- Email: [email protected]
Research on Routing Arithmetic basing on Scale-Free Centrality in Betweenness networks
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1899 – 1904 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
Research on Routing Arithmetic basing on Scale-Free Centrality in Betweenness networks Hong Cai*, Hong-yan Zhao, Rong-yao Chen School of Business and Management, Donghua University, Shanghai 200051,China
Abstract
Based on shortest path routing algorithm, a new algorithm (simply called BORA) is proposed, which optimizes node weight and changes the routing between nodes. The purpose of the algorithm is to reduce network congestions and advance network capacity .Based on Barabfisi-Albert algorithm, a scale-free networks model which has been improved on by BORA is designed. It is showed that BORA advances several abilities of network such as system delay, throughput and fairness efficiently after numbers of discursions and simulations under this new model. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Betweenness, Scale-Free networks, Node weight;
1. Introduction During the rush hours, most networks suffer from congestion and the decline of the quality of service. Network congestion is affected by many factors, and in order to obtain a satisfactory service, most network operators will choose to expand the network or replace the equipment, with little attempt on changing the existing network topology to improve network performance[1]. In fact, as the dynamic characteristics are closely related to the static structure of the network[2], network topology is one of the main factors affecting the distribution of network load.
*
Corresponding author. Email: [email protected](H. Cai )
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.354
1900 2
Hong Cai al et /al. / Procedia Engineering 15 (2011) 1899 – 1904 Hong Cai,et Procedia Engineering 00 (2011) 000–000
As link weight optimization is directly helpful, reflecting the link state, there are a couple of research findings setting the link weights to achieve more flow. However, the setting of link weight does not take into account the forwarding node's processing speed and buffer conditions, and due to a lack of ability to process, nodes in the network are a bottleneck, causing the network congestion. We can also add the link information regarding the node to the node weights setting to improve congestion and link control. Based on the above considerations, this paper finds out a simple and efficient program to optimize the node weights, and tests it through simulation performances. In the early network research, network topology model usually is completely random graph model. Recent studies show that the Internet network topology is on not only the autonomous system level but also the routing level, the node degree distribution is power-law distribution, and the network with such features is often called non-scale (scale-free) networks. On the basis of the Barabfisi-Albert (BA) algorithm to construct the scale-free network model, this paper improves the model and studies the capacity issues of such networks involved the shortest routing network policy about the delay routing. In the past researches of similar problems, the proposed models are usually the ones with little thinking about the relationship between the rate of node produce as well as forwarding bags and node degree, while the realistic model proposed in this paper thinks that different nodes have different ability of production and processing of the package with regards to the relevance of node degree to corresponding sending and forwarding rate[3, 4]. 2. The principle of the Algorithms 2.1. Basic Algorithms Betweenness Centrality (hereinafter referred to as Betweenness) derives from the importance of individuals in the analysis of social network[5]. Simply speaking, the Betweenness of a node refers to the number of the shortest paths connecting two nodes and meanwhile passing this node. Definition: if the node sets in the chart is v, the first number of shortest paths between arbitrary points s, d is δ sd , the second number of the above shortest paths passing the node w is δ sd ( w) , then the ratio of second number to the first number is δ sd ( w) / δ sd . So, the Betweenness of Node W is : B f ( w) = ∑ ∑ δ sd ( w) / δ sd s ≠ w∈V d ≠ s ≠ w∈V
