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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

We propose a scheme to attain shorter multicast delay and higher efficiency in the data transfer of sensor grid. Our scheme, in one cluster, seeks the central node, calculates the space and the data weight vectors. Then we try to find a new vector composed by linear combination of the two old ones. We use the equal correlation coefficient between the new and old vectors to find the point of game and balance of the space and data factorsbuild a binary simple equation, seek linear parameters, and generate a least weight path tree. We handled the issue from a quantitative way instead of a qualitative way. Based on this idea, we considered the scheme from both the space and data factor, then we built the mathematic model, set up game and balance relationship and finally resolved the linear indexes, according to which we improved the transmission efficiency of sensor grid. Extended simulation results indicate that our scheme attains less average multicast delay and number of links used compared with other well-known existing schemes.

A sensor grid integrates wireless sensor networks with grid infrastructures to enable real-time sensor data collection and the sharing of computational and storage resources for sensor data processing and management. It is an enabling technology for building large-scale infrastructures, integrating heterogeneous sensor, data and computational resources deployed over a wide area, to undertake complicated surveillance tasks such as environmental monitoring [

The sensor grid enables the collection, processing, sharing, and visualization, archival and searching of large amounts of sensor data. The vast amount of data collected by the sensors can be processed, analyzed and stored using the computational and data storage resources of the grid. The sensors can be efficiently shared by different users and applications, which can access a subset of the sensors to collect the desired type of sensor data. A sensor grid provides seamless access to a wide variety of resources in a pervasive manner [

In many cases the amount of data in different nodes varies considerably, the proportion between the maximum and minimum is sometimes 1:1,000,000 or even much more. These data are widely distributed in different geographical positions and dynamically updated, replicated frequently, therefore a large number of transmission is necessary [

A sensor-grid-based architecture has many applications such as environmental and habitat monitoring, healthcare monitoring of patients, weather monitoring and forecasting, military and homeland security surveillance, tracking of goods and manufacturing processes, safety monitoring of physical structures and construction sites, smart homes and offices. As shown in

To achieve the high efficiency of the system, we proposed a set of novel Game and Balance Hierarchical Multicast Architecture Algorithms for sensor grid. The conception of multicast comes from network communication. Multicast technology is an important method of IP network data transmission. Between the senders and receivers, the system implements the link of network from one point to multi-points. According to the space relationship between one point sender and multi-points received, the system constructs optimal tree architecture for optimal data transfer. The advantage of multicast is that it can get the least using links number and shortest transfer delay, so that it promotes data transfer efficiency and decrease the possibility of network block. The most famous NICE protocol is a hierarchical multicast tree technique, which is an extendable multicast protocol that supports, from one sender to a number of receivers, low bandwidth data flow appliance.

Many well-known multicast schemes have been presented in reference listed: Double-Channel XY Multicast Wormhole Routing (DCXY) [

However, in the previous work of multicast for network communication, only one factor that affect the date transmission efficiency is considered [

The former hierarchical multicast schemes only consider the factor of geographical position, which means the shortest path way using the least number of links. While constructing the hierarchical multicast tree, the system often chooses the geographical central node as the cluster core or near the core. Hence it can save the transmission distance [

As a result, the system should consider not only the space factor, but also the data quantity as the factor [

After summarizing the context of the algorithms, this subsection discusses the concrete implementation of the algorithms [

The network is partitioned into clusters in terms of some regular Sensor grid area. After group members are initially scattered into different clusters, a tree is built to connect the cluster members within each other. The connection among different clusters is done through hooking the tree roots [

To construct such an architecture, a set of novel algorithms based on the

Cluster formation algorithm that divides the group members into different clusters in terms of static delay distance;

Relative weight vectors generation algorithm that seeks the spatial central node in every cluster, calculates the space weight of every node, searches the weight of data quantity of every node, and finds the maximum;

The least weighted path tree algorithm that, after obtaining the space weight vector and the data quantity weight vector, builds binary simple equations, seeks linear parameters, determines the new weight vector according to the algebra sum of the two known vectors, and generates the least weighted path tree;

Multicast routing algorithm that efficiently dispatches the multicast packets in the group on the basis of the architecture constructed by the above three algorithms.

