Utility-Function Based Bandwidth Allocation Scheme in Heterogeneous Networks
Qixun Zhang1, Bin Fu1, and Hao Lian1
Key Laboratory of Universal Wireless Communications, Ministry of Education,
School of Information and Communication Engineering,
Beijing University of Posts and Telecommunications, Beijing, P.R.China, 100876.
email: [email protected], [email protected], [email protected]
1
Abstract
This paper proposes an efficient bandwidth allocation scheme to fully utilize the multi-access ability of
multi-mode terminals in heterogeneous networks. “Match-Degree” is proposed by using grey relational analysis to model
the suitability of different networks to different traffics. Two methods are designed to integrate “Match-Degree” into the
conventional utility-functions. Furthermore, the bandwidth allocation problem is formulated as maximizing the overall
utility by adjusting the bandwidth allocation considering energy consumption and network price. Based on the
optimization theory, an iterative algorithm is constructed to solve this problem and numerical results prove the
performance enhancement of proposed scheme.
Keywords: Utility-function, Match-Degree, optimization problem model, bandwidth allocation, heterogeneous networks
1. Introduction
With the explosive data rate growth and huge variety of wireless networks, heterogeneous wireless network is an
inevitable trend of next-generation wireless networks. Effectively integrating advantages of radio resources in different
networks will provide mobile users with better Quality of Service (QoS) and also enhance network performance[1].
Moreover, multi-mode terminals (MMTs) with multi-homing capabilities make these possible [2].
In literature, researches on specific bandwidth allocation can be roughly classified into two categories. The first
category focuses on physical layer problems which is not the concern of this paper. The second category addresses the
bandwidth allocation problem on or above the transport layer. The common methodology is to model bandwidth
allocation as an optimization problem [3,4]. In [5], utility index is used in heterogeneous networks to select the most
efficient network and controls the allocation of network resources. Brilliant as these works are, three disadvantages still
exist considering multi-traffic parallel transmission in heterogeneous networks. Firstly, most of these researches assume
that one traffic flow can only be transmitted through a single network, which is unfit for heterogeneous networks by
taking the advantage of the cooperation among networks. Secondly, the suitability of different networks to different
traffics is ignored. Other than bandwidth, parameters such as latency, packet loss rate are also important to Quality of
Experience (QoE). So there is a match-degree between networks and traffics. Thirdly, in practice, factors such as energy
consumption and network price should also be considered, which are neglected in existing research works.
Therefore, a match-degree based bandwidth allocation scheme for heterogeneous networks is proposed in this
paper. In section 2, the proposed match-degree and utility-function based allocation model in heterogeneous network is
introduced. In Section 3, the algorithm to solve the bandwidth allocation problem is constructed. Section 4 provides
numerical results to verify proposed schemes. Section 5 concludes this paper.
2. System Model
A typical heterogeneous network is depicted in Fig.1, where users in the geographical area are covered by four
different networks, including WCDMA, LTE and two WLANs. Assuming that all the users are multi-mode terminals and
several traffic flows are required by one user simultaneously. In this scenario, the bandwidth allocation problem is to
assign the available bandwidth of the networks to the traffic flows of each user to maximize the QoE of the users. Utility
which indicates the satisfaction a user obtained with a specific amount of bandwidth is usually adopted to measure the
QoE. Since different traffic flows vary in characteristics, their utility functions are different.
Fig.1 Typical scenario of multi-traffic and multi-user in heterogeneous networks.
2.1 Match-Degree Based Utility Function
Considering the traffic characteristics, we introduce different conventional utility function for three typical traffics
(voice, data and video) to represent user satisfaction to its allocated bandwidth. Thus the utility function of voice should
be a step function:
0 B  Bth
U voice ( B)  
(1)
1 B  Bth
Data traffic is a best-effort service and tts utility function is similar to the standard utility function in economy:
978-1-4673-5225-3/14/$31.00 ©2014 IEEE
 s1B
Bmax
U data ( B)  (1  e
)
(2)
Here Bmax is the bandwidth that achieves maximum utility. It should be noted that s1 is negative.
Video traffic is QoS-constrained. Its utility function curve should be S-shaped:
1
U video ( B) 
(3)
s2 *( B c )
1 e
where B  c is the switch point.
As mentioned above, different traffic flows have different preferences to networks. We use match-degree as a
measurement of this suitability. We assume that there are K networks, N users, M traffic. Each network has 
parameters and wk , j represents the value of jth parameter for kth network. Grey Relational Analysis Method and Grey
Relational Coefficient (GRC) are used to calculate the match-degree, which can be performed in 5 steps [4]:
1) Classifying the networks parameters by two situations (smaller-the-better, larger-the-better), wk , j
2) Defining the upper and lower bounds of the parameters
3) Normalizing the parameters, wk*, j
4) Calculating the GRC in (4),  j ,m represents the preference coefficient of mth traffic to jth parameter
5) Normalize the GRC and obtain the match-degree

GRCk ,m  1 / (   j ,m wk*, j  1  1)
(4)
k ,m  GRCk ,m / max GRCk ,m
(5)
j 1
m
Then we can get match-degree  k , m using (5), which shows the suitability of kth network to mth traffic.