Betweenness relates the static network topology structure with the dynamic network traffic, making a quantitative measure of the flow a node may need to deal with. The bigger the Betweenness of a node, the more data pass it, which means more congestion and a network bottleneck. Therefore, the Betweenness of the node can be part of the setting of node weight. The passing of the node will take a larger portion in routing algorithms as the node with bigger Betweenness means bigger weight. Thus, it is possible for some nodes to avoid this one in choosing the routing to reduce the congestion effectively and improve the capacity of the network system. 2.2. Improved Algorithms Suppose graph G(G,E) refers to the communication network, in which V represents nodes (vertices) set, E as the links (edges) sets. Host, routers and switches in the graph are shown as nodes (vertices), while their physical connections as the links (edges). Step 1: with digraph G (V, E),in which V = {1,... , n}, C refers to the adjacency matrix of G, and C [i] [j] has the power to approach the edge, to introduce another matrix A, to refer to the shortest path between
Hong CaiCai,et et al. al / Procedia Engineering 15 00 (2011) 1899 – 1904 Hong / Procedia Engineering (2011) 000–000
every pair of vertices. Initially, for any i ≠ j , A [i] [j] = C [i] [j]. If there is no arc between i and j, make A [i] [j] = ∞ , and make A [i] [i] = 0. If matrix B represents the number of the shortest paths the node passing the each node, initial, assume that B [i] = n - 1. Step 2: According to the Floyd algorithm, conduct n times processing with the matrix A. In the k times processing, A [I] [j] value is decided by the following formula: Ak = min( Ak −1[i ][ j ], Ak −1[i ][k ] + Ak −1[k ][ j ]) In this, Ak and Ak −1 represents respectively the value of the K times and k-1 times processing matrix A. Meanwhile, in the processing of the update B [i], when there is a new shortest path passing, then add 1 to B [i], and minus 1 from the value of B [j] when the point j is replaced. Step 3: if the value of B [i] is set as the weights of Node i, in the optimal path route computation, first multiply the node weight with the weight pointing to the edge of the node to replace the edge weight, and then use Dijkstra algorithm to make routing computation. Notes on the algorithm: (1)The initial value of B[i] is set to be n-1, on the assumption that at beginning, to any node i, there is a shortest route pointing to it from the other n-1 nodes. Thus, the Floyd algorithm need not calculate the numbers of routes with i as the target node to improve the efficiency. (2)For ease of operation, the algorithm uses the number of the shortest paths through the node as its weight, as the B [i] has just one more constant multiplier than the value of the node Betweenness, it does not affect the result. (3)In the calculation the routing of the shortest path of the hop, the number of the edges pointing to the node can also be used as the node weight. To verify the above algorithm to improve the situation of congestion of the system, make the following simulation: under the BA algorithm, apply the software Brite of topology generation to produce a 100node network, get its adjacency matrix C, finally use matlab in accordance with the BORA, to get Array B as the evaluation index. For ease of comparison, set the number of edges pointing to the node n-1 as node weight, as well as that of the edges pointing to all its neighboring nodes as the node weight. And make Floyd algorithm, and acquire respectively. The BORA method has an increase of the average optimal paths through nodes, but the variance is much less than that of Method 2 and 3, whichmeans that the fairness of the network is better, and meanwhile, the number of maximum paths of nodes is less than that of the Method 2 and 3, which shows the amount of data crossing the largest node is also less, which indicates a relatively low probability of network congestion. While in Method 2 and 3, the control of the fairness and throughput of the network is superior for method 2, if the node weight is set to be the he number of edges pointing to the node. The Comparision of Betweens of Nodes follow as: method 1: the setting of weight is ‘BORA’, the average is 115.6, the variance is 3154, the maximum is 126; method 2: the setting of weight is n-1, the average is 112.3, the variance is 8542, the maximum is 152; method 3: the setting of weight is the number of edges pointing to the node, the average is 115.2, the variance is5641, the maximum is 136. 3. Network Model 3.1. Topology Model In this paper, based on Barabfisi-Albcrt (BA) algorithm[6] to construct a scale-free network topology model, its total number of nodes is N, the number of nodes for the start is m0 , in accordance with any method to connect, in each time step add a new node with m(≤ m0 ) edges connecting the new node to m existed nodes in the network. The probability of choosing the other end of a new node to connect to the node i depends on the degree of node i, namely: ∏(ki ) = ki ∑j kj .