After checking the relative documents, this paper is one of the pioneer to use the multicast architecture for grid computing field [

The architecture of this paper as follows: After describing the motivation in Section 1., the paper presents the problem in Section 1.3. and discuss how to figure out different weights in Section 2. Section 3. depicts the four sub-algorithm and the detail steps in different sub-algorithm. Section 4. describes the performance evaluation, which explains the model and result of the simulation. At last, Section 5. draws a conclusion and talks about the future work.

To improve the efficiency of data transmission in a quantitative way, the first thing we should do is to establish the mathematical model to describe the system.

The multicast group with _{0}, . . ., _{i}_{l−1}}, where _{i}_{i,0}, . . ., _{i,j}_{i,m−1}), when 0 ≤ _{0}: 2 dimension coordinates (_{0,0}, _{0,1}) as (0, 0) and member _{1}: 2 dimension coordinates (_{1,0}, _{1,1}) as (0, 1) etc [

As illustrated in _{i}_{i,0}, . . ., _{i,j}_{i,m−1}) where _{i′} = (_{i′,0}, . . ., _{i′,j}_{i′,m−1}), where _{i}_{i′}_{i,j}_{i′,j}_{i,j′}_{i′,j′}

We also define the Manhattan distance of two nodes [_{0}, _{0}) and (_{1}, _{1}) is |_{1} − _{0}| + |_{1} − _{0}|. The sum of static delay distances from all the other nodes (_{i}_{i}_{0}, _{0}) (

Then the question we discuss next is how to configure the space factor and the data factor. We established two weight vectors to describe the space factor and the data factor in each cluster, and the value of every item means the relative weight of every node. For example, the space weight vector of the _{j}_{j,0}, . . ., _{j,i}, . . ., _{j,n−1}), _{j,i}_{j}_{j,0}, . . ., _{j,i}_{j,n−1}), _{j,i}_{j}_{j,0}, . . ., _{j,i}_{j,n−1}),_{j,i}

Next, we will discuss how to get the value of the three weight vector we defined before, which is the main point of this paper.

The data weight vector is easier to be computed than the space weight vector for its direct physical meaning of real world and easy for computer to realize. The space weight can be identified easily by people, but for computer to understand, the system has to study special algorithms. The first step we should do is to make the system to find the central node of the cluster, and then to figure out the space weight of each node to the central node according to the shortest path principle.

Generally speaking, the greater the space weight is, the nearer the node to the cluster core is, and vice versa. The node with maximum weight is the central node of the cluster namely the space cluster core. For example, _{(2,2)} = 10 and so the node is the cluster space core.

If we establish the multicast tree for one cluster, only consider the space weight, the tree should be as the one shown in

Compared with the space weight vector, the data weight vector is easier obtain, as we can just define the date weight according to the date amount on the node directly [

If we establish the multicast tree in one cluster, only consider the data weight, the tree should be in the way shown in

We define the general weight vector for one node as the function of space weight vector

Next, the question is how to calculate the linear parameters. We found one equation array to describe the problem for

Then the system can resolve the value of

Base on the weight vector

In the algorithms presented by this paper, the group members are initially split into several clusters by some management nodes (called as Rendezvous Points—RP). The cluster size is normally set as:

The expression (

The RP initially selects the left lowest end host (say U) among all unassigned members. The left lowest node is the node that has the minimum coordinates along

Cluster Formation

This sub-algorithm generates two weight vectors: the space weight vector and the data weight vector. In addition, the node with the maximum space weight is named the space core, and the node with the maximum date weight is named the data core. Hence it can be divided into four steps:

Each cluster will have a spatial center node as the space core. The space core can be the root of the tree in the cluster. The following theorem provides the sufficient and necessary conditions to select a spatial core in each cluster that is optimal in terms of the minimum sum of static delay distances to all the other cluster members.

