Radio Resource Management Scheme for ... - IEEE Xplore

JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 15, NO. 5, OCTOBER 2013

527

Radio Resource Management Scheme for Heterogeneous Wireless Networks Based on Access Proportion Optimization Zheng Shi and Qi Zhu Abstract: Improving resource utilization has been a hot issue in heterogeneous wireless networks (HWNs). This paper proposes a radio resource management (RRM) method based on access proportion optimization. By considering two or more wireless networks in overlapping regions, users in these regions must select one of the networks to access when they engage in calls. Hence, the proportion of service arrival rate that accesses each network in the overlapping region can be treated as an optimized factor for the performance analysis of HWNs. Moreover, this study considers user mobility as an important factor that affects the performance of HWNs, and it is reflected by the handoff rate. The objective of this study is to maximize the total throughput of HWNs by choosing the most appropriate factors. The total throughput of HWNs can be derived on the basis of a Markov model, which is determined by the handoff rate analysis and distribution of service arrival rate in each network. The objective problem can actually be expressed as an optimization problem. Considering the convexity of the objective function, the optimization problem can be solved using the subgradient approach. Finally, an RRM optimization scheme for HWNs is proposed. The simulation results show that the proposed scheme can effectively enhance the throughput of HWNs, i.e., improve the radio resource utilization. Index Terms: Common radio resource management, handoff rate, heterogeneous wireless networks, Markov process, subgradient approach.

I. INTRODUCTION Owing to the rapid development in communication and computer nowadays, many wireless communication systems continuously emerge, e.g., GSM, WCDMA, Wi-Fi, WiMAX, and LTE. To meet communication requirements, integration of these diverse networks, which is called heterogeneous wireless networks (HWNs), has become a trend for future-generation wireless networks. The objective of HWNs is to deliver ubiquitous services to the users. Nevertheless, these diverse networks differ greatly in terms of their data transmission rate, coverage, cost, and service-type support. Hence, research on HWNs mainly foManuscript received July 15, 2012; approved for publication by Tae-Kyoung (Ted) Kwon, Division III Editor, July 03, 2013. The corresponding author is Q. Zhu. This work was supported in part by the National Basic Research Program of China (973 Program: 2013CB329005), by the National Natural Science Foundation of China (61171094), by the National Science & Technology Key Project (2012ZX03003011-005, 2011ZX03005-004-03), and by the Key Project of Jiangsu Provincial Natural Science Foundation (BK2011027). The authors are with the Telecommunication and Information Engineering Department, Nanjing University of Posts and Telecommunications, No. 66, Xin Mo Fan Road, Nanjing, China, email: [email protected], shizheng0124@ gmail.com. Digital objective identifier 10.1109/JCN.2013.000092

cuses on the radio resource management (RRM) of HWNs. To provide users with satisfactory quality of service (QoS) and to improve the utilization of resources in HWNs, RRM should select a suitable network for the users on the basis of the difference among these networks. Accordingly, RRM is an important issue in the integration of HWNs. The 3GPP proposes the common RRM (CRRM) concept, which is an influential method for RRM. The specification in [1] proposed that the radio resources of HWNs can be jointly managed through a CRRM server, which can provide a comprehensive and unified RRM platform. Wu et al. [2] presented a CRRM interaction model that consists of RRM and CRRM entities. The RRM entity reports the information to the CRRM entity and performs RRM decisions, whereas the CRRM entity is responsible for combining these RRM entities and RRM decision making. The most important component of the RRM in HWNs is network selection in which the classical approach is based on multiple attribute decision making (MADM). In [3], the authors developed a handoff network decision mechanism on the basis of the analytic hierarchy process (AHP) and grey relational analysis (GRA). In the present work, the AHP is used to calculate the weights of the QoS parameters, and GRA ranks the candidate networks. Ioannis et al. [4] proposed the fuzzy technique for order preference by similarity to ideal solution (Fuzzy TOPSIS)based network selection. In the literature, the overall rating of the networks is calculated by the fuzzy set representation TOPSIS method, which can resolve the issue of inconsistency by employing conflicting decision criteria. However, most of the MADM-based network selection algorithms lack reasonable theoretical basis, and it is difficult to evaluate and adjust the HWN performance. Hence, a policy-based network selection scheme is proposed in the literature to solve these problems. In [5], the authors proposed a CRRM scheme which consists of radio access technologies (RATs) and vertical handoff (VHO) algorithms that is based on the service type and user mobility. The CRRM scheme allows low-mobility and nonreal-time service to select the WLAN or for the subscribers to choose CDMA2000 to access. In [6], the term soft load balancing was presented, and it involved both load-sharing and handoff techniques. The current work demonstrates that soft load balancing can reduce the outage probability for a given user traffic. The two main objectives of network selection are to deliver satisfactory QoS to subscribers [7] and to reasonably utilize radio resources [8]. In [9], the authors deemed that QoS is an important issue from the perspective of the users. Thus, they presented an optimal distributed network selection scheme with multimedia application layer QoS into consideration.