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Hong Cai al et /al. / Procedia Engineering 15 (2011) 1899 – 1904 Hong Cai,et Procedia Engineering 00 (2011) 000–000
3.2. Flow Model Use the flow model in the Reference[5], and assume the rate of the production package of the node i with a degree of ki is λ ki , λ is a parameter, the rate of the forwarding bags of node i is 1 + β ki , β ≥ 0 is a constant. The model represents the actual situation, the busier the node is, the bigger the degree ki is, the rate of the production and forwarding increases. When β equals 0, the model restores to the situation that each node forwards a bag in each time step. The specific process is described below: Step 1：In each time step, with the probability of β ki , the node i produces a package, and the destination is randomly selected. If the node has bags buffered in the queue to be forwarded, the new package will enter the the tail of the queue. Step 2: Once the package produced, the node selects the route to destination in accordance with the BORA. If there are multiple shortest paths, then randomly select one of them. Step 3: In each time step, the node i forwards 1 + β ki bags to the next hop node in the buffered queue as the first node to enter and exist. If β ki is not the score, which will be achieved I the way of probability. Step 4: When the bag arrives at a node, it will be queued for forwarding, and the length of the buffer queue of the node i is P. The newly –generated or forwarded bag arrives, if the buffer queue is full, then it will be discarded. Once the package reaches its destination, it will be removed from the system. 3.3. Network Capacity In this paper, a fixed rate of the production bag is λ , to measure the capacity with β . When the network tranmits from the free to congested state , β c is the smaller, indicating greater network capacity. β c is the smallest forward rate coefficient in the free state of the flow. As long as the the forward rate coefficient is no less than this threshold, the network can enjoy a smooth the flow, and the communication networks and transmission can handle all of the information package. Therefore, the critical bag forwarding rate coefficient can also measure the network capacity of the network system [7]. 3.4. BORAimproves the capacity of the network In this model, in each time step each source node sends data bags to a randomly selected destination node among the other n-1 nodes, and the rate of forwarding bags of node I is vi = λi ki , , the forwarding rate of the overall system is
vt = ∑ v j
. If the network is stable, in each time step the average number of
data bags reach node i is Vt B f (i ) + λi ki . So, when the forwarding rate of each node is 1 + β i ki , if Vt B f (i ) + λi ki ≤ 1 + β i ki , no congestion occurs at
the
node
i.
For
any
node
i,
βi ≥ (Vt B f (i ) − 1) / ki + λi
must
be
satisfied.
So,
β c = MAX (Vt B f (i ) − 1) / K i + λi is realized, in which λi is the forward rate of node I, K i is the degree of it. After the BORA, B f (i ) gets smaller, as Vt , λi , K i remains the same, MAX ((Vt B f (i ) − 1) / K i + λi ) is smaller. To sum up, the free communication of the network allows the decrease of the of the smallest data package which means the increase of the network capacity. In the calculation, the forward rate coefficient λi , β i are changeable, so the above conclusion of the maximum network capacity is suitable for all types of Scale-Free network models, which means BORA can effectively improve the network capacity.
Hong CaiCai,et et al. al / Procedia Engineering 15 00 (2011) 1899 – 1904 Hong / Procedia Engineering (2011) 000–000
In real networks, each node will make positive change in routing in case of congestion. Compared with the model in the Reference[5], this model gives an advanced consideration to the routing change regarding the network congestion. Hence, the model is closer to the real network. 4. Simulation of algorithm
In order to validate the above conclusions, this paper applies the OMNET++ BORA to construct a network model based on BORA to make simulation. The parameters in the simulation are set as follows: the network topology takes BA network with the N = 100 and m=3 generated by BRITE , forwarding rate coefficient λ 0.02, namely in each time step the forwarding rate of node i is Vi = 0.02ki , the forwarding bag coefficient β is 0.18, hence, in each time step the forwarding rate of node i is wi = 1 + 0.18ki , the interval between each time step in simulation is 1s. The bag is produced by GEN module, while the rate of the production bag is set according vi and the destination of the remaining nodes are selected at random; the buffering queue is constructed by FIFO module, service is provided according to the principle that earlier coming gets earlier service, the forwarding rate is set by wi , and the maximum storage of buffer is 30 data bags. If the memory is full already, as the principle, new arrived bags will be discarded. The statistical analysis of the results is done by SINK module with the average delay of the bags and the rate of total bag loss in the system as evaluation index; the routing is implemented by ROUTING module, and four routing models are classified according to the different algorithms: model 1achieves the optimal routing in accordance with BORA, model 2 bases the shortest path ROUTING algorithm on the network delay, model 3 is based on the BORA of hop point, and model 4 has the shortest path ROUTING algorithm based on the hop points, for setting the node weight as to node degree (i.e., the number of the edges pointing to the node). Figure 1, Table 1 show the specific simulation results. From Figure 1, the minimum data bags delay is found in model 1, followed by model 3 and 4, and the maximum is in model 4. Table 1 Comparison: the rate of system lost packages of different network models Total bags forwarded
