# The Extended Dijkstra s-based Load Balancing for OpenFlow Network

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3 291 ISSN: Figure 3. The flow table entry of the OpenFlow switch [10] The algorithm uses ToR (Top of Rack) Switch-to-ToR Switch Paths Table (S2SPT) and Load Allocation Table (LAT). However, maintaining S2SPT becomes a problem for the LABERIO, if the network topology changes. So, the LABERIO is not suitable in wide area network network that has dynamic topology. 2.2 The Extended Dijkstra s Algorithm Given a weighted, directed graph G=(V, E) and a single source node s, the classical Dijkstra s algorithm can return a shortest path from the source node s to every other node, where V is the set of nodes and E is the set of edges, each of which is associated with a non-negative weight (or length) [11]. In the original Dijkstra s algorithm, nodes are associated with no weight. The paper [4] shows how to extend the original algorithm to consider both the edge weights and the node weights. Figure 4 shows the extended Dijkstra s algorithm, whose input is a given graph G=(V, E), the edge weight setting ew, the node weight setting nw, and the single source node s. The extended algorithm uses d[u] to store the distance of the current shortest path from the source node s to the destination node u, and uses p[u] to store the previous node preceding u on the current shortest path. Initially, d[s]=0, d[u]= for u V, u s, and p[u]=null for u V. Extended Dijkstra s Algorithm Input:G=(V, E), ew, nw, s Output:d[ V ], p[ V ] 1: d[s] 0; d[u], for each u s, u V 2: insertu with key d[u] into the priority queue Q, for each u V 3: while(q ) 4: u Extract-Min(Q) 5: for each v adjacent to u 6: ifd[v]>d[u]+ew[u,v]+nw[u] then 7: d[v] d[u]+ew[u,v]+nw[u] 8: p[v] d[u] Figure 4. The extended Dijkstra s algorithm [4] Note that the extended Dijkstra s algorithm is similar to the original Dijkstra s algorithm. The difference is that the extended version adds the node weight in line 6 and line 7 of the algorithm. The original Dijkstra s algorithm cannot achieve the same result just by adding node weights into edge weights. This is because the node weight should be considered only at the outgoing edge of an intermediate node on the path. Adding node weights into edge weights implies that an extra node weight of the destination node is added into the total weight of every shortest path, making the algorithm return the wrong result. The extended Dijkstra s algorithm is very useful in deriving the best routing path to send a packet from a specific source node to another node (i.e., the destination node) for the SDN environment in which significant latency occurs when the packet goes through intermediate nodes and edges (or links). Below, we show how to define the edge weights and node weights so that the extended Dijkstra s algorithm can be applied to derive routing path for some specific SDN environment. Assume that we can derive from the SDN topology a graph G=(V, E), which is weighted, directed, and connected. For a node v V and an edge e E, let Flow(v) and Flow(e) denote the set of all the flows passing through v and e, respectively, let Capability(v) be the capability of v (i.e., the number of bits that v can process per second), and let Bandwidth(e) be the bandwidth of e (i.e., the number of bits that e can transmit per second). The node weight nw[v] of v is defined according to Eq. (1), and the edge weight ew[e] of e is defined according to Eq. (2). IJECE Vol. 5, No. 2, April 2015 :

7 295 ISSN: Milliseconds Proposed Round Robin Randomized LABERIO Number of Clients Mbps Proposed Round Robin Randomized Number of Clients Figure 8. End-to-End Latency Figure 9. Throughput Proposed Randomized Round Robin LABERIO Number of Clients Figure 10. Standard Deviation Load of Servers 5. CONCLUSION This paper proposes a load-balancing algorithm that takes advantage of the extended Dijkstra s shortest path algorithm. The extended Dijkstra s shortest path algorithm was used to find the nearest server for a requesting client. The extended Dijkstra s algorithmconsiders not only the edge weights but also the node weights for a graph derived from the underlying SDN topology. We use Pyretic to implement the proposed load-balancing algorithm under the Abilene network topology with the Mininet emulation tool. The simulation results show that the proposed load-balancing algorithm outperforms others in terms of the network end-to-end latency, and throughput. REFERENCES [1] H. Long, Y. Shen*, M. Guo, and F. Tang. LABERIO: Dynamic load-balanced routing in OpenFlow-enabled networks. IEEE 27th International Conference on Advanced Information Networking and Applications [2] N. Handigol, S. Seetharaman, M. Flajslik, N. McKeown, and R. Johari. Plug-n-Serve: Load-balancing web traffic using Open Flow. Demo at ACM SIGCOMM, Aug [3] M. Koerner and O. Kao. Multiple Service Load-Balancing with Open Flow. IEEE 13th International Conference on High Performance Switching and Routing [4] J.R. Jiang, H.W. Huang, J.H. Liao, and S.Y. Chen. "Extending Dijkstra s Shortest Path Algorithm for Software Defined Networking". in Proc. of the 16th APNOMS [5] Abilene Network, last accessed on March 4, [6] J. Reich, C. Monsanto, N. Foster, J. Rexford, and D. Walker, Modular SDN Programming with Pyretic. Technical Reprot of USENIX, available athttp:// IJECE Vol. 5, No. 2, April 2015 :

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