_{0}, . . ., _{j}_{m−1}) _{j} (the nodes just on j-th row) respectively. Then U is the spatial center node if and only if the following inequalities hold simultaneously:

_{0}, . . ., _{j}_{m−1}) is a spatial center node, and then to any member _{0}, . . ., _{j+1}, . . ., _{m−1}) and its multicast static delay distance _{i}_{i,0}, . . ., _{i,j}_{i,m−1}) and _{j}_{i,j}_{i}_{i}_{i}_{i,0}, . . ., _{i,j}_{i,m−1}) and _{i,j}_{j}_{i}_{i}_{>uj} + _{=uj}) members whose _{j}_{<uj} cluster members whose _{j}_{0}, . . ., _{j−1}, . . ., _{m−1}) with

(⇐): It is easy to demonstrate that if (2) is violated, and then _{>uj} − _{<uj} > _{=uj}, then _{>uj} > _{<uj} + _{=uj}. Similarly, this paper firstly considers a node _{0}, . . ., _{j+1}, . . ., _{m−1}) and its multicast static delay distance _{i}_{i,0}, . . ., _{i,j}_{i,m−1}) and _{j}_{i,j}_{i}_{i}_{i}_{i,0}, . . ., _{i,j}_{i,m−1}) and _{i,j}_{j}_{i}_{i}

The physical meaning of the theory is obvious. Firstly, we process on _{=2} = 4, namely there are 4 nodes just on of second row: (2, 6), (2, 4), (2, 2), (2, 1); _{<2} = 2, namely there are 2 nodes in the left of second row: (1, 3), (1, 1); _{>2} = 4, namely there are 4 nodes in the right of second row (3, 5), (3, 1), (5, 5), (5, 2), so |_{<2} − _{>2}| ≤ _{=2}. Thus _{=2} is satisfied coordinates on _{=3} = 2, including (3, 5), (3, 1); _{<3} = 6, including (2, 6), (2, 4), (2, 2), (2, 2), (1, 3), (1, 1); _{>3} = 2, including (5, 5), (5, 1), so |_{<3} − _{>3}| ≥ _{=3}. Thus

At the beginning of this discussion, it can be presumed that the system establishes a multicast tree to transfer data packet, which choose the space core as the root and organize the architecture according to the space weight vector [

_{0}, _{0}) and (_{1}, _{1}), let _{min}_{0}, _{1}}, _{max}_{0}, _{1}}, _{min}_{0}, _{1}} and _{max}_{0}, _{1}}. They uniquely define a rectangle area [_{0}, _{0}] × [_{1}, _{1}]. Each node (_{0}, _{0}] × [_{1}, _{1}], which is on one of the shortest paths between (_{0}, _{0}) and (_{1}, _{1}), so it is called the shortest path area nodes (SPAN) between (_{0}, _{0}) and (_{1}, _{1}).

_{j}_{j}_{j}_{0}, _{0}] × [_{i}_{i}_{i}_{i}_{i}_{i}

In general, if the space weight of the node is

After figuring out the space weight vector _{i,j}

According to the

The relatively Weighted Vectors Generation algorithm in the

Relative Weighted Vectors Generation

In

In the sensor grid, the data quantities of nodes are very different, for instance, about 20% nodes process 80% of the data quantity of the whole system. These nodes are very important in the multicast data transfer, therefore when researching the algorithm in multicast, the node’s data quantity weight

In general, the Relative Weighted Vectors Generation algorithm, finds the spatial core _{i,a}_{i}_{i,j}_{i,j}_{i}_{i,b}

After the Relative Weighted Vectors Generation algorithm generates the space weight vector _{i,a}_{i,b}

_{i,j}

_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}

_{i}

_{i}

_{i}, W″_{i}, their linear combination W_{i,j}_{i}W′_{i,j}_{i}W″_{i,j}, α_{i}, β_{i} is linear relation modulus, α_{i}, β_{i}_{i}, β_{i}

_{i,j}_{i}W′_{i,j}_{i}W_{i,j}, and α_{i}_{i}_{i}_{i}_{i}_{i}

_{i}_{i,0}, . . ., _{i,j}_{i,m−1}), _{i}_{i,0}, . . ., _{i,j}_{i,m−1}) _{i}_{i,0}, . . ., _{i,j}_{i,m−1}), _{i}_{i}W′_{i}_{i}W″_{i}_{i}, β_{i} is linear relation modulus, α_{i}, β_{i}_{i}, β_{i}_{i} and W_{i} is

_{i}_{i,0}, . . ., _{i,j}_{i,m−1}), _{i}_{i,0}, . . ., _{i,j}_{i,m−1}) _{i}_{i,0}, . . ., _{i,j}_{i,m−1}), _{i}_{i}W′_{i}_{i}W″_{i}, as show in

_{1}=_{2}, _{1}=_{2}.