Lost bags
The percent of lost bags %
Model1
500
12
2.4
Model2
500
80
16
Model3
500
20
4
Model4
500
22
4.4
It can be concluded that Model 1 reduces the forwarding delay of data bags, in that optional routing in accordance with BORA considers both the routing delay and the possible flow passing the node. Model 1 is the most superior. Model 2 takes the shortest path as the optional routing, but it pays little attention to the possible congestions, which leads to long time waiting in the transmission process, resulting in longer system delay. Model 3, with not the delay in routing but only the possible flow in the node considered has a longer delay in Model 1. And in the scale-free network, there is few circles, so the delay of the system mainly caused by the waiting of the data bags. Model 3 has a better way dealing with the node congestion, so it is superior in performance than Model 2. In Table 1, presuppose the number of total forwarded bags is 500, it can be seen that the total lost bags of the nodes in Model 1 is 12, the rate is 2.4%, while that in Model 2 is 16% and Model 3 4%. The result
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Hong Cai al et /al. / Procedia Engineering 15 (2011) 1899 – 1904 Hong Cai,et Procedia Engineering 00 (2011) 000–000
shows that Model 1 is superior in bag loss, which means in the BA network model closer to the real one, the network based on BORA has larger throughput than the BORA Model 3 based on the hop count and Model 3 based on the shortest path routing algorithm to get the shortest routing delay. Figure 1 Comparison: average system delay of different network models
5. Conclusion
Through the study of node Betweenness, this paper explores the method of setting a node weight through Betweenness to improve the capacity of the system network and applies it to the Scale-Free network based on BA algorithm close to real network. Through the universal network capacity formula deduced, the network model constructed on this algorithm is more close to real Internet. Finally, through the modeling simulation in applying the network OMNET++ simulation software, through the comparison with the previous models, the system BORA effectively reduces transmission time, improve the system throughput and fairness in performance. References
[1] N GUPTE, B K SINGH. Role of Connectivity in Congestion and Decongestion in Networks. The Proceedings of the 3rd International Conference NEXT-SigmaPhi.2005.9. [2] P HOLME. Congestion and Centrality in Traffic Flow on Complex Networks. Advances in Complex Systems (S0219-5259), 2003, 6：163-176. [3] LIU Z H, MA W C,ZHANG H,et al. An Efficient Approach of Controlling Traffic Congestion in Scale-Free Networks. Physica A (S0378-4371), 2006, 370(2): 843-853. [4] CHEN Z Y, WANG X F. Eflects of Network Capacity under Variations of Network Structure and Routing Strategy. Pbys. Rev. E(S1063-65I) 73.036107,2006. [5] L C FREEMAN.A Set of Measureas of Centrality based on Betweenness. Sociometry (S0038— 0431), 1977,40: 35-41. [6] BARABASI AL,ALBERT R.Emergence of Scaling in Random Networks. Science(S0036-8075), 1999,286(5439): 509-512.
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1899 – 1904 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
Research on Routing Arithmetic basing on Scale-Free Centrality in Betweenness networks Hong Cai*, Hong-yan Zhao, Rong-yao Chen School of Business and Management, Donghua University, Shanghai 200051,China
Abstract
Based on shortest path routing algorithm, a new algorithm (simply called BORA) is proposed, which optimizes node weight and changes the routing between nodes. The purpose of the algorithm is to reduce network congestions and advance network capacity .Based on Barabfisi-Albert algorithm, a scale-free networks model which has been improved on by BORA is designed. It is showed that BORA advances several abilities of network such as system delay, throughput and fairness efficiently after numbers of discursions and simulations under this new model. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Betweenness, Scale-Free networks, Node weight;
1. Introduction During the rush hours, most networks suffer from congestion and the decline of the quality of service. Network congestion is affected by many factors, and in order to obtain a satisfactory service, most network operators will choose to expand the network or replace the equipment, with little attempt on changing the existing network topology to improve network performance[1]. In fact, as the dynamic characteristics are closely related to the static structure of the network[2], network topology is one of the main factors affecting the distribution of network load.
