Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network

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Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network

Jiun-Long Huang and Jui-Nan Lin Department of Computer Science

National Chiao Tung University Hsinchu, Taiwan, ROC

E-mail: [email protected], [email protected]

Abstract

We propose in this paper a two-phase algorithm, named algorithm Layered-Cutting, to address the problem of broadcast program generation in a multi-system heteroge- neous overlayed wireless network. The experimental results show that algorithm Layered-Cutting is able to efficiently generate broadcast programs of high quality for a multi- system heterogeneous overlayed wireless network.

Keywords: Data broadcast, heterogeneous overlayed network, mobile computing

1 Introduction

A multi-system heterogeneous wireless network with multiple wireless access technologies is deemed a key part of 4G networks [7]. A 4G network can be conceptually visualized as a collection of multiple independent access subnetworks. This vision leverages the relative merits of multiple cellular access systems, with significant hetero- geneity in their individual characteristics such as coverage area, transmission range and channel bandwidth. By using multiple, physical or software-defined radio interfaces, mobile devices are able to switch between these wireless access technologies to obtain better service quality. Service providers should take advantage of the relative merits of different subnetworks to provide high quality network access at anytime in anywhere.

In order to provide power conserving and high scalable services in a mobile environment, a data delivery architecture in which a server continuously and repeatedly broad- casts data to a client community through a single broadcast channel was proposed in [1]. Unfortunately, most of the prior studies in data broadcast only deal with data indexing, broadcast program generation or other issues in a single- system wireless network (i.e, in one network with one or multiple broadcast channel(s)). Therefore, the approaches proposed by these studies cannot be directly used in a multi-

system heterogeneous overlayed wireless network. We ar- gue that with the development of 4G networks, designing a proper scheme to employ data broadcast on multi-system networks will become an important issue in the development of mobile information systems.

In view of this, we propose a two-phase algorithm, named algorithm Layered-Cutting, to address the problem of broadcast program generation in a multi-system heterogeneous overlayed wireless network. Specifically, algorithm Layered-Cutting consists of two phases: inter- network data allocation and intra-network data allocation, and cooperates with a designated broadcast program generation algorithm for a single-system network. For better readability, the employed broadcast program generation algorithm for a single-system network is referred to as algorithm BPG-Single (standing for Broadcast Program Gener- ation for Single-system networks) in the rest of this paper.

In inter-network data allocation phase, algorithm Layered- Cutting allocates a set of data items to each subnetwork.

Since broadcast program generation algorithms are usually of high complexity, for better scalability, the times of executing algorithm BPG-Single should be minimized. To achieve this, algorithm Layered-Cutting employs an overall average access time estimation method to estimate the quality of different data allocation settings, and determines a data allocation setting with smaller estimated overall access time as the result of inter-network data allocation phase.

After determining a proper data allocation setting in inter- network data allocation phase, algorithm Layered-Cutting steps into intra-network data allocation phase to generate one broadcast program for each subnetwork according to the number of channels in the subnetwork and the proper- ties (including data access probabilities and object sizes) of the data items allocated to the subnetwork. To evaluate the performance of algorithm Layered-Cutting, several exper- iments are conducted. The experimental results show that algorithm Layered-Cutting is able to efficiently generate broadcast programs of high quality for a multi-system heterogeneous overlayed wireless network. To the best of our

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knowledge, there is no prior work considering data broadcast on heterogeneous overlayed networks. This character- istic distinguishes this paper from others.

The rest of this paper is organized as follows. First, problem description and formulation are given in Section 2.

Then, the details of algorithm Layered-Cutting are shown in Section 3. Section 4 shows the experimental results, and finally, Section 5 concludes this paper.

2 Preliminaries

2.1 System Model

Consider a multi-system heterogeneous overlayed net- work N= {N1,N2,···,N|N|} consisting of |N| subnetworks, and suppose that these subnetworks are ordered by the sizes of their coverage areas in ascending order. To facilitate the following discussion, we make the following two assumptions.

1. The service area of subnetwork Niis totally covered by that of subnetwork Njif j> i.

2. When being able to connect to subnetwork Niand sub- network Njsimultaneously, users prefer using subnet- work Nithan using subnetwork Njif j> i.