Conventional utility ignores the suitability of network to traffic, namely match-degree. Therefore we use two methods to
integrate match-degree into the conventional utility function.
A. The Weighted Bandwidth Factor
Conventionally, the utility of mth traffic flow of nth user is written as U n, m ( Bn, m, k ) , where Bn, m,k is the allocated
k
bandwidth for mth traffic of nth user in kth network. We can directly use Weighted Bandwidth Factor (WBF) in (7) to
assess the “quality” of the bandwidth allocated to the traffic flow.
K
K
k 1
k 1
H m  (   k ,m  Bn,m,k ) / (  Bn,m,k )
(6)
Here H m is the WBF of the mth traffic and the range of [0,1]. It is straightforward to rewrite the conventional
utility using WBF as:
K
K
k 1
k 1
U n,m (  Bn,m,k )  U n,m (  Bn,m, K )  H m
(7)
B. The Cumulative Utility Function
Observing the utility functions in equation (2) and (3), it can be found that we can control how fast the utility
increases by adjusting the coefficients s1 and s2 . Therefore, if we define the coefficient of the most suitable network to
one traffic flow as sk , m , the coefficients of other networks to that traffic can be defined as:
sk , m  f ( k , m ) sk , m
(8)
The function f ( k , m ) can take various forms, but it has to be an increasing function in the range of [0,1] and
satisfies f ( k , m  1)  1 . In this paper, we will use f ( k , m )   k ,m for simplicity.
Therefore we propose the Cumulative Utility Function in (9) to rewrite the conventional utility function:
K
U n,m (  Bn,m,k )  U n,m,1 ( Bn,m,1 
k 1
K
 U n,m,11 (U n,m,k ( Bn,m,k )))
(9)
k 2
2.2 Utility-Based Bandwidth Allocation Problem Model
Energy consumption in user terminals is another important problem and also needs to be considered in bandwidth
allocation. Assuming the channel is AWGN, the energy consumption of base stations can be formulated as [6]:
Bn , m , k
max
PBS ( Bn,m,k )  Pbst  Pcst  [(2 Bm
Where
N0
2
 1) N 0 Bmmax ] / g  Pcst
(10)
and g are the power spectral density and the channel power gain respectively. Pcst denotes the fixed
power consumption.
Considering that users always want to get the best service with the lowest price, the price of network traffic should
be taken into account. Thus, we assume that the unit price of bandwidth in the kth network is pth .
Combining the discussions above, utility –based bandwidth allocation in heterogeneous wireless network can be
formulated as an optimal problem in (11) :
N M
K
n 1 m 1
N K
k 1
max   Cn,m (  Bn,m,k )
N M
K
N M
K
K
   U n,m (  Bn,m,k )  1    Bn,m,k  pk   2  (    Pbst ( Bn,m,k )   Pcst )
n 1 m 1
k 1
N M
s.t .
n 1 k 1
  Bn,m,k  Bkmax
n 1 m 1
K
 Bn,m,k  Bnmin
,m
n 1 m 1 k 1
(11)
k 1
k  {1, 2,3, , K }
m  {1, 2,3, M }
k 1
Bn,m, k  0 m  {1, 2,3, M } k  {1, 2,3, , K }
The utility should be written according to the method adopted. For Weighted Bandwidth Factor Method,
K
K
k 1
k 1
U n,m (  Bn,m,k ) is represented in (7), while for Cumulative Utility Function Method, U n,m (  Bn,m,k ) is in (9).
3. Optimization Solution
The single-objective optimization problem (11) can be transformed into an equivalent lagrange function:
N M
K
K
M
n 1 m 1
k 1
k 1
m 1
L( Bn,m,k , k , m )    Cn,m (  Bn,m,k )   k ( Bkmax   Bn,m,k ) 
M
K
m 1
k 1
 m (  Bn,m,k  Bnmin
,m )
(12)
Where k , m is the Lagrange factor. Based on Karush-Kuhn-Tucker (KKT) conditions (13):
L
L
 0, Bn,m,k  0, Bn,m,k 
0
Bn,m,k
Bn,m,k
Then using gradient iterative method, we have Bni ,m1 ,k  [ Bni , m,k  
(13)
L 
] . Here [ B]  max{B, 0} .  is the
Bn,m,k
non-negative length vector of iterative step.
k , m also needs to be updated , we consider the continuously differentiable dual function :
D(k , m )  max L( Bn,m,k , k , m )
(14)
Bn , m, k
Using a gradient-based search, we have：
ki 1  [ki  1
The iteration stops if
D 
]
k
i 1
i
， m
 [ m
 2
D 
]
 m
(15)
Bni ,m1 ,k  Bni ,m,k   (  is the iteration accuracy) or iterations i reach the limit, then Bni ,m1 ,k is
the optimization result.
