A Method Based on the Combination of Dynamic and Static Load Balancing Strategy in Distributed Rendering Systems

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1 Journal of Computational Information Systems : 4 (24) Available at A Method Based on the Combination of Dynamic and Static Load Balancing Strategy in Distributed Rendering Systems Wei YAO, Huawei PAN, Chunming GAO College of Information Science and Engineering, Hunan University, Changsha 482, China Abstract For lacking of effective load balancing strategy to improve the performance of distributed rendering systems or poor result of load balancing strategy, this paper proposes a load balancing method based on the combination of dynamic and static load balancing strategy. At first, static load balancing strategy is used in the initial stage of assigning task. Then, using dynamic load balancing strategy balance the load of each node during the process of rendering. It can reduce the processing time of the whole system and improve system performance effectively. Experiment results show that the method can give better balance and higher processing capacity than traditional load balancing methods. Keywords: Distributed Rendering System; Dynamic Load Balancing; Static Load Balancing; Processing Capacity Introduction Load balancing problem is also called task scheduling problem, which directly affects the efficiency and performance of distributed systems. It can be divided into two categories: static load balancing [] and dynamic load balancing [2]. Using static load balancing means we can determine load partition in advance. While using dynamic load balancing means we can detect load of each node and divide load during run phase. The standard of classifying load balancing strategies, Wang et al., [3] proposed, was to judge the sponsor between sender and receiver. The standard took into account trigger position of strategy and dependent information. The classification proposed by Casavant et al., [4] was not unique, in other word, the classification existed overlaps. Baumgartner et al., [5] presented a unique and non-overlapping classification. Yang et al., [6] divided dynamic load balancing strategies into distributed, centralized and hybrid/hierarchical strategies according to the characteristics of controlling position. Distributed strategies contained diffusion method, dimension exchange method, gradient method; centralized strategies [7] contained RandCentLB, Project supported by the Science and Technology Plan of Science and Technology Agency of Hunan Province (No. 23WK323). Corresponding author. address: gcm2@63.com (Chunming GAO) / Copyright 24 Binary Information Press DOI:.2733/jcis9566 February 5, 24

2 76 W. Yao et al. /Journal of Computational Information Systems : 4 (24) RefineLB, RefineKLB [8] and so on; hybrid/hierarchical strategies mainly contained HBM [9] and HybridLB [7], HBM used the hierarchy tree to balance multilevel load, HybridLB divided processors into some independent and autonomous groups, and organized these groups according to hierarchical structure. Currently, some common dynamic load balancing methods [, ] in distributed systems were fastest response method, least connection method, polling method and so on. The disadvantage of fastest response method was that the responding time of each node interconnecting via Gigabit Ethernet was almost same. did not take into account the intensity of task request and server performance, because consumption and utilization of system resource for different task were very different and the number of connection could not really reflect load condition. was the simplest and easiest method that every node was selected equally, but it needed the same node environment to run better. In this paper, we propose a load balancing method based on the combination of dynamic and static load balancing strategy, which can balance load of each node of distributed rendering system, thus system needs less time to render a certain amount of data. Meanwhile, we put forward load index to estimate the system performance and load balancing condition. 2 Distributed Rendering System This paper presents a distributed rendering system which adopts Client/Server mode. Fig. is the flow chart of the system whose nodes connect server via Mbit Ethernet, server submits task and uses static load balancing strategy to divide and assign task, so that every node receives task with the same size. When some nodes turn into idle state, server uses dynamic load balancing strategy to redistribute task through load transferring to balance load of each node, so as to improve resource utilization and the performance of the distributed rendering system. Server Nodes Start Static load balancing Distributing render task sending command of distributing the task Receiving assignment Rendering Dynamic load balancing Sending the command of load transference and receiving request command response command Sending the request of load transferring RenderingF file_ j_ rest response RenderingF file _ j _ rest Receiving information of load transference and sending response information command Receiving request of load transference information Completion of rendering End Fig. : The flow chart of the distributed rendering system