_{i} and W″_{i} should be the point that has the equal correlation coefficient to each of the vectors. That is to say:

Combining (4) and (5), the paper builds the liner binary simple equations:

For _{i}_{i}W′_{i}_{i}W″_{i}

For _{i}_{i}

So: 0 < _{i}_{i}_{i}_{i}

According to the above data table, the algorithm figures out _{i}_{i}

According to the above all, the algorithm gets the weight vector (as _{i}

Given a shortest path, the path weight is the sum of all on-path node weights. For example, the weight of path < (2, 2), (2, 3), . . ., (2, 5), . . ., (5, 5) > is ∑_{i} α_{i}W_{i}_{i} β_{i}W_{i}

Let the cluster with

After obtaining the space weight vector _{i,a}_{i,b}

The main idea of the least weighted path tree generation algorithm can be sketched as follows. After obtaining the space weight vector and the data quantity weight vector, we tried to find a new vector composed by linear combination of the two old ones. And it builds binary simple equations between them, seeks linear parameters. Then they generate a least weighted path tree, namely multicast tree. The least weighted path tree generation algorithm is shown in

Least Weighted Path Tree Generation.

For example: in the cluster, the spatial center node is _{i}_{i}_{i}_{i}_{i}, W_{i}_{i}_{i}

Notice that since the dimension of the space weight vector and the data quantity weight vector may be different, the data quantity weight vector may stem from a function of the nature data quantity.

Firstly, the network is partitioned into clusters by some regular Sensor grid area; after group members are divided into different clusters, a tree is built to connect the cluster members in each cluster; at last, the connection among different clusters is done through hooking the tree roots.

Multicast routing for group G

_{0}._{0} sends them to all other cores _{i}_{0} routes the multicast packets to its own cluster members along the cluster tree._{i}_{i} |

We evaluated the newly-proposed optimal hierarchical multicast algorithms with the simulation developed by C++ [

In the simulation environment, the network topology used in the simulation is a 2-_{i}_{i}

The average delay metric under the light and heavy load of network is shown in

Under the light load circumstance, the delay is mainly decided by the distance from the source to the group members

Under a heavy load circumstance, the delay is mainly decided by the source of the data quantity, and certainly relates to the space of the nodes too

At heavy load, the number of links is mainly decided by both the source of the data quantity and the space of the node

It reveals that under the same condition, GBMASG obtains the best balance over the performance parameters, i.e., the less resource a system consumes, the higher the throughput and the shorter the delay under heavy traffic load [

A sensor grid integrates wireless sensor networks with grid infrastructures to enable real-time sensor data collection and the sharing of computational and storage resources for sensor data processing and management. It is an enabling technology for building large-scale infrastructures. When the system constructs the hierarchical tree, it should consider not only the factor of the space, but also the data quantity. Their relationship is game and balance. We tried to draw an elaborate balance between them, and uses the basic idea to construct the hierarchical multicast tree in this paper.

The network is partitioned into clusters in terms of the static delay distance of Sensor grid area. After group members are initially scattered into different clusters, a tree is built to connect the cluster members with each other. The connection among different clusters is done through hooking the tree roots. To construct such architecture, a set of novel algorithms based on the

Cluster formation algorithm. It divides the group members into different clusters in terms of static delay distance;

Relative weight vectors generation algorithm. It figures out two weight vectors: the space weight vector _{i,a}_{i,b}

Least weighted path tree algorithm. After the Relative Weighted Vectors Generation algorithm generates the space weight vector _{i,a}_{i,b}

Multicast Routing Algorithm. Firstly, the network is partitioned into clusters in terms of some regular sensor grid area. After group members are initially scattered into different clusters, a tree is built to connect the cluster members within each cluster. At last, the connection among different clusters is done through hooking the tree roots to implement the inter-cluster routing.