These two assumptions hold in many cases. As mentioned in [6], wireless networks with larger coverage areas are usually of higher connection fee and of lower bandwidth than those with smaller coverage areas. For example, the service area of a GPRS network is larger than the service area of a Wi-Fi network, and the service area of a Wi-Fi network is usually totally covered by a GPRS network. In addition, when being able to connect to these two networks, users usually prefer using the Wi-Fi network rather than using the GPRS network since Wi-Fi networks are cheaper and of bandwidth higher than GRPS networks.

2.2 Problem Description and Formulation Suppose that in subnetwork Ni, the service provider allo- cates Cichannels to provide the data broadcast service and the bandwidth of each channel is Bi. Suppose that the data- base D contains |D| data items, D1,D2,···,D|D|. Also let the size of Di be si and let the access probability of data item Dibe pi.

In this paper, we take the access time as the measure- ment of the performance of broadcast programs. Note that in broadcast environments, “a user issues a request” does not mean that the mobile device has to explicitly issue a data request to the server. In fact, it means that the user issues a data request to the “mobile device,” and the mobile

device will tune to the broadcast channel, wait for the ap- pearance of the required data item and retrieve the required data item from the broadcast channel.

As mentioned in [5], in a single-system network with one broadcast channel of bandwidth B, to minimize the over- all average access time, instances of each item have to be equally spaced, and the broadcast frequency of data item Di should be proportional to

pi

li, where li is defined as the time to broadcast Diin the broadcast channel. That is, liis equal to ^s_Bⁱ where B is the bandwidth of the broadcast channel. This result is also called square-root rule. When square-root rule is satisfied, the lower bound of overall average access time is

t_Opt.=1 2

_|D|

∑

j=1

pi× li

2

. (1)

On the other hand, if the network contains multiple chan- nels, say ChannelNo broadcast channels, the lower bound of overall average access time will be

t_Opt.^Multi= t_Opt.

ChannelNo. (2)

For ease of presentation, we assume that all data items have been reordered according to their

p_i

l_i values in descending order in the rest of this paper.

We now consider the cases in a multi-system heterogeneous overlayed wireless network. We first observe the case that data items D1,D2,···,D_|D| are broadcast in a multi- system heterogeneous overlayed wireless network consist- ing of two subnetworks, N1 and N2. Since N2 is of the largest service area, all data items have to be broadcast in N2in order to provide the highest data availability. On the other hand, to minimize the overall average access time, N1

will only broadcast some data items with high broadcast fre- quencies (i.e., high

pi

li values). Therefore, we have to de- termine a cutting point Cut1so that data items from D1to DCut₁ are broadcast in N1 and data items from D1to D_|D|

(i.e., all data items) are broadcast in subnetwork N2. Here we say that data items from D1to DCut₁are allocated to sub- network N1and data items from D1to D_|D|are allocated to subnetwork N2. Since access time is taken as the perfor- mance metric, we should determine a proper value of Cut1

to minimize overall average access time.

We then extend the above observation to a more gen- eral case with|N| subnetworks. When we have to broadcast data items D1,D2,···,D|D|in a multi-system heterogeneous wireless network consisting of |N| subnetworks, N1, N2,

··· N|N|, we shall first determine the values of|N| − 1 cutting points,|Cut1|,|Cut2|,···,|Cut|N|−1|, where Cuti≤ Cutj

when i< j. Then, for i = 1,2,···,|N| − 1, data items from D1to DCut_i are allocated to subnetwork Ni. All data items

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D1 D2 D3 D|D|

Cut1 Cut2 Cut|N|-1

Subnetwork N1

Subnetwork N2

Subnetwork N|N|

D1~D|Cut1|

D1~D|Cut2|

D1~D|D|

allocate

allocate Data Items

Subnetworks

Partitions

Figure 1. Flowchart of inter-network data al- location

are allocated to subnetwork N_|N|. Hence, we have the following definition.

Definition 1 A cutting configuration is defined as a setting of the values of Cut1,Cut2,···,Cut|N|−1 so that (1) Cuti≤ Cutjif i≤ j and (2) 1 ≤ Cuti≤ |D| for all i.