3 W. Yao et al. /Journal of Computational Information Systems : 4 (24) Server is the central part of the system and all nodes connect it via high-speed Ethernet, its stability directly affects system performance. The main work of server can be summarized as follows. () Task Allocation: According to frame-to-frame coherence, server uses average cycle division method to divide all frames of every render file. (2) Load Transferring and Monitoring: According to the size of load, sever decides and executes load transferring, and monitors running status and the load condition of every node. Nodes, the real executor of system, are responsible for rendering task. Meanwhile, according to load condition, they send request of load transferring to server or receive command of load transferring from server. 3 Load Balancing Method Task transferring of dynamic load balancing strategy will increase communication time and waiting time, sometimes decrease system performance, even its effect is worse than static load balancing strategy [2]. To solve the problem, static load balancing strategy is used to average task and assign them to each node when server submits task. When nodes are rendering, using dynamic load balancing strategy balance load by transferring a part of load of heavy-load nodes to light-load nodes. 3. Static load balancing strategy When server submits task, average cycle division method (ACDM) is used to divide task according to frame-to-frame coherence and assign them to each node. We set the set of n nodes and the set of s render files as Node = {N, N 2,, N n }, file = {file, file 2,, file s }, respectively. For conveniently expressing our method, we set sequence number of the start frame of every render file as, and the corresponding frame number of render files is F file, F file 2,, F file s, respectively. ACDM is to assign all frames of file j (j =, 2,, s) to N, N 2,, N n in rotation, the number of frames for every node is F j = F file j /n, and x indicates rounding down x, the set of frames for N i is sf i,j = {k n + i k =,,, F j }. We call the frames allocating by ACDM as allocated frames, and call the rest of frames as unallocated frames, the number of unallocated frames is F file j rest = F file j n F file j /n. We define a mark of having completed task for N i as r i, if N i has completed task, we set r i =, otherwise r i =. 3.2 Dynamic load balancing strategy When some nodes turn into idle state, we use dynamic load balancing strategy to improve the processing efficiency of system. The rendering process of file j is as follows. When some nodes complete the assigned task at the moment, we set the subscript set of nodes as L = {l i r li =, i =, 2,, n l }, and set the subscript set of the rest of nodes as M = {m i r mi =, i =, 2,, n m }. We record the time which each node complete a frame,

4 762 W. Yao et al. /Journal of Computational Information Systems : 4 (24) and compute the average rendering time T li of the corresponding nodes of L. We sort nodes in ascending order according to the value of T li, and reset the subscript set of these nodes L = {l i r li =, i =,, n l }. When n l and F file j rest >, server will assign unallocated frames to the corresponding nodes of L. If F file j rest n l, as shown in Fig. 2(a), server distributes unallocated frames to the first F file j rest corresponding nodes of L one by one, we use F (F file j rest ) F (L, F file j rest ) to express this procedure; then update node state r li =, where i =,, F file j rest, and set F file j rest =, L = L C L A and M = M A, where A = {l i r li =, i =,, F file j rest }. Otherwise, as shown in Fig. 2(b), server distributes the first n l frames of unallocated frames to the all corresponding nodes of L one by one, we use F (n l ) F (L, n l ) to express this procedure; then update node state r li =, where i =,, n l, and set F file j rest = F file j rest n l, M = M L and L =. Nl thenf file_ j n -th frame Nl the nf n file_ j -th frame N Nl 2 l Ffile _ j _ rest the nf n the file_ j 2 Ffile_ j -th frame -th frame unallocated frames F file _ j _ rest Nl nl thenf file_ j n nl-th frame unallocated frames F file _ j _ rest Nl Ffile _ j _ rest thef file _ j -th frame thef file _ j -th frame (a) (b) Fig. 2: The procedure of assigning unallocated frames If F file j rest =, card(m) and card(l) (card(x) indicates the number of set X), system will transfer load. We discuss load transferring process from the following two cases. () When card(l) card(m), server assigns the last frame of the corresponding nodes of M to the first card(m) corresponding nodes of L one by one, using F (M, card(m)) F (L, card(m)) to express the procedure, then update r li, L and M. (2) When card(l) < card(m), server assigns the last frame of the first card(l) corresponding nodes of M to the all corresponding nodes of L one by one, using F (M, card(l)) F (L, card(l)) to express the procedure, then update r li, L and M. 4 Experimental Results When the distributed rendering system uses our method, this experiment is used to estimate system performance from two aspects: the time of finishing task and the load balancing condition of system. 4. Experimental environment Our system is built by two different computers, PC and PC2, whose hardware configuration respectively are: Inter(R) Core(TM) i3 4GB RAM, Quad-Core Processor, In-