At present, the algorithm in this paper mostly focuses on optimal data transfer strategy in 2-

In the paper the space weight vector is complex, but the data quantity weight vector is definite, therefore the system can gain it directly. However, in some situation the data quantity could be changing, so that we should study special sub-algorithm for it. For example, in Pervasive Computing, the data quantity weight vector is not definite, therefore it is a function:

Moreover, we just discussed about the liner relationship of two vectors in this paper. On the other level, the above method can just resolve the linear relationship of two vectors. But, in practice, the system sometimes does not transform linearly but exponentially. The paper can resolve one exponential equation in the situation. For example, we can define the nodes weights as

Furthermore, after discussed two vectors correlation: the space weight vector and data weight vector, the paper can easily be extended to three weight vectors correlation, for instance the economy weight vector. In this situation, the costs of server in different place vary, therefore the clients prefer the node with cheaper cost. Therefore the system should take the economy factor into account, while constructing multicast tree. The three weight vectors are game and balance with each other. The relationship of the weight should be _{i,j}_{i}W_{i,j}_{i}W_{i,j}_{i}W_{i,j}

After discussing two and three vectors correlation, the algorithm can be extended to N-vectors correlation. Because in the realistic world, people should consider a number of factors while constructing the multicast tree, for example: space, data, economy, politics, military, etc. In this mode, every factor is a vector. As long as the physic mean of different factor is independent, the weight vector is linear (non-relative). Even if the two vectors are linear related, there are the ways to turn it to be linear (non-relative). All these factors can be denoted by a series of weight vectors. All of them game and balance with each other.

The relationship of the weight can be defined as

It can be solved by mathematical induction.

Moreover, these factors are based on linear non-relationship condition, so their cardinal number is accountable infinite. But in realty many factors are linear relationship, so that we can turn these to be linear non-relationship. If factors are of linear relationship, then their cardinal number is unaccountable infinite.

The authors acknowledge Professor Weijia Jia of Department of Computer Science, City University of Hong Kong. The authors acknowledge partial financial support form the SAP Business Objects company.

Sensor Grid Architecture.

The multicast tree according to the space weight.

The multicast tree according to the data weight.

Selecting the spatial center nodes in the members of one cluster of a 2-

Shortest path area nodes (SPAN) in a 2-

The relationship of _{i}_{i}_{i}

Simulation results for SPACE, DATA and our GBMASG.

The space weight vector

Y=6 | 0 | 1* | 0 | 0 | 0 |

Y=5 | 0 | 3 | 2* | 1 | 1* |

Y=4 | 0 | 4* | 2 | 1 | 1 |

Y=3 | 1* | 5 | 2 | 1 | 1 |

Y=2 | 2 | 10* | 4 | 2 | 2* |

Y=1 | 1* | 3* | 1* | 0 | 0 |

X=1 | X=2 | X=3 | X=4 | X=5 |

The data weight vector

Y=6 | 0 | 1* | 0 | 0 | 0 |

Y=5 | 0 | 3 | 2* | 1 | 0* |

Y=4 | 0 | 5* | 2 | 2 | 1 |

Y=3 | 2* | 4 | 3 | 2 | 1 |

Y=2 | 2 | 1* | 4 | 3 | 2* |

Y=1 | 3* | 10* | 3* | 0 | 0 |

X=1 | X=2 | X=3 | X=4 | X=5 |

The weight vector

Y=6 | 0 | 1.00* | 0 | 0 | 0 |

Y=5 | 0 | 3 | 2.00* | 1 | 0.53* |

Y=4 | 0 | 4.47* | 2 | 2 | 1 |

Y=3 | 1.47* | 4 | 3 | 2 | 1 |

Y=2 | 2 | 5.79* | 4 | 3 | 2.00* |

Y=1 |
1.94* |
6.27* |
1.94* |
0 |
0 |