c 2013 KICS 1229-2370/13/$10.00

528


Most of the previous works on RAT selection have concentrated on the provision of a desired QoS for users, whereas the utilization of HWN resources and the effect of the mobility of the users on the HWN’s performance are seldom considered. Nevertheless, [10] discussed the performance of HWNs consisting of two RATs using a Markov model. By considering the network selection of the users in the overlapping region of two wireless networks, the proportion of service arrival rate that accesses each network in the region can be regarded as an optimized factor in the performance analysis of the HWNs, where the service arrival rate of each network represents the mean number of services (or calls) accessing it in a unit time. The throughput of the HWNs is maximized by choosing the appropriate factors, and the optimization problem is resolved using the golden selection method. However, the optimization algorithm cannot work if more than two wireless networks are present in the overlapping region. Because of the inadequacy of [10], the present study analyzes the performance of a complex HWN scenario consisting of more than two RANs. The throughput and blocking probability parameters are derived on the basis of the Markov process. Moreover, we propose an RRM scheme to optimize the total throughput of HWNs. The simulation results show that the proposed algorithm can effectively improve the utilization of radio resources in HWNs. The rest of this paper is organized as follows. In Section II, we first present the system model of HWNs, and the handoff rate and Markov process theory are then introduced. Section III analyzes the performance of the HWNs based on the Markov process. Section IV proposes an optimization scheme for the HWN throughput. In Section V, the simulation results show that the proposed scheme can effectively improve the utilization of HWNs. Finally, we conclude the study in Section VI. II. SYSTEM MODEL AND HANDOFF RATE A. System Model The HWNs system model and the CRRM module structure are shown in Fig. 1 [11]. The RRM entity of each network collects the parameters of the corresponding network, e.g. service arrival rate, coverage radius, and user mobile speed. Initially, the measurement is reported to CRRM server, which is in charge of processing these data. Afterward, the CRRM server sends the processed information back to each RRM entity, and the RRM entities finally perform the management of radio resource. To facilitate the analysis, we define some parameters for the HWNs as follows. We let N denote the number of networks. di defines the coverage radius of the ith network, where 1 ≤ i ≤ N . We let Ci denote the number of basic channels allocated to the ith network, and we let Ri be the data transmission rate per channel in the ith network. The service arrival of the communication system always follows the Poisson arrival process, and the service arrival rate is a key parameter in the service arrival process. Hence, we let λo denote the total service arrival rate in the overlapping region, which is shown as the shadowed area in Fig. 1. λi defines the service arrival rate of the ith network with the exception of the overlapping region. The user call duration is exponentially distributed with mean 1/µ, where µ is

Fig. 1. System model of HWNs and structure of CRRM module.

the average call completion rate. B. Calculation of Handoff Rate The mobility of the users is an important factor in the performance analysis of wireless networks, and [5] and [12] adopted the average mobile speed to calculate the cell residence time. In this study, the mobility of the users mainly affects the handoff rate of the wireless network, and the mobile feature of the users can be described from a macro perspective. Considering that the analysis of a single user mobility is unnecessary, we let denote the average mobile speed of the users. References [13] and [14] presented a formulation of the handoff rate according to the fluid flow model, but it was only applicable to the calculation of the horizontal handoff rate. Generally, the handoff rate refers to the VHO rate in HWNs. Hence, [15] provided a general formulation for the handoff rate based on the angle mobility model. The calculation methods of the vertical and horizontal handoff rates are the same under this model. The expression of the handoff rate is λh =

2qv πd

(1)

where d denotes the coverage radius of the cell, q represents the number of users, and the users are defined as those who perform ongoing communication; the same definition also applies to the following users. In addition, [15] illustrated the theory in which the number of cell users is in a dynamic equilibrium, that is, the number of users moving from the inside to the outside of the cell is equal to that moving from the outside to the inside of the cell.

SHI AND ZHU: RADIO RESOURCE MANAGEMENT SCHEME FOR HETEROGENEOUS...

Fig. 2. Markov chain for each network.

C. Markov Chain of Each Network The paper employs Markov process of time continuous and state discrete [16] to analyze the performance of HWNs, namely Markov chain. Each Markov state represents the occupied situation of channels in wireless network, namely the number of users engaged in calls. Assuming that the total basic channel number of network is denoted by C, that means the maximum number of users accessing to the network is C. The Markov chain for each network is shown in Fig. 2. The total state number of Markov chain is C + 1, because the occupied channels can be an arbitrary number from 0 to C. Let λk denote the state transmission rate from the kth state to the (k + 1)th state, namely new call arrival rate, where 0 ≤ k ≤ C −1. µl is defined as the state transmission rate from the lth state to the (l − 1)th state, namely call completion rate, where 1 ≤ l ≤ C. According to Markov chain theory, the steady state balance equations are given by λj−1 π j−1 + µj+1 π j+1 = λj + µj π j , 0 < j < C, µj+1 π j+1 = λj π j , j = 0, λj−1 π j−1 = µj π j , j = C, (2) C P j π =1

529

in the overlapping region. We let p~ represent the vector of pi , where p~ = (p1 , p2 , · · ·, pN ). p~ is the optimization factor of the HWN throughput, and the total throughput can be maximized by choosing the optimal p~. This study analyzes the performance of each network on the basis of the Markov chain theory. According to the introduction in Section II, Ci +1 Markov states are present in the ith network. The Markov chain of the ith network is analyzed as follows. We let λki denote the state transmission rate from the kth state to the (k + 1)th state for the ith network, where 0 ≤ k ≤ Ci − 1. Because the proportion of service arrival rate accessing the ith network in the overlapping region is pi , the service arrival rate of the ith network in the overlapping region is given by λio = pi λo . λki includes not only λi and λio but also the average handoff rate from the outside to the inside of the ith network. We let λhi denote the average handoff rate. Hence, λki is expressed as λki = λi + pi λo + λhi ,

πj =

1+

C X

m=1

m−1 Y k=0

λk

,m Y

l=1

µl

!!−1

×

j−1 Y

λk

k=0

III. PERFORMANCE ANALYSIS

, j Y

The steady-state distribution of the ith network can be expressed using (3) as πij

=

Ci X

!−1

m

((ξi ) /m! )

m=0

where

ξi = µl

(4)

We let µli be the state transmission rate from the lth state to the (l − 1)th state of the ith network, where 1 ≤ l ≤ Ci . µli includes the average call completion rate and the handoff rate from the inside to the outside of the ith network. Because l users exist in the ith network, the average call completion rate of the ith network can be calculated as lµ, and the average handoff rate is given by 2lv/(πdi ) according to (1). Hence, µli is calculated as 2v l , l = 1, · · ·, Ci . (5) µi = l µ + πdi

j=0

where π j is the steady-state probability of the jth state, which represents the probability of j users accessing the network or that j basic channels of the network are occupied. From (2), the steady-state distribution of the Markov chain is determined by

k = 0, · · ·, Ci − 1.