5 W. Yao et al. /Journal of Computational Information Systems : 4 (24) ter(r) HD Graphics Card; Inter(R) Core(TM) 4GB RAM, Eight-Core Processor, NVIDIA GeForce GTX 46 Graphics Card; Operating System of all computer is Windows XP. We divide experiments into three groups that they are consist of 2 nodes, 4 nodes and 8 nodes, where 2 nodes are divided into PC + PC2 and 2 PCs two cases; 4 nodes are divided into 2 PCs + 2 PC2s and 4 PCs; 8 nodes represents 6 PCs + 2 PC2s. Table shows the detailed information of five render files: polygon number, file size, the number of frames, output image resolution and others. Table : Detailed information of five render files file file 2 file 3 file 4 file 5 Polygon number Size(MB) F file j Renderer mental ray mental ray mental ray mental ray mental ray Output image format.tga.tga.tga.tga.tga Image resolution(pixel pixel) The time of finishing task Table 2 shows the time needed for the system to finish the five files when we use no load balancing, least connection method (LCM), polling method (PM) and our method for every experiment, and unit of time is second (s). Obviously, when system does not use load balancing method, namely no load balancing, the time needed is the maximum; even we increase the number of nodes, it does not improve system performance effectively. When system uses the same load balancing method and the same number of nodes, except 2 nodes system using least connection method, compared with system using the same configured computers, system using the different configured computers needs less time to complete the five files, because the hardware configuration of PC2 is better than which of PC. We know from Table 2, when the system uses the same number of nodes and the same configured computers, the time needed for system using our method is the least. Experiments show that our method can decrease time for system to complete a certain amount of task. Table 2: The time (s) for the system finishing the five files Experiment nodes PC PC2 no load balancing LCM PM One (s) (s) (s) (s) Two (s) (s) (s) (s) Three (s) (s) 857.5(s) (s) Four (s) (s) (s) (s) Five (s) (s) 98.53(s) (s) Fig. 3 indicates the average time for 2 nodes, 4 nodes and 8 nodes system using least connection method, polling method and our method to complete the five files, and vertical axis indicates time, horizontal axis indicates the number of nodes. Red solid line indicates the time for system using our method, and it is the least. As the number of nodes increases, rendering time decreases

6 764 W. Yao et al. /Journal of Computational Information Systems : 4 (24) gradually for system using any one method. When nodes increases exponentially, rendering time does not decrease strictly exponentially, because the more the nodes, the more overhead and waiting time for server assigning task and transferring load node number Fig. 3: Variation of the average time for 2 nodes, 4 nodes and 8 nodes system 4.3 The load balancing condition of system We use load index to estimate the system performance. We set the load of node N i as load i at the present moment that system is running. First, we compute the ratio of the load of node N i and the average load of all nodes: ratio i = load i /µ load, (µ load ), where µ load = n i= load i/n, n is the number of nodes. Then, we set ratio = {ratio, ratio 2,, ratio n }, assume the probability of each node is /n, and compute the D(ratio) of ratio. D(ratio) = E{(ratio µ ratio ) 2 } = n n i= (ratio i) 2 (µ ratio ) 2 = [ n n i= (ratio i) 2 n] The value range of D(ratio) is [, n-]. When the value of D(ratio) decreases, the load tends to be more balanced, and system performance increases; and vice versa. Fig. 4 indicates the load balancing condition of 2 nodes, 4 nodes and 8 nodes system, where (a) and (b) denote the load balancing condition of 2 nodes system using the same configured computers and the different configured computers, respectively; (c) and (d) denote the load balancing condition of 4 nodes system using the same configured computers and the different configured computers, respectively; (e) denotes the load balancing condition of 8 nodes system using 6 PCs + 2 PC2s. It can be seen from the following five graphs, the fluctuation of 2 nodes system is large and frequent, because load of whichever node changes, the load balancing condition will change a lot. When there are a large number of nodes, changing the load of a few nodes have a little influence on the balance, therefore, the more the nodes, the smaller the fluctuation, and the more stable the system performance. Compare with (b) and (d) respectively, we can know D(ratio) and fluctuation of (a) and (c) using any load balancing method are slightly smaller, which indicates when the hardware configuration is same, the processing capacity is almost same, the time for nodes rendering adjacent frames is also similar and load tends to be more balanced. The red solid line in Fig. 4 denotes the load balancing condition of system using our method; similarly, the green dotted line denotes using least connection method and blue dot and dash line denotes using polling method. Experiment results show that our method is more stable,