Since overall average access time is taken as the performance metric in this paper, the determination of the values of these cutting points has to be under the goal of minimizing overall average access time. This procedure is called inter-network data allocation. The flowchart of inter- network data allocation is shown in Figure 1.

After inter-network data allocation, each subnetwork is assigned some data items. Then, for each subnetwork, we should determine how to broadcast the assigned data items by all broadcast channels of this subnetwork. That is, to generate a broadcast program for each subnetwork. Such procedure is called intra-network data allocation. For- tunately, the problem of intra-network data allocation is equivalent to the problem of broadcast program generation in a single-system network with multiple broadcast channels which has been widely studied in many prior studies [3][4][8]. Hence, we will focus on inter-network data allocation in the rest of this paper and employ one prior broadcast program generation algorithm in a single-system network with multiple broadcast channels to deal with intra- network data allocation for each subnetwork.

As a consequence, the problem of broadcast program generation on heterogeneous overlayed wireless networks can be formulated as follows.

Definition 2 Given a multi-system heterogeneous wireless network N = {N1,N2,···,N|N|}, the number of allocated channels Ci in each subnetwork Ni, the number of data items, and the access probabilities and sizes of all data items, for each subnetwork Ni, we shall determine:

1. which data items will be broadcast in subnetwork Ni

(i.e., a proper cutting configuration), and

2. how these data items are broadcast in subnetwork Ni

(i.e., one proper broadcast program for each subnetwork).

3 Broadcast Program Generation on a Multi- System Heterogeneous Overlayed Wireless Network

3.1 Overview

In this section, we design algorithm Layered-Cutting to address the problem of broadcast program generation in a multi-system heterogeneous overlayed wireless network.

Basically, algorithm Layered-Cutting is a two-phase algorithm consisting of inter-network data allocation phase and intra-network data allocation phase. The objective of inter- network data allocation phase is to determine a proper cutting configuration so that the overall average access time of the whole multi-system network is minimized. Then, in intra-network data allocation phase, algorithm Layered- Cutting will generate one broadcast program for each subnetwork according to the resultant cutting configuration.

In intra-network data allocation phase, algorithm Layered- Cuting will execute algorithm BPG-Single only |N| times to generate one broadcast program for each subnetwork.

In addition, instead of evaluating all possible cutting configuration, algorithm Layered-Cutting only evaluates some cutting configurations with high probability to be optimal.

With the above two characteristics, algorithm Layered- Cutting is able to obtain suboptimal cutting configurations efficiently.

3.2 Phase One: Inter-Network Data Allo- cation Phase

Since the objective of inter-network data allocation phase is only to determine a proper cutting configuration to minimize overall average access time, knowing the broadcast programs of all subnetworks is not necessary in inter- network data allocation phase. Therefore, when evaluating a cutting configuration, we use Equation (1) and Equa- tion (2) to obtain the lower bound of overall average ac- cess time of each subnetwork and take the weighted sum- mation of these lower bounds as the lower bound of the whole multi-system network. Suppose that the data access probabilities of all data items observed by subnetwork Nj

are p₁^j, p₂^j,···, p_|D|^j .¹ Hence, the weight of a subnetwork is defined as below.

1The method to determine the values of p_i^jis omitted in this paper due to space limitation.

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Definition 3 The weight of subnetwork Njis defined as the probability that a data request is served by subnetwork Nj. Therefore, the weight of subnetwork Njis equal to∑^|D|_i=1p_i^j. By employing Equation (1) and Equation (2), algorithm Layered-Cutting can use the lower bounds of the overall average access time of cutting configurations as the esti- mated overall average access time without executing algo- rithm BPG-Single.

3.2.1 Merging Subnetworks

To facilitate the design of algorithm Layered-Cutting, we first consider the effect of merging some subnetworks into a logical subnetwork. Suppose that the data access probabilities of all data items observed by the combination of subnetworks N1,N2,···,Nj are p^{1∼ j}₁ , p^{1∼ j}₂ ,···, p^{1∼ j}_|D| .² We then merge the combination of N1,N2,···,Njinto a logical single-system subnetwork, denoted as N_{1∼ j}, with service area of size Aj and one logical broadcast channel of band- width B_{1∼ j}. Consider a subnetwork Ni, 1≤ i ≤ j, which has Cibroadcast channels and each is of bandwidth Bi. The weight of logical subnetwork N_{1∼ j}is defined as below.