*
Corresponding author. Email: [email protected](H. Cai )
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.354
1900 2
Hong Cai al et /al. / Procedia Engineering 15 (2011) 1899 – 1904 Hong Cai,et Procedia Engineering 00 (2011) 000–000
As link weight optimization is directly helpful, reflecting the link state, there are a couple of research findings setting the link weights to achieve more flow. However, the setting of link weight does not take into account the forwarding node's processing speed and buffer conditions, and due to a lack of ability to process, nodes in the network are a bottleneck, causing the network congestion. We can also add the link information regarding the node to the node weights setting to improve congestion and link control. Based on the above considerations, this paper finds out a simple and efficient program to optimize the node weights, and tests it through simulation performances. In the early network research, network topology model usually is completely random graph model. Recent studies show that the Internet network topology is on not only the autonomous system level but also the routing level, the node degree distribution is power-law distribution, and the network with such features is often called non-scale (scale-free) networks. On the basis of the Barabfisi-Albert (BA) algorithm to construct the scale-free network model, this paper improves the model and studies the capacity issues of such networks involved the shortest routing network policy about the delay routing. In the past researches of similar problems, the proposed models are usually the ones with little thinking about the relationship between the rate of node produce as well as forwarding bags and node degree, while the realistic model proposed in this paper thinks that different nodes have different ability of production and processing of the package with regards to the relevance of node degree to corresponding sending and forwarding rate[3, 4]. 2. The principle of the Algorithms 2.1. Basic Algorithms Betweenness Centrality (hereinafter referred to as Betweenness) derives from the importance of individuals in the analysis of social network[5]. Simply speaking, the Betweenness of a node refers to the number of the shortest paths connecting two nodes and meanwhile passing this node. Definition: if the node sets in the chart is v, the first number of shortest paths between arbitrary points s, d is δ sd , the second number of the above shortest paths passing the node w is δ sd ( w) , then the ratio of second number to the first number is δ sd ( w) / δ sd . So, the Betweenness of Node W is : B f ( w) = ∑ ∑ δ sd ( w) / δ sd s ≠ w∈V d ≠ s ≠ w∈V
Betweenness relates the static network topology structure with the dynamic network traffic, making a quantitative measure of the flow a node may need to deal with. The bigger the Betweenness of a node, the more data pass it, which means more congestion and a network bottleneck. Therefore, the Betweenness of the node can be part of the setting of node weight. The passing of the node will take a larger portion in routing algorithms as the node with bigger Betweenness means bigger weight. Thus, it is possible for some nodes to avoid this one in choosing the routing to reduce the congestion effectively and improve the capacity of the network system. 2.2. Improved Algorithms Suppose graph G(G,E) refers to the communication network, in which V represents nodes (vertices) set, E as the links (edges) sets. Host, routers and switches in the graph are shown as nodes (vertices), while their physical connections as the links (edges). Step 1: with digraph G (V, E),in which V = {1,... , n}, C refers to the adjacency matrix of G, and C [i] [j] has the power to approach the edge, to introduce another matrix A, to refer to the shortest path between
Hong CaiCai,et et al. al / Procedia Engineering 15 00 (2011) 1899 – 1904 Hong / Procedia Engineering (2011) 000–000
every pair of vertices. Initially, for any i ≠ j , A [i] [j] = C [i] [j]. If there is no arc between i and j, make A [i] [j] = ∞ , and make A [i] [i] = 0. If matrix B represents the number of the shortest paths the node passing the each node, initial, assume that B [i] = n - 1. Step 2: According to the Floyd algorithm, conduct n times processing with the matrix A. In the k times processing, A [I] [j] value is decided by the following formula: Ak = min( Ak −1[i ][ j ], Ak −1[i ][k ] + Ak −1[k ][ j ]) In this, Ak and Ak −1 represents respectively the value of the K times and k-1 times processing matrix A. Meanwhile, in the processing of the update B [i], when there is a new shortest path passing, then add 1 to B [i], and minus 1 from the value of B [j] when the point j is replaced. Step 3: if the value of B [i] is set as the weights of Node i, in the optimal path route computation, first multiply the node weight with the weight pointing to the edge of the node to replace the edge weight, and then use Dijkstra algorithm to make routing computation. Notes on the algorithm: (1)The initial value of B[i] is set to be n-1, on the assumption that at beginning, to any node i, there is a shortest route pointing to it from the other n-1 nodes. Thus, the Floyd algorithm need not calculate the numbers of routes with i as the target node to improve the efficiency. (2)For