A Distributed Resource Allocation Algorithm in ...

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A Distributed Resource Allocation Algorithm in Heterogeneous Wireless Access Medium Muhammad Ismail and Weihua Zhuang Centre for Wireless Communications (CWC) Department of Electrical and Computer Engineering University of Waterloo, Ontario, Canada Email: {m6ismail, wzhuang}@bbcr.uwaterloo.ca Abstract—In this paper, the radio resource allocation in a heterogeneous wireless access medium for mobile terminals (MTs) with multi-homing capabilities is investigated. A novel algorithm is proposed for such problem. Unlike the existing solutions in literature, this algorithm does not require a central resource manager to perform the allocation. Each network can perform its own resource allocation to support MTs with multi-homing capabilities. Each MT plays an active role in the resource allocation operation by performing coordination among the available wireless access networks to satisfy its bandwidth requirement. Numerical results are presented to demonstrate the validity of the proposed algorithm. Index Terms—Heterogeneous wireless networks, resource allocation, distributed solutions, multi-homing, network utility.

I. I NTRODUCTION The future wireless communication network is expected to be a heterogeneous environment with different access technologies that differ in bandwidth, latency, coverage area or cost [1]. These different access technologies include wireless metropolitan area networks (WMANs), wireless local area networks (WLANs), cellular networks, Bluetooth, and so on. In such a heterogeneous environment, to support mobile users’ requirements and make efficient utilization of the available resources from different networks, radio resource management mechanisms for bandwidth allocation and admission control are a key issue. The problem of resource allocation in a heterogeneous environment has been studied in several works in literature. Two types of resource allocation mechanisms in such a heterogeneous environment can be distinguished. The first type utilizes a single interface of a mobile terminal (MT), so that the MT obtains its required bandwidth from a single access network. The second type utilizes multiple interfaces of an MT simultaneously to support the user’s requirement; the associate mechanisms are referred to as multi-homing solutions. The MT in this type of solutions obtains its required bandwidth from all available access networks. In this paper, the resource allocation problem in a heterogeneous wireless access environment for MTs with multi-homing capabilities is considered. A novel algorithm is proposed to address such problem. The novelty of the algorithm lies in 1 This work was supported by a research grant from the Natural Science and Engineering Research Council (NSERC) of Canada.

that it allows each network to solve its own network utility maximization (NUM) problem to find the optimum resource allocation for an MT with multi-homing capabilities. Hence, no central resource manager is required. The MT performs the coordination among different available access networks via its various radio interfaces to eventually obtain its required bandwidth. The rest of this paper is organized as follows: In the next Section, the related work is discussed. The system model is introduced in Section III. The problem formulation is presented in Section IV. The proposed algorithm is introduced in Section V. Numerical results and discussions are given in Section VI. Finally, Section VII draws the conclusion and discusses the future work. II. R ELATED W ORK The radio resource allocation problem in a heterogeneous wireless access medium is studied in [2] - [6]. The existing mechanisms can be divided into two types. The first type utilizes only a single interface of an MT, while the second type utilizes multiple interfaces simultaneously for the same application. The resource allocation solutions that belong to the first type are studied in [2] and [3]. In [2], a utility function based resource allocation scheme is introduced for code division multiple access (CDMA) cellular network and WLAN respectively. The authors of [3] propose two resource management schemes for bandwidth allocation and admission control in a heterogeneous wireless access environment for different types of traffic. The first scheme allocates the resources based on the traffic type and the bandwidth availability. In the second scheme, the resource management process is formulated as a Markov decision process. Some drawbacks of this type of solutions based on a single interface of the MT are that: 1) if no network in the service area can individually support the bandwidth requirement of the MT, the requested call is blocked; and 2) this type of solutions does not improve the system capacity of the individual networks. The resource allocation solutions for MTs with multihoming capabilities are studied in [4] - [6]. An MT with the multi-homing capability can obtain its required bandwidth using multiple wireless access technologies simultaneously. This type of solutions has the following advantages [7]: Firstly,