Definition 4 The weight of logical subnetwork N_{1∼ j} is defined as the probability that a data request is served by one of subnetworks N1,N2,···,Nj. Hence, the weight of logical subnetwork N_{1∼ j}is equal to∑^|D|_i=1p^{1∼ j}_i .

In addition, the aggregate bandwidth of subnetwork Ni is Ci× Bi. Since the sizes of service areas of subnetwork Ni

and logical subnetwork N_{1∼ j} are Ai and Aj, respectively, the contribution of subnetwork Ni on bandwidth of logical subnetwork N_{1∼ j} can be estimated by uniformly spreading the bandwidth from service area with size Aito service area with size Aj. Therefore, B_{1∼ j}is defined as the summation of the contributions of subnetwork N1,N2,···,Nj. As a result, B_{1∼ j}can be formulated as∑_i=1^j A^Aⁱ_j×Ci× Bi.

Therefore, the lower bound of the overall average access time of subnetwork N1∼ j can be obtained by Equation (1) with data access probabilities p^{1∼ j}₁ , p^{1∼ j}₂ ,···, p^{1∼ j}_|D| . Finally, the lower bound of overall average access time of the com- bination of subnetworks N1,N2,···,Njcan be approximated by the lower bound of the overall average access time of subnetwork N_{1∼ j}.

3.2.2 Layered Cutting

The objective of inter-network data allocation phase is to determine a proper cutting configuration (i..e, determine the

2The method to determine the values of p¹_i^{∼ j}is omitted in this paper due to space limitation.

Subnetwork N|N|-j+1

Subnetwork N|N|-j

Subnetwork N|N|-j-1

Subnetwork N1

Logical Network N1~(|N|-j)

Subnetwork N|N|-j+1

2. Determine the value of Cut|N|-j

1. Merge

3. Determine the values of pi|N|-j+1

and pi1~(|N|-j)

Figure 2. Layered Cutting in the j-th iteration

values of Cut1,Cut2,···,Cut|N|−1) to minimize overall average access time of the whole multi-system network.

Basically, inter-network data allocation phase of algorithm Layered-Cutting is an iterative algorithm and deter- mines the value of Cut_{|N|− j} in the j-th iteration. In the first iteration, we have a multi-system network with |N|

subnetworks. Since subnetwork N_|N| is of the largest service area, all data requests will be served by the combi- nation of subnetworks N1,N2,···,N|N|. Hence, we have p^1∼|N|_i = pifor each data item Di. We then merge subnet- works N1,N2,···,N_|N|−1 into logical subnetwork N1∼|N|−1

with service area of size A_|N|−1 and a broadcast channel of bandwidth B1∼|N|−1. As a result, determining the value of Cut_|N|−1 in a multi-system network with|N| subnetworks is transformed into determining the value of Cut_|N|−1 in a multi-system network with two networks (i.e., logical sub- network N_{1∼( j−1)} and subnetwork Nj). We then design a heuristic, named procedure Test-and-Prune, to determine the value of the cutting point between logical subnetwork N_{1∼( j−1)}and subnetwork Nj. For ease of presentation, we defer the description of procedure Test-and-Prune to Sec- tion 3.2.3 and assume that value of Cut_|N|−1can be obtained right now. We then determine the access probabilities ob- served by logical subnetwork N_1∼|N|−1(i.e., p^1∼|N|−1_i ) and by subnetwork N_|N|(i.e., p^|N|_i ). After p^1∼|N|−1_i and p^|N|_i have been calculated, algorithm Layered-Cutting finishes the first iteration and starts the second iteration.