!

j

(ξi )

.

j! ,

0 ≤ j ≤ Ci

λi + pi λo + λhi . µ + 2v/(πdi )

(6)

(7)

, According to the theory of dynamic equilibrium in [15], the average handoff rate λhi can be derived. Using (6), the average 0 ≤ j ≤ C. number of users in the ith network is given as (3) Ci X (8) jπij = ξi 1 − Pib = ξi Pinb M (ξi , Ci ) = l=1

A. Steady-State Distribution of Each Network The objective of the HWNs is to maximize the system throughput to effectively utilize the radio resources. In [10], an effective optimization method was proposed to optimize the throughput of the HWNs in overlapping regions. However, this method can only apply to HWNs that consist of two wireless networks. Hence, we propose a CRRM method to maximize the throughput of the HWNs through a reasonable radio resource allocation for users in overlapping regions where more than two wireless networks exist. Here, we let pi denote the proportion of the service arrival rate accessing the ith networks

j=0

where Pib and Pinb are the blocking and non-blocking probabilities of the ith network, respectively, and Pib = 1 − Pinb = πiCi = P (ξi ) .

(9)

According to the theory of dynamic equilibrium, if Mi (ξi ) users access the ith network, the handoff rate from the inside to the outside of the network is equal to λhi . On the basis of (1), λhi can be expressed as λhi =

2M (ξi , Ci ) v 2vPinb λi + pi λo + λhi = . πdi πdi µ + 2v/(πdi )

(10)

530


From (10), we can derive the relationship between λhi and Pib as λhi =

2vPinb (λi + pi λo ) = φ Pib . b πdi µ + 2vPi

(11)

By substituting (11) into (9), Pib can be derived as Pib = P (ξi )|

(12)

b ( ) = ϕ Pi .

λi +pi λo +φ P b ξi = µ+2v πd i /( i )

This optimization problem is a convex optimization problem because the objective function is a convex function, and the feasible region is a convex set. The proof of the convexity of the objective function is given in Appendix A. Here, the subgradient method is adopted to resolve the optimization problem [17], [18], and variable α is updated according to the following expression "

α(k+1) = α(k) + s(k)

From (12), Pib is the zero point of the following function ψ (x) = x − ϕ (x) = x − P (ξi )|ξ

i=

λi +pi λo +φ(x) µ+2v /(πdi )

.

(13)

To calculate Pib when pi is determined, [10] proves that the zero point of (13) can be worked out using the bisection method. Because both Pib and λhi are functions of pi , Pib can be expressed as Pib = ~i (pi ) . (14) By substituting (14) into (11), λhi =

λhi

can be rewritten as

2v (1 − ~i (pi )) (λi + pi λo ) =λ ¯i (pi ) . πdi µ + 2v~i (pi )

(15)

B. Optimization Problem for the HWNs Throughput From the above derivation, the average total throughput of the HWNs can be given as − T (→ p)=

N X

Ri M (ξi , Ci )

i=1

=

N X

Ri (1 − ~i (pi ))

i=1

λi + pi λo + λ ¯i (pi ) . µ + 2v/(πdi )

(16)

The average total throughput of the HWNs can be maximized → by choosing an appropriate − p ; hence, it can be expressed as an optimization problem as follows max T =

N X

Ri (1 − ~i (pi ))

i=1

s.t.

N X

λi + pi λo + λ ¯i (pi ) µ + 2v/(πdi )

pi ≤ 1,

i=1

(17)

p1 , · · ·, pN ≥ 0.

According to (17), the optimization problem can be transformed into a Lagrangian problem N P +pi λo +¯ λi (pi ) → Ri (1 − ~i (pi )) λi µ+2v/(πd max L (− p , α) = i) i=1 N P −α pi − 1 , α > 0

(18)

i=1

s.t. p1 , · · ·, pN ≥ 0.

The partial derivative of (18) with respect to pi can be derived as − ∂L(→ p ,α) ∂ξi 1 − Ci + 1 − ξi Pinb Pib − α, (19) = Ri ∂p ∂pi i i = 1, 2, · · ·, N.

N X

!#+

pi − 1

i=1

.

(20)

Equation (19) is a decreasing function of pi by taking into ac2 i ,Ci ) count ∂ M(ξ < 0; hence, the bisection method is used to ∂pi 2 solve the equations → ∂L (− p , α) ~ =0 → ∂− p

(21)

iT − ∂L(→ p ,α) . ∂pN → − ∂L( p ,α) We assume that the solved roots of the equations ∂ → = − p − ∂L(→ p ,α) → − → − are defined by p ∗, where p ∗ = (p1 ∗, · · ·, pN ∗). If ∂pi