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it can support applications with high bandwidth requirements by aggregating the bandwidth offered by multiple networks to provide high bandwidth services using multiple threads at the application layer; Secondly, it allows for mobility support since at least one of the interfaces will remain active during the call duration; Finally, by applying the multi-homing concept, the call blocking rate is reduced and the system capacity is improved. The work in [4] and [5] introduces a radio resource management framework to support MTs with multi-homing capabilities. The framework is based on the game theory. In [6], the network utility concept is applied to allocate bandwidth to different types of traffic, depending on utility fairness, not only within a wireless access network but also among different wireless access networks. The existing resource allocation schemes in a heterogeneous wireless access medium have a limitation in that they call for a central controller to perform the resource allocation and admission control. This is not a practical solution for a business model where different networks are operated by different service providers. The existing solutions assume an external entity (the central controller) to have an authority over the network resources. A more practical solution should enable each network to solve its own NUM problem and perform its own resource allocation and admission control. In the following, a distributed solution for resource allocation in a heterogeneous wireless access environment is proposed, where each wireless access network solves its own NUM problem and performs resource allocation to support MTs with multi-homing capabilities. The MT plays an active role in the resource allocation operation by performing coordination among different access technologies to obtain its required amount of bandwidth. III. S YSTEM M ODEL The system model under consideration is similar to that in [6]. In a heterogeneous wireless access environment, three different access technologies are available, namely, IEEE 802.11 WLAN, 3G cellular network, and IEEE 802.16 WMAN, as shown in Figure 1. A geographical region that is totally covered by a WMAN base station and partially covered by a cellular base station and WLAN access point is studied. Three service areas can

be distinguished. In area 1, only WMAN service is available. In area 2, services from WMAN and cellular networks are available. In area 3, services are available from all the three networks. The different wireless access networks are operated by different service providers. MTs are assumed to have multihoming capabilities such that an MT can receive its required bandwidth from all the available wireless access networks in its service area. During a given period, MTs in one service area may move within this area, but do not make a handoff to another service area. Considering resource allocation only at the connection level, the objective is to allocate resources to a set of MTs in a particular service area from each of the available networks in that service area in a given period. This resource allocation can be performed according to the average (or steady state) connection level statistics in the different service areas [5]. As a result, a static system is considered without arrivals of new calls and departures of existing calls. Also, it is assumed that a call admission control procedure is in place [8], so that feasible resource allocation solutions exist. IV. P ROBLEM F ORMULATION In this section, the resource allocation problem in the heterogeneous wireless access environment is formulated. A distributed solution for such a problem is presented. Let uj (bij ) denotes the utility function of user j for an allocated resource bij from network i. This utility function measures the user satisfaction level towards the allocated resource from the network. The utility function can be expressed in the following form [6] uj (bij ) = ln(1 + bij ).

The utility function is concave and is suitable to model data applications, such as file downloading. The objective of network i is to maximize its total utility (satisfaction) for the users within its coverage area, given by uj (bij ) (2) Ui (bi ) = j∈ai

where Ui (bi ) is the total utility of network i, ai is the set of MTs within coverage area of network i, and bi = (bij : j ∈ ai ). The summation in (2) is established over the users within the coverage area of the network. For the geographical region in Figure 1 , the objective is to find the allocation bij that maximizes the total utility in the region, i.e., 3 Ui (bi ) (3) max bi ≥0

Fig. 1: Illustration of the heterogeneous wireless networking environment

(1)

i=1

where i = {1, 2, 3} refers to the WMAN, the cellular network and the WLAN respectively . Each network i in the geographical region is required to allocate its resources such that the total load in the area is within its capacity limitation Ci , that is bij ≤ Ci , ∀i. (4) j∈ai


The total allocated resources from different available wireless access technologies to a given MT should satisfy the MT application required bandwidth Bj , i.e., 3

bij = Bj ,

∀j.

(5)

i=1

To summarize, the resource allocation problem in the heterogeneous wireless access environment for MTs with multihoming capabilities can be expressed by the following optimization problem max bi ≥0

s.t.