ease of operation, the algorithm uses the number of the shortest paths through the node as its weight, as the B [i] has just one more constant multiplier than the value of the node Betweenness, it does not affect the result. (3)In the calculation the routing of the shortest path of the hop, the number of the edges pointing to the node can also be used as the node weight. To verify the above algorithm to improve the situation of congestion of the system, make the following simulation: under the BA algorithm, apply the software Brite of topology generation to produce a 100node network, get its adjacency matrix C, finally use matlab in accordance with the BORA, to get Array B as the evaluation index. For ease of comparison, set the number of edges pointing to the node n-1 as node weight, as well as that of the edges pointing to all its neighboring nodes as the node weight. And make Floyd algorithm, and acquire respectively. The BORA method has an increase of the average optimal paths through nodes, but the variance is much less than that of Method 2 and 3, whichmeans that the fairness of the network is better, and meanwhile, the number of maximum paths of nodes is less than that of the Method 2 and 3, which shows the amount of data crossing the largest node is also less, which indicates a relatively low probability of network congestion. While in Method 2 and 3, the control of the fairness and throughput of the network is superior for method 2, if the node weight is set to be the he number of edges pointing to the node. The Comparision of Betweens of Nodes follow as: method 1: the setting of weight is ‘BORA’, the average is 115.6, the variance is 3154, the maximum is 126; method 2: the setting of weight is n-1, the average is 112.3, the variance is 8542, the maximum is 152; method 3: the setting of weight is the number of edges pointing to the node, the average is 115.2, the variance is5641, the maximum is 136. 3. Network Model 3.1. Topology Model In this paper, based on Barabfisi-Albcrt (BA) algorithm[6] to construct a scale-free network topology model, its total number of nodes is N, the number of nodes for the start is m0 , in accordance with any method to connect, in each time step add a new node with m(≤ m0 ) edges connecting the new node to m existed nodes in the network. The probability of choosing the other end of a new node to connect to the node i depends on the degree of node i, namely: ∏(ki ) = ki ∑j kj .
1901 3
1902 4
Hong Cai al et /al. / Procedia Engineering 15 (2011) 1899 – 1904 Hong Cai,et Procedia Engineering 00 (2011) 000–000
3.2. Flow Model Use the flow model in the Reference[5], and assume the rate of the production package of the node i with a degree of ki is λ ki , λ is a parameter, the rate of the forwarding bags of node i is 1 + β ki , β ≥ 0 is a constant. The model represents the actual situation, the busier the node is, the bigger the degree ki is, the rate of the production and forwarding increases. When β equals 0, the model restores to the situation that each node forwards a bag in each time step. The specific process is described below: Step 1：In each time step, with the probability of β ki , the node i produces a package, and the destination is randomly selected. If the node has bags buffered in the queue to be forwarded, the new package will enter the the tail of the queue. Step 2: Once the package produced, the node selects the route to destination in accordance with the BORA. If there are multiple shortest paths, then randomly select one of them. Step 3: In each time step, the node i forwards 1 + β ki bags to the next hop node in the buffered queue as the first node to enter and exist. If β ki is not the score, which will be achieved I the way of probability. Step 4: When the bag arrives at a node, it will be queued for forwarding, and the length of the buffer queue of the node i is P. The newly –generated or forwarded bag arrives, if the buffer queue is full, then it will be discarded. Once the package reaches its destination, it will be removed from the system. 3.3. Network Capacity In this paper, a fixed rate of the production bag is λ , to measure the capacity with β . When the network tranmits from the free to congested state , β c is the smaller, indicating greater network capacity. β c is the smallest forward rate coefficient in the free state of the flow. As long as the the forward rate coefficient is no less than this threshold, the network can enjoy a smooth the flow, and the communication networks and transmission can handle all of the information package. Therefore, the critical bag forwarding rate coefficient can also measure the network capacity of the network system [7]. 3.4. BORAimproves the capacity of the network In this model, in each time step each source node sends data bags to a randomly selected destination node among the other n-1 nodes, and the rate of forwarding bags of node I is vi = λi ki , , the forwarding rate of the overall system is
vt = ∑ v j
. If the network is stable, in each time step the average number of
data bags reach node i is Vt B f (i ) + λi ki . So, when the forwarding rate of each node is 1 + β i ki , if Vt B f (i ) + λi ki ≤ 1 + β i ki , no congestion occurs at
the
node
i.
For
any
node
i,
βi ≥ (Vt B f (i ) − 1) / ki + λi
must
be
satisfied.