where

− ∂L(→ p ,α) − ∂→ p

=

h

− ∂L(→ p ,α) ∂p1

− ∂L(→ p ,α) ∂p2

···

~0 does not have a zero point, it can be processed as follows: If − ∂L(→ p ,α) > 0 for arbitrary pi in [0, 1], α is too small. To increase ∂pi the value of α, pi ∗ should be set to one. pi ∗ should be likewise − ∂L(→ p ,α) < 0 for arbitrary pi in [0, 1]. Hence the set to zero if ∂pi updating expression for pi ∗ can be written as  − ∂L(→ p ,α)   = 0, p , ∃p ∈ [0, 1] ∧ i i  ∂p i  − ∂L(→ p ,α) pi ∗ = (22) 1, ∀pi ∈ [0, 1] ∧ ∂pi > 0,   −  ∂L(→ p ,α)  < 0. 0, ∀pi ∈ [0, 1] ∧ ∂pi IV. OPTIMIZATION SCHEME OF THE RRM The CRRM framework comprises the RRM entity and the CRRM server. The RRM entity collects the parameters of each network. The parameters can be divided into two types: Static and dynamic parameters. The static parameter means that it can remain unchanged for a long time, such as the basic channels, coverage radius, and data transmission rate. These static parameters require no periodic measurement and can be treated as constants. However, the dynamic parameters should be measured frequently to provide optimal performance for the HWNs, e.g., service arrival rate of each network and mobile speed of the users. The dynamic parameters should be periodically sent to the CRRM server, whereas the static parameters need not be reported if their values are unchanged. After the measured information from the RRM entities is reported to the CRRM server, the CRRM server processes the measured data. Considering the convexity of the optimization problem, the subgradient approach is employed here to resolve this problem. The optimization problem turns into a solution of equations using the subgradient approach according to (21). From (19), each equation in (21) is actually a function of pi , which is independent of pj (j 6= i). In addition, considering the monotonicity


of expression (19), the bisection method can be used to solve (21) for a given α. Finally, pi is updated according to (22). In fact, the CRRM optimization problem is divided into a series of one-dimensional optimization problems through the subgradient approach; thus, the complexity of the problem is reduced. The CRRM algorithm includes three phases. The first phase is the measurement of the network parameters. The parameters are monitored by the RRM entities, including the static and dynamic parameters. Measurement mainly refers to the collection of dynamic parameters, e.g., the service arrival rate (λi and λo ) and the average mobile speed of the users (v). The static parameters are the coverage radius of the cell (di ), data transmission rate (Ri ), and number of basic channels (Ci ). Then, the measured data are reported to the CRRM server. The second phase is the processing of the reported data from the RRM entities. The CRRM server analyzes the measured data and provides an optimization scheme. According to the analysis in Section III, the main work in this phase involves providing the CRRM optimization algorithm. The detailed procedures of the proposed CRRM optimization algorithm are given as follows. (0) → Step 1: − p = p1 (0) , · · ·, pN (0) = (0, · · ·, 0) is initialized, and s(0) = 1 is set. The steady-state distribution of → each network can be obtained for arbitrary − p by solving the zero point of (13) using the bisection method; thus, Pib (1 ≤ i ≤ N ) is determined. Step 2: On the basis of the value of Pib , α(0) can be initialized by " #+ N X 1 ∂ξ i α(0) = . Ri 1 − Ci + 1 − ξi Pinb Pib N i=1 ∂pi (23) And set k = 0. → Step 3: On the basis of (21), − p ∗ is calculated by the bisection (k+1) → − method, and p is updated by (22). − (k+1) (k) → → − Step 4: If p − p < ε, then the iteration is stopped and Step 6 is performed; otherwise, Step 5 is performed. Step 5: α(k+1) is updated according to (20), and k = k + 1 is set; then, Step 3 is performed. → Step 6: The optimal allocation factor − p is obtained, where (k+1) → − → − p = p . The third phase includes performing the CRRM scheme. The CRRM server provides the CRRM scheme according to the opti→ mal allocation proportion − p . Further, the CRRM scheme is sent back to each entity, and the entities perform RRM according to the CRRM that is sent back. The users can select an appropriate network for satisfactory service delivery according to their preference, service type, and mobility feature [19], [20]. However, the RRM entities should guarantee the optimal allocation → proportion − p. V. SIMULATION ANALYSIS This section presents the simulation results of the proposed CRRM optimization algorithm. The simulation software is Matlab 7.1. In our simulation scenarios, HWNs that are composed of three RANs are employed. The three RANs are UMTS, WiMAX1, and WiMAX2, and they correspond to RANs 1, 2,

531

Table 1. The parameters of HWNs.

Parameters di (m) Ci Ri (kbps) λi (calls/s) µi (calls/s) v (m/s) λo (calls/s)

UMTS 500 10 9.6 3/60

WiMAX1 WiMAX2 500 1000 10 15 13.6 13.6 4/60 5/60 1/120 0, 5, 10 0.6/60 ∼ 3/60

and 3, respectively, as shown in Fig. 1. The detailed parameters of the HWNs are given in Table 1, and the simulation results are shown in Figs. 3–13. To explain the advantages of the proposed CRRM p~0 is employed for comparison, where algorithm, ~p = → − p = p1 p2 p3 , and p~0 = [1/3; 1/3; 1/3]. Fig. 3 shows the plot of the total throughput of the HWNs (T (~p)) versus the total service arrival rate in the overlapping region (λo ) for the optimal p~, where ~p = p~0 . The throughput of the optimal ~p is greater than that of p~ = p~0 , which illustrates that the optimization algorithm can effectively improve the utilization of the radio resource. As λo increases from 0.01 to 0.05, the throughput of the HWNs also increases because an increase in λo illustrates an increase in the users in the overlapping region, which causes enhancement of the throughput. Additionally, the throughput decreases with an increase in the user mobile speed v. The reason can be approximately analyzed as follows: By assuming that the average number of users in i λo +2Mv/(πdi ) . the ith network is M , we obtain ξi = λi +pµ+2v/(πd i) The increment in the mobile speed causes an increase in the handoff rate according to (1). If the mobile speed v has an increment ∆v and the average number of users in the ith network is approximately equal to M , the corresponding ξi ′ can λo +2Mv/(πdi ) +2M∆v/(πdi ) . From be calculated as ξi ′ = λi +piµ+2v/(πd i )+2∆v/(πdi ) ξi > ξi Pinb = M ⇒