3

Ui (bi ) bij ≤ Ci ,

∀i

bij = Bj ,

∀j.

(6)

j∈ai 3

h(λ, μ) =

3 i=1

bi ≥0

+

i

μj (Bj −

j

j∈ai

bij )

μj bij }. (10)

j∈ai

j∈ai

Each network now can find its optimum allocation bi for a fixed value of λ and μ by applying the Karush - Kuhn -Tucker (KKT) conditions on (11) [9], and we have (12)

Using the utility function of (1), (12) results in bij = [

1 − 1]+ λi + μj

(13)

where the notation [.]+ is a projection on the positive quadrate to account for the fact that bi ≥ 0. To find the optimum values of λ and μ to solve (13), the dual problem of (9) needs to be solved. For a given allocation bi , the dual problem can be simplified to 3 i=1

min{λi (Ci − λ≥0

bij )} +

j∈ai

j

min{μj (Bj − μ

bij )}.

i

(14) For a differentiable dual function, a gradient descent method can be applied to obtain the optimum values for λ and μ [9], given by (n+1) (n) = [λi − α(Ci − bij )]+ (15) λi j∈ai

j∈ai

(7)

i

where B = {bij } is a matrix of resource allocation, i = {1, 2, 3} , j = {1 . . . N }, N is the total number of ongoing connections in the geographical region, and bij is equal to zero if user j is not in the coverage area of network i. In (7), λ = (λi : i = {1,2,3}) is a vector of Lagrange multipliers corresponding to the capacity constraint of (4) with λi ≥ 0 and μ = (μj : j = 1 . . . N ) is a vector of Lagrange multipliers corresponding to the MT application required bandwidth constraint of (5). The dual function is defined as (8) h(λ, μ) = maxL(B, λ, μ) bi ≥0

and the dual problem corresponding to the primal problem defined in (6) is (9) min h(λ, μ). λ≥0,μ

j∈ai

∂Ui (bi ) − λi − μj = 0. ∂bij

For the utility functions defined in (1) and (2), the objective function of problem (6) is concave and the problem has linear constraints. Therefore, problem (6) is a convex optimization problem and a local maximum is a global maximum as well [9]. The problem introduced in (6) can be solved in a centralized manner, where a central controller performs the resource allocation. Such a solution, however, is not suitable for a practical situation where different networks are operated by different service providers. It is desirable to have a distributed solution for (6). The constraint defined in (5) is in fact a coupling constraint that makes it difficult to obtain a distributed solution for (6). A full dual decomposition can be introduced to (6) to obtain a distributed solution for such a problem [10] - [14]. The Lagrangian function for (6) can be expressed as Ui (bi ) + λi (Ci − bij ) L(B, λ, μ) = i

bij −

Consequently, each network can solve its own NUM problem, given by bij − μj bij }. (11) max{Ui (bi ) − λi

i=1

max{Ui (bi ) − λi

bi ≥0

i=1

Since the primal problem of (6) is a convex optimization problem, a strong duality exists [9]. Thus, the optimal values for the primal and the dual problems are equal. Hence, it is appropriate to solve (6) through its dual problem of (9). The maximization problem defined in (8) can be simplified to

(n+1)

μj

(n)

= μj

− α(Bj −

bij )

(16)

i

where n is the iteration index and α is a fixed step size. Convergence towards the optimum solution is guaranteed for a sufficiently small step size α and as long as the gradient of (14) satisfies the Lipchitz continuity condition [9]. V. A DISTRIBUTED RESOURCE ALLOCATION ALGORITHM The decomposition method applied to the optimization problem of (6) has two levels. One is a lower level where sub-problems are solved at each network to find the optimum allocation bij . These sub-problems are defined in (11) and result in the optimum solution of (13). The other is a higher level, where the master problem exists. The master problem is defined in (14) and the solution is obtained using the iterative method of (15) and (16). The master problem is to set the variables λ and μ so that the sub-problems can be solved at


as compared to the other approachs which require a central controller to reach the optimal resource allocation [4]- [6]. VI. N UMERICAL RESULTS AND DISCUSSION