In essence, the process of the j-th iteration is similar to that of the first iteration. In the j-th iteration, only sub- networks N1,N2,···,N|N|− j+1are considered. First, subnet- works N1,N2,···,N|N|− jare merged into logical subnetwork N_{1∼|N|− j}. The value of Cut_{|N|− j}is then determined by pro- cedure Test-and-Prune according to p^{1∼|N|− j+1}_i which has been determined in the ( j− 1)-th iteration. Finally, the val- ues of p¹_i^{∼|N|− j} and p^{|N|− j+1}_i are calculated. Inter-network data allocation phase of algorithm Layered-Cutting repeats the above steps until the value of Cut1has been determined.

That is, after iterating |N| − 1 times, algorithm Layered- Cutting terminates inter-network data allocation phase and steps into intra-network data allocation phase.

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3.2.3 Determining Values of Cutting Points

After describing the process of inter-network data allocation phase in algorithm Layered-Cutting, we now describe how to determine the values of cutting points in this subsection.

Note that the determination method, called procedure Test- and-Prune, is used in Section 3.2.2.

We now consider the example of the j-th iteration, and the example is shown in Figure 2. In the j-th it- eration, we have to determine the value of Cut_{|N|− j}, where 1 ≤ Cut_{|N|− j} ≤ Cut_{|N|− j+1}, so that the overall average access time of logical subnetwork N_{1∼(|N|− j)} and subnetwork N_{|N|− j+1} is minimized.³ To facilitate the following discussion, when Cut_{|N|− j}is set to p, we denote the lower bound of the overall average access time of logical subnetwork N_{1∼(|N|− j)} obtained by Equation (1) as LB_{1∼(|N|− j)}(p). Also let LB_{|N|− j+1}(p) be the lower bound of subnetwork N_{|N|− j+1}calculated by Equation (1) or Equation (2) as LB_{|N|− j+1}(p).⁴ As mentioned in Section 3.2.1, the lower bound of overall average access time of the combination of subnetworks N1,N2,···,Nk

can be approximated by the lower bound of the overall average access time of subnetwork N_1∼k. Hence, the overall average access time of logical subnetwork N_{1∼|N|− j} and subnetwork N_{1∼|N|− j+1} when Cut_{|N|− j} = p can be deter- mined as LBCut_{|N|− j}(p) = w_{1∼|N|− j}(p) × LB_{1∼(|N|− j)}(p) + w_{|N|− j+1}(p) × LB_{|N|− j+1}(p), where w_{1∼|N|− j}(p) and w_{|N|− j+1}(p) are the weights of logical subnetwork N_{1∼|N|− j} and subnetwork N_{|N|− j+1}, respectively, when Cut_{|N|− j}= p.

To obtain the optimal value of Cut_{|N|− j}, it is intuitive to scan all possible values of the cutting point and to select the best one as the value of Cut_{|N|− j}. However, this method is unscalable since the number of data items is usually large.

In view of this, we design an efficient heuristic, named procedure Test-and-Prune, to determine a proper value of a cutting point in a “test-and-prune” manner. For better scalability, the objective of procedure Test-and-Prune is to find a lo- cal optimal value, instead of the optimal value, of Cut_{|N|− j}. Hence, we have the following definition.

Definition 5 A value of the cutting point, say p, is said local optimal if LBCut_{|N|− j}(p − 1) > LBCut_{|N|− j}(p), and LBCut_{|N|− j}(p + 1) > LBCut_{|N|− j}(p).

Definition 6 A value of the cutting point, say q, is said to be better than another value of the cutting point, say p, if LBCut_{|N|− j}(q) > LBCut_{|N|− j}(p).

The process of procedure Test-and-Prune is as follows.

First, variables le f t and right are set, respectively, to the

3The value of Cut_|N|is defined as|D|.

4Equation (1) is designed for a single-system network with one broad- cast channel while Equation (2) is for a single-system network with multi- ple broadcast channels.

smallest and the largest possible values of Cut_{|N|− j}, and variable middle is set to

right+le ft 2

. Procedure Test-and- Prune checks whether setting Cut_{|N|− j} to middle is local optimal. If so, procedure Test-and-Prune stops and sug- gests middle as the value of Cut_{|N|− j}. Otherwise, procedure Test-and-Prune checks the superiorities of setting Cut_{|N|− j} to middle− 1,middle and middle + 1. If set- ting Cut_{|N|− j} to p− 1 is better than setting Cut_{|N|− j} to middle and middle+ 1, values from middle to Cut_{|N|− j+1} are pruned and right is set to middle− 1. Otherwise, when setting Cut_{|N|− j}to middle+1 is better than setting Cut_{|N|− j} to middle− 1 and middle, values from 1 to p are pruned and le f t is set to middle+ 1. The above procedure repeats until a local optimal value of Cut_{|N|− j}is found.