λi +pi λo +2Mv/(πdi ) > 1, we obMµ+2Mv/(πdi ) λi +pi λo +2Mv/(πdi ) +2M∆v/(πdi ) > Mµ+2Mv/(πdi ) +2M∆v/(πdi ) ;

i λo +2Mv/(πdi ) tain λi +p Mµ+2Mv/(πdi ) ′ hence, ξi < ξi . Thus, an increase in the mobile speed is equivalent to a decrease in λo . As discussed earlier, the HWN throughput decreases. Figs. 4–6 show the proportions of the service arrival rate accessing each HWN (p1 , p2 , and p3 ) against the total service arrival rate (λo ) in the overlapping region. p1 and p2 remain almost at zero for the optimal ~p when λo < 0.017, whereas p3 remains at one, which illustrates that the throughput can be maximized only if all the users in the overlapping region access the WiMAX2 RAT. When λo > 0.017, p1 and p2 increase with an increase in λo , whereas p3 decreases for the optimal p~ because the load of WiMAX2 will be heavy if p3 remains at one, which will cause an increase in the blocking probability of WiMAX2. As a result, the increase rate of WiMAX2 gradually slows down relative to the increase rates of UMTS and WiMAX1 in terms of the throughput. To maintain the increase in the throughput of the HWNs, the CRRM server requires some users to select UMTS and WiMAX1. Hence, p1 and p2 increase whereas p3 decreases. Moreover, we can observe that p1 and p2 decrease as v increases for a given value of λo whereas p3 increases. Because the rise

532


4

1.25

x 10

0.14 Optimal p = p

v = 0 m/s

0.12

1.2

v = 0 m/s v = 5 m/s v = 10 m/s

2

0.1 Proportion p

Throughput (kbps)

0

1.15

1.1

v = 5 m/s

0.02 0.03 0.04 Service arrival rate λo(calls/s)

0.06 0.04

v = 10 m/s 1.05 0.01

0.08

0.02 0 0.01

0.05

Fig. 3. Total throughput of the HWNs versus arrival rate in the overlapping region.


0.05

Fig. 5. Proportion p2 versus service arrival rate in the overlapping region.

1

0.25

0.95 0.9

0.2 Proportion p

Proportion p1

3

0.85

0.15

0.1

v = 0 m/s v = 5 m/s v = 10 m/s

0.8 0.75 0.7 0.65 0.6

0.05

0.55 0.5 0.01

0 0.01

v = 0 m/s v = 5 m/s v = 10 m/s


0.05

0.02 0.03 0.04 Service arrival rate λ (calls/s)

0.05

o



in v will lead to a decrease in ξi following the same explanation as that in Fig. 3, it corresponds to a decrease in λo . Figs. 4 and 5 show that p1 and p2 increase with an increase in λo for a given value of v; therefore, p1 and p2 will decrease if the mobile speed v increases. Fig. 6 shows that p3 increases with an increase in λo for a given value of v; therefore, p3 will decrease if the mobile speed v increases. Figs. 7–9 show the blocking probabilities of the HWNs (P1b , P2b , and P3b ) against the total service arrival rate (λo ) in the overlapping region. P1b and P2b remain almost unchanged for the optimal ~p when λo < 0.017, but P3b increases with an increase in λo because no user accesses the UMTS and WiMAX1 RATs in the overlapping region when λo < 0.017, as shown in Figs. 4 and 5, and all the users in the overlapping region select the WiMAX2 RAT. We can also see that P1b , P2b , and P3b increase with an increase in λo for the optimal p~ when λo > 0.017, and the increase rate of P3b slows down because the users in the overlapping region begin accessing UMTS and WiMAX1, as shown in Figs. 4 and 5, which leads to an increase in their blocking probability. In addition, the increase rate of the users in WiMAX2 gradually slows down as p3 decreases, as shown in

Fig. 6. Figs. 4 and 5 also show that the blocking probability of the optimal p~ is lower than that of the specified p~0 for the UMTS and WiMAX1 RATs because the proportion of users accessing UMTS and WiMAX1 (p1 and p2 ) in the overlapping region is lower than one-third, as shown in Figs. 4 and 5. The number of users for the optimal p~ are smaller than those for the specified p~0 in the overlapping region. Hence, the blocking probability of the optimal p~ is lower than that of the specified ~p0 for UMTS and WiMAX1. However, the blocking probability of the optimal p~ is greater than that of the specified ~p0 for the WiMAX2 RAT, as shown in Fig. 9, because the proportion of users accessing WiMAX2 (p3 ) is greater than one-third; a similar explanation has been presented for the conditions shown in Figs. 7 and 8. In Figs. 10–12 show the plot of the average handoff rate of the HWNs (λh1 , λh2 , and λh3 ) versus the total service arrival rate (λo ) in the overlapping region. The average handoff rate λhi is equal to zero when the user mobile speed remains at zero, as shown in Figs. 10–12, because the users are stationary when v = 0; the users do not perform handoff without changes in the location. Hence, the handoff rate is zero for v = 0. For a given value of λo , the average handoff rate λhi increases with an increase in v, as shown in Figs. 10–12, because the mobile speed v is pro-


533

0.14

0.14

v = 0 m/s v = 5 m/s v = 10 m/s

b 3

0.12 Blocking probability P

1

Blocking probability Pb

0.12 0.1 0.08

p=p

0

0.06

v = 0 m/s v = 5 m/s v = 10 m/s

0.1 0.08

Optimal

0.06 0.04

0.04

p=p

Optimal 0.02 0.01

0


0.02 0.01

0.05

Fig. 7. Blocking probability of UMTS versus service arrival rate in the overlapping region.

Fig. 9. Blocking probability of WiMAX2 versus service arrival rate in the overlapping region.