Fig. 2: Decomposition of problem (6)

each network to obtain the optimum solution, as illustrated in Figure 2. The Lagrange multipliers have the following interpretations. Following the classical interpretation of λi in economics as the price of resources [10], λi is the price of network i access link in the system. It serves as an indication of the capacity limitation experienced by network i access link. When the total traffic load on network i access link in the system ( j∈ai bij ) reaches the capacity limitation, the link access price (λi ) increases to capture the fact that it is expensive to use that link. On the other hand, μj is a coordination parameter used by connection j for coordination among different available networks, so that the required bandwidth from connection j can be satisfied by these networks. The Lagrange multiplier λi is calculated at each network, based on its capacity limitation and the total load experienced in the coverage area. The Lagrange multiplier μj is calculated at each MT based on the allocated bandwidth from different wireless access networks and its required bandwidth. Then, the value of μj is broadcasted by the MT to the different available wireless access networks through the MT different interfaces, in order to obtain its required bandwidth from the networks. The distributed algorithm for resource allocation in a heterogeneous wireless access environment is described in Algorithm 1. Algorithm 1 The Distributed Resource Allocation Algorithm (0)

This section presents analytical results for problem (6) using the distributed algorithm in Algorithm 1. Consider an IEEE 802.16e based WMAN with transmission data rate of 20 Mbps. For the 3G cellular network, the total transmission rate in the cell is 2 Mbps. For the WLAN, the IEEE 802.11b is considered with the channel capacity being 11 Mbps. The average number of ongoing connections in service area 1 (N1 ) is set to be 15, to be 20 in service area 2 (N2 ) and the number in service area 3 (N3 ) varies. In each service area, half of the users have a required transmission rate of 256 kbps and the other half has a required transmission rate of 512 kbps. Figure 3 shows the total resource allocation performed by each network versus the number of ongoing connections in service area 3. The cellular network reaches its capacity limitation in the cell, independent of the N3 value. For the WMAN and WLAN respectively, the total allocation increases as the number of ongoing connections in area 3 increases, in order to satisfy the required bandwidth of the ongoing connections. At N3 = 44 the WMAN reaches its capacity limitation. Hence, for N3 ≥ 44, the WMAN allocation remains constant at 20 Mbps. As the WLAN does not reach its capacity limitation over the N3 range, its resource allocation increases with N3 since it is the only network with sufficient resources to satisfy the required bandwidth of the ongoing connections. Figure 4 shows the total resource allocation to each service area from all the available networks in that area versus the number of ongoing connections in area 3. Since the numbers of ongoing connections in service areas 1 and 2 are constant, the amounts of resources allocated to these areas are constant. The amount of resources allocated to service area 3, however, increases with the number of connections in this area, as expected.

(0)

Initialization: n ←− 0; λi ≥ 0; μj ; While(not optimal) { (n) bij = [ (n) 1 (n) − 1]+ λi +μj (n+1) (n) (n) λi = [λi − α(Ci − j∈ai bij )]+ (n) (n+1) (n) μj = μj − α(Bj − i bij ) n ←− n + 1 } Stop

The algorithm has the following features: 1) it is a distributed algorithm, where each network solves its own NUM problem and performs its resource allocation. No central controller is needed; 2) the MT plays an active role in the resource allocation operation by performing coordination among different networks to satisfy its required bandwidth. As a result, the algorithm exhibits a different treatment of the problem

Fig. 3: Total resource allocation by each network


Fig. 4: Total resource allocation to each service area

Fig. 5: Total resource allocation by each network to the three service areas

Figure 5 shows the resource allocation from each network to each service area versus the number of ongoing connections in service area 3. For service area 1, the total allocation is obtained only from the WMAN (M1) and is not affected by the variation in N3 . The allocation from the cellular network (C1) and the WLAN (L1) to service area 1 is zero since this area is out of the coverage area of the cellular network and WLAN. For service area 2, the allocation from the WLAN (L2) is zero since this area is out of its coverage area. The allocation from the cellular network to service area 2 (C2) slightly decreases as N3 increases, because more resources are allocated from the cellular network to area 3 (C3) and the total transmission rate (C2 + C3) from the cellular network is constant (2Mbps). As a result, the allocation from the WMAN to service area 2 (M2) slightly increases to compensate for the decrease in C2. However, for N3 > 44, as the WMAN reaches its capacity limitation the allocation M2 starts to decrease (to satisfy the requirements M1 in area 1) and C2 starts to increase