3.3 Phase Two: Intra-Network Data Al- location Phase

The objective of intra-network data allocation phase is to determine the broadcast programs of all subnetworks according to the resultant cutting configuration. It is intuitive that generating the broadcast program of subnetwork Nj is equivalent to executing algorithm BPG-Single on subnet- work Njwith data access probabilities p₁^j, p₂^j,···, p_|D|^j .

4 Performance Evaluation

4.1 Simulation Model

In addition to algorithm Layered-Cutting, we also im- plement algorithm Brute-Force which is able to obtain the optimal broadcast programs for multi-system networks in a brute-force manner. Similar to [2], we assume that the access probabilities of all data items follow a Zipf distribution with parameter θ. The default value ofθ is set to be 0.8 with a reference to the analysis of real Web traces. We also assume that there are 1000 data items and the data sizes are assumed to follow a normal distribution with mean 1 KB- byte.

In the model of subnetworks, we assume that there are

|N| subnetworks in the multi-system heterogeneous over- layed network, and the service provider allocates three channels in each subnetwork for broadcasting data items.

We also assume that subnetwork |N| is able to cover the whole service area of the multi-system network and the rate between the sizes of the service areas of subnetwork i and subnetwork i+ 1 is set to 0.8. That is, _A^A_i₊₁ⁱ = 0.8 for all 1≤ i ≤ |N| − 1. In addition, the ratio between the band- width of one broadcast channel in subnetwork i and that in subnetwork i+ 1 is set to 2

i.e., _B^Bⁱ

i+1 = 2

, and B_|N|is set to 10KBytes/sec. We use the broadcast program generation algorithm proposed in [5] as algorithm BPG-Single. That is,

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0 2 4 6 8 10 12 14

250 500 750 1000 1250

Number of Data Items Average Access Time (sec) Brute-Force

Layered-Cutting

(a) Average access time

0 200 400 600 800 1000 1200 1400 1600 1800

250 500 750 1000 1250

Number of Data Items Execution Time (sec) Brute-Force

Layered-Cutting

(b) Execution time

Figure 3. Impact of the number of data items

the algorithm proposed in [5] is used to generate broadcast programs for all subnetworks in intra-network data allocation phase.

4.2 Impact of Number of Data Items This experiment investigates the impact of the number of data items by setting the number of data items from 250 to 1250. The quality of resultant broadcast programs of algorithm Brute-Force and algorithm Layered-Cutting is shown in Figure 3a. As observed, the solutions generated by algorithm Layered-Cutting is much close to those generated by algorithm Brute-Force (i.e., optimal solutions) even the number of data items is set to 1250. In this experiment, the degradation of solutions of algorithm Layered-Cutting over solutions of algorithm Brute-Force is smaller than 4%.

Figure 3b shows the execution time of both algorithms with the number of data items varied. It is intuitive that the execution time increases as the number of data items increases. As observed in Figure 3b, execution time of algorithm Brute-Force is much sensitive on the number of data

items than algorithm Layered-Cutting. The execution time of algorithm Brute-Force increases drastically as the number of data items increases. Under the same case, the execution time of algorithm Layered-Cutting only increases slightly and can be terminated within one second. This result shows that algorithm Layered-Cutting is much scalable than algorithm Brute-Force.

5 Conclusion

In this paper, we employed data broadcast in a multi- system heterogeneous overlayed wireless network and proposed a two-phase algorithm, named algorithm Layered- Cutting, to address the problem of broadcast program generation in a multi-system heterogeneous overlayed wireless networks. The experimental results showed that algorithm Layered-Cutting is able to efficiently generate broadcast programs of high quality for a multi-system heterogeneous overlayed wireless network.

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