7 W. Yao et al. /Journal of Computational Information Systems : 4 (24) thus the system performance is better. Especially, for 4 nodes and 8 nodes system, D(ratio) is or slightly greater than during intermediate period, which indicates that load of each node tends to balance. While the fluctuation of D(ratio) which the blue dot and dash line represents is frequent. It indicates when system assigns task to each node in rotation, load of each node changes fast and frequently, resulting in poor overall balance. The fluctuation and D(ratio) which green dotted line indicates are smaller than which of polling method, but a little bit bigger than which of our method (a) (b) (c) (d) (e) Fig. 4: Load balancing condition of different system: (a) 2 PCs system, (b) PC + PC2 system, (c) 4 PCs system, (d) 2 PCs + 2 PC2s system, (e) 6 PCs + 2 PC2s system We can see from Fig. 4, the value of D(ratio) instantly rises to the maximum for all load balancing methods at the last moment, because there is only one node which owns load, so D(ratio) = [ n n i= (ratio i) 2 n] = (n2 n) = n. Similarly, the value of D(ratio) is n n during the initial stage of assigning task, because every node receives task in order. As every node receives or completes task, the value of D(ratio) will change a lot, so the fluctuation is large during the early period and the late period. In general, our method is better than least connection method and polling method on improving system performance.

8 766 W. Yao et al. /Journal of Computational Information Systems : 4 (24) Conclusions and Future Work In order to solve load balancing problem in distributed rendering systems, we propose this method based on the combination of dynamic and static load balancing strategy, it can effectively balance load, reduce time for processing a certain amount of task, and improve system performance. Meanwhile, we propose load index to estimate the load balance of system, we can judge the overall balance at every moment. The disadvantage of this method is that it limits to be used in distributed rendering systems, and we cannot guarantee its good performance when it is used in other distributed systems. The future work is to generalize this method so that it can be applied to different distributed systems, and achieve good balance and high treatment efficiency. References [] H.P. Chen, H. Li and G.L. Chen, Heuristic task scheduling in parallel distributed computing, Computer Research and Development 34 (997) [2] R.Diekmann, A. Frommer and B. Monien, Efficient schemes for nearest neighbor load balancing, Parallel Compute 25 (999) [3] Y.T. Wang, et al., Load sharing in distributed system, IEEE Transactions on Computers 34 (985) [4] T.L. Casavant, J.G. Kuhl, A taxonomy of scheduling in general-purpose distributed computing systems, IEEE Transactions on Software Engineering 4 (988) [5] K.M. Baumgartner, et al., A global load balancing strategy for a distributed computer system, in: Proc of the 988 International Conference on Distributed Computer Systems, 988, pp [6] J.X. Yang, G.Z. Tan and R.S. Wang, A Survey of Dynamic Load Balancing Strategies for Parallel and Distributed Computing, Acta Electronica Sinica 38 (2) [7] G.B. Zheng, Achieving high performance on extremely large parallel machines: performance prediction and load balancing, Urbana: UIUC, 25. [8] T. Agarwal, Strategies for topology-aware task mapping and for rebalancing with bounded migrations, Urbana: UIUC, 25. [9] M.H. Willebeek-LeMair, A.P. Reeves, Strategies for dynamic load balancing on highly parallel computers, IEEE Transactions on Parallel and Distributed Systems 4 (993) [] Y.L. Wang, B.L. Ye, Research on dynamic load balancing of parallel field, Science Technology and Engineering 5 (25) [] G. Pei, W.D. Zeng, et al, Research of network load balancing in distributed systems, Computer CD Software and Applications 6 (2). [2] S. Penmatsa, A.T., Chronopoulos, Dynamic Multi-user Load Balancing in Distributed Systems, in: Proc of the International Conference on Parallel and Distributed Processing Symposium, 27, pp. -.