Fig. 6: Link access price

to compensate for the decrease. Now C3 has to decrease to allow for an increase in C2. The allocation from the WMAN (M3) and WLAN (L3) to area 3 increases as N3 increases, until the WMAN reaches its capacity limitation and stays saturated for N3 > 44. Figure 6 shows the variation in the link access price (λi ) versus the number of ongoing connections in area 3. The link access price for the WMAN is equal to zero for N3 < 44 since it has not yet reached its capacity limitation. For N3 > 44, the link access price for the WMAN increases with N3 . This indicates that it is expensive to use the link. For the cellular network, the link access price increases with N3 . Again, this is because the cellular network already reaches its capacity limitation. For N3 > 44, the rate of increase in the link access price for the cellular network increases with N3 . This is because the WMAN also reaches its capacity limitation for N3 > 44, the cellular network has to allocate less resources per user in order to accommodate more users. This calls for a more expensive link access price in the cellular network for N3 > 44. The WLAN has a zero link access price, as it has not reached its capacity limitation yet. These results follow the complementary slackness condition [9]. Figure 7 shows the resource allocations from the three networks to a user in service area 3 with a required transmission rate of 512 kbps. The allocation from the cellular network decreases as N3 increases, to accommodate more users. This is compensated by an increase in the allocation from the WMAN and WLAN in order to satisfy the user’s requirement. However, for N3 > 44, the allocation from the WMAN decreases since it reaches its capacity limitation, which is compensated by an increase in the WLAN allocation. An MT always gets its required rate (512 kbps) for the number of connections under consideration. Figure 8 shows the resource allocation for a user in area 3 with a required transmission rate of 256 kbps. The allocation comes only from the WMAN and WLAN although the user is covered by all three networks. This is because the cellular


VII. C ONCLUSION AND F UTURE W ORK

Fig. 7: Resource allocation from the networks to a user in service area 3 with 512 kbps required transmission rate

In this paper, a distributed resource allocation algorithm in a heterogeneous wireless access environment is proposed. The proposed algorithm has the following features: Firstly, each network solves its own NUM problem and performs its own allocation. As a result, no central controller is required, which is a very important feature to enable the algorithm for implementation in a practical scenario where different networks are operated by different service providers. Secondly, with multi-homing capabilities, each MT can obtain its required bandwidth from all available networks. Finally, the MTs play an active role in the resource allocation by performing coordination among different networks to allocate the required bandwidth. The convergence speed of the gradient search method for the coordination parameter μj towards the optimal solution depends on the type of the step size. A fixed step size is used in this work. Other types of step size can be employed [9]. In the future work, we will address the implementation issues of the distributed algorithm such as complexity, speed of convergence towards the optimal solution and signaling overhead. R EFERENCES

Fig. 8: Resource allocation from the networks to a user in service area 3 with 256 kbps required transmission rate

network mainly uses its resources in service area 3 to support users with a higher required rate (512 kbps). For N3 < 44 the MT has an equal resource allocation from the WMAN and WLAN. However, for N3 > 44, the allocation from the WMAN decreases due to its capacity limitation, which is compensated by an increase in the WLAN allocation. As before, each of the MTs always obtains its required rate (256 kbps). The numerical results for users in service areas 1 and 2 are omitted due to space limitation. For a user in service area 1, the resource allocation comes only form the WMAN. This is because the user is out of the coverage area of the cellular network and the WLAN. For a user in service area 2, the resource allocation comes from the cellular network and the WMAN. This is because the user is out of the coverage area of the WLAN. In all cases, users obtain the required amount of bandwidth.

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