0.1

v = 0 m/s v = 5 m/s v = 10 m/s

1

2

Blocking probability Pb

Average handoff rate λh (calls/s)

0.22

0.18

p=p

0

0.16 0.14

Optimal

0.12 0.1 0.08 0.01

0.05

o

o

0.2



0.05

o

0.09 0.08 0.07 0.06 0.05

Optimal p = p

v = 10 m/s

0

0.04 0.03 0.02

v = 5 m/s v = 0 m/s

0.01 0 0.01


0.05

o

Fig. 8. Blocking probability of WiMAX1 versus service arrival rate in the overlapping region.

Fig. 10. Average handoff rate of UMTS versus service arrival rate in the overlapping region.

portional to the handoff rate according to (1). As a result, the average handoff rate increases. Additionally, as shown in Figs. 10 and 11, the average handoff rate of the optimal p~ is lower than that of the specified ~ p0 for the UMTS and WiMAX1 RATs because the optimal p1 and p2 are lower than one-third, similar to the explanation given for the conditions shown in Figs. 7 and 8. Similarly, as shown in Fig. 9, the average handoff rate of the optimal p~ is greater than that of the specified p~0 for the WiMAX2 RAT. To illustrate the effectiveness of the proposed algorithm, we present a random HWN scenario that consists of five wireless networks. We assume that the coverage radius, data transmission rate, and channels of each network are fixed because these static parameters are always unchangeable in the real scenario. However, the service arrival rate of each network changes frequently. We suppose that the service arrival rate is uniformly distributed in a range. To show the correctness of the proposed → algorithm, a random − p is given to prove the validity of the opPN → − timal p , where i=1 pi = 1. Their coverage radii are 500, 500, 1000, 500, and 1000 m; their channels are 10, 10, 15, 10, and 15; and their data transmission rates are 384, 512, 512, 384,

and 512 kbps, respectively. The service arrival rate of each network excluding the overlapping region is uniformly distributed in the range of 2/60–5/60 calls/s, whereas the overlapping region is uniformly distributed in the range of 1/60–3/60 calls/s. The average mobile speed is 5 m/s, and the call duration is exponentially distributed with a mean of 1/120 calls/s. Fig. 13 shows the total throughput of the HWNs plotted versus time T for the optimal and random p~ ’s. The throughput of the optimal ~p is always greater than that of the random p~. Thus, the simulation results reveal the validity of the proposed CRRM algorithm. VI. CONCLUSION A CRRM scheme for HWNs has been proposed in this paper. First, the HWN model and the CRRM module are introduced. Considering that the users in the overlapping region must perform network selection, the proportion of the service arrival rate that accesses each network should be optimized to improve the utilization of the radio resources for the HWNs. On the basis of the Markov chain, the performance of each network was analyzed, and the parameters of the Markov chain were obtained

534


4

2

x 10

Optimal p Random p

0.09

1.9

0.08 0.07 0.06

Optimal p = p

v = 10 m/s

Throughput (kbps)

2

Average handoff rate λh (calls/s)

0.1

0

0.05 0.04 0.03 0.02

v = 5 m/s

1.7 1.6

v = 0 m/s

1.5

0.01 0 0.01

1.8


0.05

1.4 0

5

10

o

Fig. 11. Average handoff rate of WiMAX1 versus service arrival rate in the overlapping region.

0.07 0.06 v = 10 m/s

3

20

25

Fig. 13. Total throughput of the HWNs versus time.

arrival rate in each region by counting the users per unit time. Obviously, these dynamic parameters should be measured in a long term. These dynamic parameters also consume some traffic, computation resource, and time. However, we can use these parameters to improve the performance of the HWNs.

0.08 Average handoff rate λh (calls/s)

15 Time T

0.05

APPENDIX A

0.04 0.03 v = 5 m/s

0.02 v = 0 m/s

Optimal p = p0

0.01 0 0.01


0.05

o

Fig. 12. Average handoff rate of WiMAX2 versus service arrival rate in the overlapping region.

according to the calculation of the handoff rate and the distribution of the service arrival rate in each network. The objective of the HWNs is to maximize the total throughput; thus, we derived the total throughput according to the steady-state distribution of the Markov chain. The accessing proportion in the overlapping region was considered as an optimized factor to maximize the throughput. Finally, the optimization problem was solved using the subgradient method. The simulation results show that the proposed algorithm can effectively improve the utilization of the radio resources. All related parameters can be obtained through the CRRM framework. Two types of network parameters exist. The first type is the parameters that are always unchangeable and static during a long time, such as the data transmission rate, channels, and coverage radius. These parameters can be provided directly by each RRM entity. The second type is the parameters that are always dynamic and vary frequently. They must be periodically measured and monitored by the RRM entity and the CRRM server, such as the service arrival rate. More specifically, each RRM entity reports the users engaged in calls to the CRRM server. Then, the CRRM server analyzes the distribution of these users in the HWNs and then obtains the service

To illustrate the convexity of objective function (17), we 2 T is a negative definite should prove that the Hessian matrix ∂∂→ − p2 matrix, and

∂2 T − ∂→ p2

can be written as

2

∂ T = − ∂→ p2  2 1 ,C1 ) R1 ∂ M(ξ ∂p1 2   0   ..  .  0

0 R2 ∂

2

M(ξ2 ,C2 ) ∂p2 2

.. . 0

···

0

··· .. .

0

0

To prove the negative definite matrix of trate that

∂ 2 M(ξi ,Ci ) ∂pi 2



0 RN ∂ ∂2T , − ∂→ p2

2

M(ξN ,CN ) ∂pN 2

  .    