So,
β c = MAX (Vt B f (i ) − 1) / K i + λi is realized, in which λi is the forward rate of node I, K i is the degree of it. After the BORA, B f (i ) gets smaller, as Vt , λi , K i remains the same, MAX ((Vt B f (i ) − 1) / K i + λi ) is smaller. To sum up, the free communication of the network allows the decrease of the of the smallest data package which means the increase of the network capacity. In the calculation, the forward rate coefficient λi , β i are changeable, so the above conclusion of the maximum network capacity is suitable for all types of Scale-Free network models, which means BORA can effectively improve the network capacity.
Hong CaiCai,et et al. al / Procedia Engineering 15 00 (2011) 1899 – 1904 Hong / Procedia Engineering (2011) 000–000
In real networks, each node will make positive change in routing in case of congestion. Compared with the model in the Reference[5], this model gives an advanced consideration to the routing change regarding the network congestion. Hence, the model is closer to the real network. 4. Simulation of algorithm
In order to validate the above conclusions, this paper applies the OMNET++ BORA to construct a network model based on BORA to make simulation. The parameters in the simulation are set as follows: the network topology takes BA network with the N = 100 and m=3 generated by BRITE , forwarding rate coefficient λ 0.02, namely in each time step the forwarding rate of node i is Vi = 0.02ki , the forwarding bag coefficient β is 0.18, hence, in each time step the forwarding rate of node i is wi = 1 + 0.18ki , the interval between each time step in simulation is 1s. The bag is produced by GEN module, while the rate of the production bag is set according vi and the destination of the remaining nodes are selected at random; the buffering queue is constructed by FIFO module, service is provided according to the principle that earlier coming gets earlier service, the forwarding rate is set by wi , and the maximum storage of buffer is 30 data bags. If the memory is full already, as the principle, new arrived bags will be discarded. The statistical analysis of the results is done by SINK module with the average delay of the bags and the rate of total bag loss in the system as evaluation index; the routing is implemented by ROUTING module, and four routing models are classified according to the different algorithms: model 1achieves the optimal routing in accordance with BORA, model 2 bases the shortest path ROUTING algorithm on the network delay, model 3 is based on the BORA of hop point, and model 4 has the shortest path ROUTING algorithm based on the hop points, for setting the node weight as to node degree (i.e., the number of the edges pointing to the node). Figure 1, Table 1 show the specific simulation results. From Figure 1, the minimum data bags delay is found in model 1, followed by model 3 and 4, and the maximum is in model 4. Table 1 Comparison: the rate of system lost packages of different network models Total bags forwarded
Lost bags
The percent of lost bags %
Model1
500
12
2.4
Model2
500
80
16
Model3
500
20
4
Model4
500
22
4.4
It can be concluded that Model 1 reduces the forwarding delay of data bags, in that optional routing in accordance with BORA considers both the routing delay and the possible flow passing the node. Model 1 is the most superior. Model 2 takes the shortest path as the optional routing, but it pays little attention to the possible congestions, which leads to long time waiting in the transmission process, resulting in longer system delay. Model 3, with not the delay in routing but only the possible flow in the node considered has a longer delay in Model 1. And in the scale-free network, there is few circles, so the delay of the system mainly caused by the waiting of the data bags. Model 3 has a better way dealing with the node congestion, so it is superior in performance than Model 2. In Table 1, presuppose the number of total forwarded bags is 500, it can be seen that the total lost bags of the nodes in Model 1 is 12, the rate is 2.4%, while that in Model 2 is 16% and Model 3 4%. The result
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shows that Model 1 is superior in bag loss, which means in the BA network model closer to the real one, the network based on BORA has larger throughput than the BORA Model 3 based on the hop count and Model 3 based on the shortest path routing algorithm to get the shortest routing delay. Figure 1 Comparison: average system delay of different network models
5. Conclusion
Through the study of node Betweenness, this paper explores the method of setting a node weight through Betweenness to improve the capacity of the system network and applies it to the Scale-Free network based on BA algorithm close to real network. Through the universal network capacity formula deduced, the network model constructed on this algorithm is more close to real Internet. Finally, through the modeling simulation in applying the network OMNET++ simulation software, through the comparison with the previous models, the system BORA effectively reduces transmission time, improve the system throughput and fairness in performance. References
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