub>1</sub> class</td><td>1/μ<sub>1</sub></td><td>200 s</td></tr><tr><td>Session holding time of C<sub>2</sub> class</td><td>1/μ<sub>2</sub></td><td>150 s</td></tr><tr><td>Dual coverage probability</td><td>P<sub>dual</sub></td><td>0.6</td></tr></tbody></table>

class $C_γ$ is computed as:

$$P_{b,\gamma} = 1 - \frac{E[x]}{A_{\gamma}}, \gamma \in \{1, 2\}. \quad (5)$$

**Throughput** The throughput of a certain class of service is the product of its carried traffic by the throughput of the total allocated bbu for this class in the serving RAT. Hence, the throughput for service class $C_γ$ can be defined as:

$$Th_{\gamma} = \sum_{\alpha} E[x] \cdot b_{\gamma} \cdot r_{\alpha}, \gamma \in \{1, 2\}. \quad (6)$$

where: $r_α$ is the throughput (in Mbps) per bbu of RAT $α$, $x = i$ for $γ = 1$, $x = j$ for ($γ = 2 \land α = \text{LTE}$), and $x = k$ for ($γ = 2 \land α = \text{WiFi}$).

# 4 Validating the Analysis

To validate the analytical model, a system-level simulation has been conducted in Matlab. The simulation was run for 5000 time units, and the same simulation repeated 100 times to get its average performance. The applied RAT selection policy in simulation follows the state feasibility conditions imposed for the Markov model. For ease of presentation, we used the settings in Table 2 to analyze the performance of the proposed RAT selection policy. The analysis may be further extended for other more realistic settings. The results are plotted in Fig. 3 and Fig. 4, with the 95% confidence intervals provided. The results show a good matching between the model and the simulation, proving the validity of our proposed Markovian model.

Fig. 3 depicts the blocking probabilities for classes $C_1$ and $C_2$, considering different values of $θ$, ranging from 0 i.e., no $C_2$ sessions can be admitted to LTE, to 1 where the whole capacity of LTE can be shared by traffic of both classes. It is shown that, when the admission to LTE is restricted to $C_1$ class solely, the
<figure><img src="image_4.png" /><figcaption>Fig. 3. $C_1$ and $C_2$ blocking probabilities for different values of $\theta$.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. $C_1$ and $C_2$ throughput variations for different values of $\theta$.</figcaption></figure>

low-priority class suffers from extremely high blocking probability. This is a consequence of the limited coverage and smaller capacity of WiFi as compared to LTE. Therefore, denying the access of $C_2$ sessions to LTE decreases their probability of being admitted to the system. However, when the admission of $C_2$ class to LTE is allowed, through an increase of the value of $\theta$, the blocking probability of $C_2$ class drops fast, leading to an enhancement of the QoS perceived by the low-priority users. On the other hand, the blocking probability of class $C_1$ is not severely affected by the admission of $C_2$ sessions to LTE.

Another performance metric is depicted in Fig. 4, namely the throughput. With the increase of the value of $\theta$, the throughput of $C_2$ sessions increases fast. This is directly related to the decrease of the blocking probability of $C_2$ class in similar conditions as discussed earlier. Also, even when $C_2$ sessions are allowed to share the entire capacity of LTE, this does not cause a dramatical decrease of the throughput of $C_1$ sessions, which are granted the double number of bbu per session as compared to $C_2$ class.

# 5 Revenue Maximization

In the previous sections, a RAT selection strategy in HWNs with profile differentiation has been proposed, and several performance metrics have been derived with the help of a Markovian model. According to the proposed scenario, the number of users that can be admitted to LTE is directly related to the value of the load threshold $\theta$. Therefore, the parameter $\theta$ plays a key role in determining the revenue generated in the overall system, and any variation of its value can cause an increase or decrease of the operator's profit. In this section, we aim to find the optimal value of $\theta$ that leads to maximizing the network revenue, while guaranteeing that the user's perceived QoS in terms of blocking probability stays below a predefined threshold $\beta$.
<figure><img src="image_6.png" /><figcaption>Fig. 5. Optimal threshold value for $\beta_1 = 5\%$ and $\beta_2 = 10\%$.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Revenue for arbitrary and optimal load thresholds, $A_1 = 0.8$ Erlang.</figcaption></figure>

Fig. 5 depicts the selected values of $\theta^*$ for different traffic loads of $C_1$ and $C_2$ classes. It shows that, for small values of $A_1$, $C_2$ class can share up to 60% of $C_{LTE}$. When $A_1$ increases, the value of $\theta^*$ decreases, and it becomes less likely to find a $\theta^*$ that solves the optimization problem.