(A.1) we need to illus-

< 0 according to (A.1). Here, we first ∂ 2 M(ξi ,Ci ) ∂ξi 2

prove the inequality ≤ 0. The partial derivative of b Pi with respect to ξi can be derived as P b Ci − ξi Pinb ∂Pib = i . (A.2) ∂ξi ξi Then, the first-order partial derivative of M (ξi , Ci ) with respect to ξi can be derived as ∂M (ξi , Ci ) = 1 − Pib Ci + 1 − ξi Pinb . ∂ξi

(A.3)

Further, the second-order partial derivative of M (ξi , Ci ) with respect to ξi can be derived as ∂ 2 M(ξi ,Ci ) ∂ξi 2

Pb

= − ξii × Ci + 1 − ξi Pinb Ci − ξi Pinb + ξi Pib − ξi .

(A.4)


The upper and lower bounds of the blocking probability are given as follows 1 , Pib < Ci + 1 − ξi Pinb Pib >

535

After (B.2) is simplified, we can rewritten it as . (Ci − k) ξi k k! < C −1k=0 . C i P Pi k . ξi k k! ξi k!

(A.5)

Ci − ξi Pinb 1 − . ξi Ci + 1 − ξi Pinb

(A.6)

k=0

(A.7)

∂ 2 M (ξi , Ci ) < 0. ∂ξi 2

(A.8)

Then the first and second-order partial derivative of M (ξi , Ci ) with respect to pi can be derived as ∂M (ξi , Ci ) ∂M (ξi , Ci ) ∂ξi = , ∂pi ∂ξi ∂pi 2 ∂ 2 M (ξi , Ci ) ∂ξi ∂ 2 M (ξi , Ci ) = ∂pi 2 ∂pi ∂ξi 2 +

∂M (ξi , Ci ) ∂ 2 ξi ∂ξi ∂pi 2

(A.9)

=

λo µ+2v/(πdi )

× 1+

1+

2vPinb πdi µ+2vPib

2πPib di v(λi +pi λo )(Ci −ξi Pinb ) 2 πdi µ+2vPib ξi

)

(

−1

Ci X

Inequality (A.12) shows that Ci − ξi Pinb > 0; hence, that 2

∂ T − ∂→ p2

∂M(ξi ,Ci ) ∂pi

> 0 and

2

∂ M(ξi ,Ci ) ∂pi 2

k=0 2CP i −1

(A.12) ∂ξi ∂pi

> 0.

< 0. Thus, we prove

is a negative definite matrix.

ξi n (n−m)! m!

(B.4) .

Clearly, (B.4) is correct; thus (B.2) is proven. From (B.1) and (B.2), we have b nb Ci + 1 − ξi Pi,C (B.5) Pi,Ci < 1. i

nb Considering Ci + 1 − ξi Pi,C > 1, we can obtain i

1 . nb Ci + 1 − ξi Pi,C i

(B.6)

APPENDIX C

b b + Pi,C > Pi,C i −1 i

t=−

1 +t ξi

(C.1)

APPENDIX B

j=0

First, we must prove

(B.2)

nb C − ξi Pi,C i −1

ξi 2

(C.2)

b b − Pi,C ξi 2 Pi,C i −1 i nb nb Ci − ξi Pi,C . > ξi − Ci + 1 − ξi Pi,C i −1 i

After (C.3) is simplified, we obtain C C Pi (Ci +1−n)ξi n Pi ξi Ci +1 + n! N! n=0 Ci P

n=0

b We let Pi,C denote the blocking probability of the ith neti b work with Ci basic channels, and Pi,C is given according to (9) i as . ξi Ci Ci ! b nb . (B.1) = C Pi,C = 1 − Pi,C i i Pi k . ξi j!

nb C + 1 − ξi Pi,C i

which proves that

>

1 . ξi

min(C Pi ,n)

where

< 0, which illustrates that

b b + Pi,C < Pi,C i −1 i

m!(n−m)! ξi . n=0 m=max(n−Ci ,0)

! 



 n  ξi  (C.5)

536


Expression (C.5) can be proven if the (C.6) and (C.7) are correct. When n ≤ Ci , n X

n X

m (Ci + 1 − m) (Ci − n + m) > . m! (n − m)! m! (n − m)! m=0 m=0 (C.6) When n > Ci , Ci P

m=n−Ci Ci P

≥

(Ci +1−m)(Ci −n+m) m!(n−m)!

m=n−Ci

m m!(n−m)! .

+

(2Ci +1−n) N !(n−Ci −1)!

b Pi,C i

∂ξi Pb ∂Pib = i Ci − ξi Pinb . ∂pi ξi ∂pi

−2v (λi + pi λo ) (πdj µ + 2v) ∂Pib 2vPinb λo ∂λhi . = + 2 ∂pi ∂pi πdi µ + 2vPib πdi µ + 2vPib (D.3) By substituting (D.2) into (D.3), and then substituting (D.3) into ∂ξi (D.1), ∂p can be obtained as i ∂ξj ∂pi

=

λo µ+2v/(πdi )

× 1+

1+

2vPinb πdi µ+2vPib

2πPib di v(λi +pi λo )(Ci −ξi Pinb )

(πdi µ+2vPib )2 ξi

−1

(D.4) .