4. Results and Analyses
The simulation scenario is depicted in Fig.1. We assume that there are three users and they can access to four
networks simultaneously. Eight traffic flows are transmitted from the networks to the users. The detailed information of
the traffic flows and networks can be seen in Table 1 and Table 2, respectively.
Table 1: Detail information of the traffic
Bmax (kbps)
Bmin (kbps)
Traffic
Data-1
300
60
User 1
Video-1
600
60
Voice-2
40
Less than 40
User 2
Data-2
200
60
Video-2
600
100
Voice-3
30
Less than 30
User3
Data-3
400
60
Video-3
900
120
Table 2: Detail information about networks
Bmax
Latency
Packet Loss
Jitter
Throughout
600 kbps
35ms
5%
15 ms
400 kbps
800 kbps
25 ms
3%
4 ms
500 kbps
Users
WCDMA
LTE
WLAN-1
WLAN-2
1200 kbps
1000 kbps
100 ms
150 ms
1%
1%
3 ms
3 ms
800 kbps
600 kbps
To evaluate the performance of proposed scheme, two other allocation schemes are chosen as comparisons,
namely the Load-Balancing scheme and the Best-Network-First scheme.
(a)
(b)
(c)
(d)
Fig.2 (a) Load Balancing, total utility 5.1958; (b) Best-Network-First, total utility 5.4098;
(c) WBF Method, total utility 6.7496;
(d) CUF Method, total utility 7.6532.
In Fig.2, it shows that the bandwidth allocation results of our proposed scheme and two comparison schemes. It
shows that the WBF Method and CUF Method tend to allocate more bandwidth from the networks with higher
match-degree to traffic, leading to higher total utilities than the other two schemes. This proves that our proposed
match-degree algorithm to consider the suitability between networks and traffic is effective. Another interesting finding
is that allocating bandwidth from multi-networks is not always good, as the performance of load balancing is the worst. It
should be noted that our algorithm will also encounter this problem if the CUF method isn't applied. And the
Best-Network-First algorithm produces poor result because it is a greedy algorithm which neglects an overview of the
entire bandwidth allocation strategy. It should also be noted that the performance increment of CUF method over WBF
method comes at a price, as the computation of utility for CUF method is complex.
5. Conclusion
In this paper, we proposed a match-degree based bandwidth allocation scheme for multi-traffic parallel
transmission in heterogeneous networks. Using Grey Relational Analysis, the “Match-Degree” which indicates the
suitability of networks to traffic is calculated. To integrate “Match-Degree” into the utility functions, two methods -Weighted Bandwidth Factor Method and Cumulative Utility Function Method -- are proposed. Energy consumption and
network price are also considered in this paper. By modeling the bandwidth allocation problem as an optimization
problem, an iterative algorithm based on optimization theory is proposed and solved. The superiority of our proposed
schemes over other schemes is proved via numerical results. Proposed bandwidth allocation schemes by considering the
suitability between networks and traffic provide useful insights on how to manage resources in heterogeneous networks
effectively.
6. References
1. Venes, Jorge, and Luis M. Correia. “Performance of a Heterogeneous Network with UMTS, Wi-Fi and WiMAX”,
EUROCON, IEEE, 2011.
2. Yiping C, Yuhang Y. “A new 4G architecture providing multimode terminals always best connected services”,
Wireless Communications, IEEE, 2007, vol. 14, no. 2, pp. 36-41.
3. Y. Choi, H. Kim, S. Han, and Y.Han. “Joint resource allocation of parallel multi-radio access in heterogeneous
wireless networks”. IEEE Transactions on wireless communications, vol. 9, no. 11, Nov. 2010.
4. K. Lin, S.Po Chou ,C. Chou. “Video Multicast with Heterogeneous User Interests in Multi-Rate Wireless Networks”,
2012 IEEE Wireless Communications and Networking Conference(WCNC), pp. 2092-2097.
5. Chan, Ho, Pingyi Fan, and Zhigang Cao. “A utility-based network selection scheme for multiple services in
heterogeneous networks”, Wireless Networks, Communications and Mobile Computing, 2005 International Conference
on. vol. 2. IEEE, 2005.
6. Xiao Ma, Min Sheng, Yan Zhang. “Green Communications with Network Cooperation: A Concurrent Transmission
Approach”, IEEE Communications Letters, vol. 16, pp. 1992-1955, 2012.