Finding the optimal threshold has an important impact on the generated revenue. This can be deduced from Fig. 6 that depicts the revenue of the network for arbitrary load thresholds compared to the revenue achieved with the optimal threshold, for an offered traffic $A_1 = 0.8$ of class $C_1$. Fig. 6 clearly shows that the optimal threshold always achieves the highest revenue.

When the offered traffic for $C_2$ is low, e.g. $A_2 = 1.5$, an arbitrary threshold of 25% or 40% provide the same revenue as $\theta^*$. However, for a load traffic of $C_2$ profile exceeding the value of 3, a threshold of 25% is no more sufficient. It leads to significantly lower achieved revenue than the optimal threshold, because it cannot satisfy the QoS constraint for $C_2$ profile. This choice of the threshold
<table><caption>**Table 3.** Values of $P_{b,1}$ and $P_{b,2}$, $A_1 = 0.8$ Erlang.</caption><thead><tr><th></th><th></th><th>θ = 25%</th><th>θ = 40%</th><th>θ*</th></tr></thead><tbody><tr><td rowspan="2">A<sub>2</sub> = 1.1</td><td>P<sub>b,1</sub></td><td>0.33 %</td><td>0.36 %</td><td>0.31 %</td></tr><tr><td>P<sub>b,2</sub></td><td>2.2 %</td><td>0.77 %</td><td>2.52 %</td></tr><tr><td rowspan="2">A<sub>2</sub> = 3.1</td><td>P<sub>b,1</sub></td><td>0.55 %</td><td>0.99 %</td><td>0.99 %</td></tr><tr><td>P<sub>b,2</sub></td><td><b>11.3 %</b></td><td>1.52 %</td><td>1.52 %</td></tr><tr><td rowspan="2">A<sub>2</sub> = 4.1</td><td>P<sub>b,1</sub></td><td>0.61 %</td><td>1.34 %</td><td>1.30 %</td></tr><tr><td>P<sub>b,2</sub></td><td><b>16 %</b></td><td>3.44 %</td><td>3.7 %</td></tr></tbody></table>

results in blocking $C_2$ sessions, and hence deprives the operator from the profit that could be achieved from the potential admittance of the blocked $C_2$ sessions if a proper choice of the load threshold was initially made. These results are indeed consistent with the ones given by Fig. 5. Similarly, when choosing the value of 40% for the LTE load threshold, less revenue could be achieved due to blocking of $C_2$ sessions when the traffic load of this latter is high. The blocking probabilities $P_{b,1}$ and $P_{b,2}$ for the same values of $\theta$ are presented in Table 3. For targeted blocking probabilities $\beta_1 = 5\%$ and $\beta_2 = 10\%$, a choice of threshold of 25% will cause unacceptable blocking probabilities for $C_2$ class when the load of this latter exceeds the value of 3. Therefore, the network operator has interest in knowing, based on a pre-assessment of the users' load and profiles, the optimal setting of the load threshold in LTE that allows the maximum number of users to be admitted to the system and leads to the highest achievable revenue.

## 6 Conclusion

In this paper, we present an algorithm for RAT selection in HWNs where different user profiles are supported, with the objective of enhancing the system capacity and maximizing the network operator's revenue, without degrading the QoS. An LTE/WiFi heterogeneous network is chosen as a representative of HWN, and a load threshold in LTE is defined to reserve resources for the high-priority user profile. Sessions of low-priority are preferably admitted to WiFi, unless the user was not in a dual-coverage area or WiFi was overloaded. In these latter cases, LTE's load is considered to decide on whether to admit the low-priority session to LTE or reject it. A 3-D Markov model is defined to study and analyze the proposed RAT selection scheme that is further validated by simulation. Then, an optimization problem is presented, and a solution is provided in order to find the optimal load threshold that ensures the highest achievable revenue, while satisfying the blocking probability constraints. Finally, the importance of defining the optimal value of the load threshold is highlighted.

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