APPENDIX E The second-order partial derivative of ξi with respect to pi can be derived using (D.1) as ! 2 ∂ 2 λhi ∂ξi 1 ∂λhi ∂ 2 ξi ∂ 2 ξi . = + ∂pi 2 µ + 2v/(πdi ) ∂ξi 2 ∂pi ∂ξi ∂ 2 pi (E.1)

2vM (ξi , Ci ) . πdi

(E.3)

2v ∂M (ξi , Ci ) ∂λhi = , ∂ξi πdi ∂ξi

(E.4)

∂ 2 λhi 2v ∂ 2 M (ξi , Ci ) . 2 = πd ∂ξi ∂ξi 2 i

(E.5)

∂ 2 ξi ∂pi 2

can be derived

2 2v/(πdi ) ∂ 2 M (ξi , Ci ) ∂ξi ∂ 2 ξi = ∂pi 2 µ + 2v/(πdi ) ∂pi ∂ξi 2 −1 2v/(πdi ) ∂M (ξi , Ci ) × 1− . µ + 2v/(πdi ) ∂ξi Considering that 0 < 0 . nb ξ Ci + 1 − ξi Pi,C i i

From (E.1), we can obtain

∂M(ξi ,Ci ) ∂ξi

< 1, then

2v/(πdi ) ∂M (ξi , Ci ) < 1. µ + 2v/(πdi ) ∂ξi

(E.7)

∂ 2 M(ξi ,Ci ) ∂ 2 ξi are the same according ∂pi 2 and ∂ξi 2 ∂ 2 M(ξi ,Ci ) ∂ 2 ξi < 0. ∂pi 2 < 0 is proven because ∂ξi 2

The signs of (E.6). Then

(E.6)

to

REFERENCES [1] [2] [3] [4] [5]

[6] [7] [8] [9]

3GPP, “Improvement of RRM across RNS and RNS/BSS (release 5),” 2001. L. Wu and K. Sandrasegaran, “A survey on common radio resource management,” in Proc. AUSWIRELESS, 2007, p. 66. F. MA, G.-X. XU, and F.-X. YANG, “Capability adaptation algorithm based on joint network and terminal selection in heterogeneous networks,” The J. China Univ. Posts Telecommun., vol. 18, pp. 76–82, 2011. I. Chamodrakas and D. Martakos, “A utility-based fuzzy topsis method for energy efficient network selection in heterogeneous wireless networks,” Applied Soft Comput., vol. 12, no. 7, pp. 1929–1938, 2012. A. Hasib and A. O. Fapojuwo, “Analysis of common radio resource management scheme for end-to-end qos support in multiservice heterogeneous wireless networks,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2426– 2439, 2008. H. Son, S. Lee, S.-C. Kim, and Y.-S. Shin, “Soft load balancing over heterogeneous wireless networks,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2632–2638, 2008. P. Si, H. Ji, and F. R. Yu, “Optimal network selection in heterogeneous wireless multimedia networks,” Wireless Netw., vol. 16, no. 5, pp. 1277– 1288, 2010. Q.-B. Chen, W.-G. Zhou, R. Chai, and L. Tang, “Game-theoretic approach for pricing strategy and network selection in heterogeneous wireless networks,” IET commun., vol. 5, no. 5, pp. 676–682, 2011. S. Kim, “Adaptive call admission control scheme for heterogeneous overlay networks,” J. Commun. Netw., vol. 14, no. 4, pp. 461–466, 2012.


[10] Z. Shi and Q. Zhu, “Performance analysis and optimization based on markov process for heterogeneous wireless networks,” J. Electron. Inf. Technol., vol. 34, no. 9, pp. 2224–2229, 2012. [11] J. Perez-Romero and O. Salient, “Loose and tight interworking between vertical and horizontal handovers in multi-rat scenarios,” in Proc. IEEE MELECON, 2006, pp. 579–582. [12] A. Hasib and A. Fapojuwo, “Mobility model for heterogeneous wireless networks and its application in common radio resource management,” IET Commun., vol. 2, no. 9, pp. 1186–1195, 2008. [13] W. Shen and Q.-A. Zeng, “Cost-function-based network selection strategy in integrated wireless and mobile networks,” IEEE Trans. Veh. Technol., vol. 57, no. 6, pp. 3778–3788, 2008. [14] L. Wang and D. Binet, “Mobility-based network selection scheme in heterogeneous wireless networks,” in Proc. IEEE VTC, 2009, pp. 1–5. [15] Z. Shi, Q. Zhu, and S. Zhao, “A vertical handoff rate analysis based on angle mobility model in heterogeneous networks,” Signal Process., vol. 28, no. 7, pp. 1029–1036, 2012. [16] T. S. Rappaport et al., Wireless Communications: Principles and Practice. vol. 2. Prentice Hall PTR New Jersey, 1996. [17] W. Yu and R. Lui, “Dual methods for nonconvex spectrum optimization of multicarrier systems,” IEEE Trans. Commun., vol. 54, no. 7, pp. 1310– 1322, 2006. [18] D. P. Palomar and M. Chiang, “A tutorial on decomposition methods for network utility maximization,” IEEE J. Sel. Areas Commun., vol. 24, no. 8, pp. 1439–1451, 2006. [19] M. Lopez-Benitez and J. Gozalvez, “Common radio resource management algorithms for multimedia heterogeneous wireless networks,” IEEE Trans. Mobile Comput., vol. 10, no. 9, pp. 1201–1213, 2011. [20] H. Wang, L. Ding, P. Wu, Z. Pan, N. Liu, and X. You, “Qos-aware load balancing in 3gpp long term evolution multi-cell networks,” in Proc. ICC, Kyoto, Japan, 2011, pp. 1–5.

537

Zheng Shi was born in Anhui, China, in 1989. He received a B.S. degree in Communication Engineering from the Academy of Physics and Electronic Information, Anhui Normal University, Wuhu, China in 2010 and M.S. degree in Communication and Information System from the Academy of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Jiangsu, China in 2013. His research interests include network selection in heterogeneous wireless network, vertical handoff, and radio resource management.

Qi Zhu was born in Suzhou, Jiangsu, China in 1965. She received B.S. and M.S. degrees in Radio Engineering from Nanjing University of Posts and Telecommunications, Jiangsu, China in 1986 and 1989, respectively. She is currently a Professor with the Department of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications. Her research interests focus on technology of next-generation communication, broadband wireless access, OFDM, channel and source coding, and dynamic allocation of radio resources. She has worked as a Leader in several China government projects and published over 100 papers in several journals and conference proceedings.