A Scalable Multiprocessor Architecture for Pervasive Computing

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1 A Scalable Multiprocessor Architecture for Pervasive Computing Long Zheng 1,2, Yanchao Lu 3,JingyuZhou 3,,MinyiGuo 3,HaiJin 1, Song Guo 2, Yao Shen 3, Jiehan Zhou 4, and Jukka Riekki 4 1 Huazhong University of Science and Technology, Wuhan, , China 2 The University of Aizu, Aizu-wakamatsu, , Japan 3 Shanghai Jiao Tong University, Shanghai, , China 4 University of Oulu, FIN Oulu, Finland zhou-jy@cs.sjtu.edu.cn Abstract. In a case study of a pervasive computing system, we have implemented a system for a JPEG encoding application. The previous system uses static deployment of computing resources, which limits computation capability.to address this limitation, this paper proposes a novel scalable architecture that allows extending a system by adding new subsystems, to meet increasing computation requirements. The novel architecture allows several subsystems to share their Resource Routers (RRs) and Processing Elements (PEs) to improve the efficiency of PEs by introducing a Share Degree (SD) mechanism. Experimental results show that when SD is equal to three, the system achieves the highest performance. Keywords: ubiquitous multiprocessor, computing resource allocation, scalable. 1 Introduction Olympus Future Creation Laboratory and University of Aizu have conducted a collaborative research on developing a general framework for the coming ubiquitous society, where a ubiquitous computing scenario named Ubiquitous Multi- Processor (UMP) that consists of many heterogeneous processing nodes has been extensively studied. A basic framework of multiprocessor simulation system has been implemented based on a multi-way cluster [7] and a double-buffered communication model [6] has been incorporated into the system that can improve the performance over 50%. M. Kubo et al. extends the system and implements a ubiquitous multi-processor network-based pipeline processing framework at the hardware simulation level to support the development of high performance pervasive applications [5]. Our previous work [2,1,3] did not consider the extensibility of the system, thus limiting computation capacity, because only one Resource Router (RR) manages all Processing Elements (PEs), which becomes a bottleneck during high Corresponding author. J. Riekki, M. Ylianttila, and M. Guo (Eds.): GPC 2011, LNCS 6646, pp , c Springer-Verlag Berlin Heidelberg 2011

2 A Scalable Multiprocessor Architecture for Pervasive Computing 43 workload. This motivates us to design a new, scalable architecture to support increasing computation requirements. With the new architecture, computation capacity can be easily extended by simply adding new PEs and RRs. Specifically, our architecture consists of several subsystems. Each subsystem is composed the fixed number of PEs and a RR that manages these PEs. PEs are isolated by subsystems; and RRs are connected with the ring topology. This symmetric architecture allows us to add as many subsystems as needed to meet the computation requirement. In order to increase the efficiency of PEs usage, two mechanisms are proposed in our new architecture that are Deploy as Needed and Share with Neighbors. The latter mechanism allows several neighbor subsystems to share their RR and PEs. We introduce a Shared Degree (SD) to represents the number of neighbor subsystems that share their RRs and PEs with each other. We model and analyze performance of the new architecture. Our analysis shows that SD affects both the efficiency of PEs usage and the workload of RR, both of which eventually affect the performance of system positively and negatively, respectively. The optimal value of SD is the key to optimize the performance of our new architecture. With the performance model we construct, we can find the optimal SD theoretically. The similar thinking in performance model also appears in [8,4]. The remainder of this paper is structured as follows. Section 2 proposes our novel scalable multiprocessor architecture for pervasive computing system. Section 3 analyzes our novel architecture, introduces the SD and constructs a performance model. Performance evaluation is given in Section 4. Section 5 summarizes our findings and concludes this paper. 2 A Novel Scalable Multiprocessor Architecture The UMP system has many PEs working as calculation nodes, and provides various functions by combining some PEs. This is very important to match a wide variety of users needs and provide services they want. In our earlier work, we have implemented a prototype UMP system that offers the JPEG encoding service for transforming from BMP into JPEG format. This paper takes this prototype as a case study. In the rest of this section, we first introduce the previous architecture of UMP, and then propose our new architecture. 2.1 The Drawbacks of Previous Architecture In the previous architecture of UMP system, there are three kinds of nodes: Client Terminal (CT), PE, and RR, as illustrated in Fig. 1. A CT is usually a mobile device with which users can submit BMP pictures to a RR. The RR receives BMP pictures from different CTs and maintains these pictures in a task queue. RR processeseachbmp picture in the task queue sequentially till the task queue is empty. Six PEs are managed by a RR to perform the transformation, since the transformation from BMP into JPEG has six phases and each PE is responsible for one phase.

3 44 L. Zheng et al. Fig. 1. The previous architecture of UMP system The previous architecture limits the scalability of a UMP system. Because there is only one RR managing all PEs that must request RR to transfer tasks to the next PEs, RR becomes the bottleneck of the whole UMP system during high workload and limits the number of PEs that can be deployed. Furthermore, because RR receives tasks from users, the solo RR design limits the physical area that the service of UMP system covers. The above drawbacks motivate us to design a new architecture to make the UMP system extensible. 2.2 Overview of Our Architecture We propose a novel architecture that is scalable for both computation capacity and service coverage. Fig. 2 illustrates the new scalable multiprocessor architecture for ubiquitous computing. In this architecture, we have several solo-router UMP systems to meet computation capacity requirements. The solo-router UMP system in the new architecture is called a UMP subsystem: PEs in each UMP subsystem connect to their own RR; and RRs are connected in a ring topology. According to the demand, the subsystems are located in different places to increase service coverage. In Fig. 2, there are 10 subsystems distributed at location A, B, till F. Because the new architecture is decentralized and all subsystems are symmetric to each other, the new subsystems can be easily added when they are needed. In our new architecture, the Deploy as Needed and Share with Neighbors mechanisms are used to guarantee the service quality for scalable usage and optimize the efficiency of the whole system. Deploy as Needed. The Deploy as Needed mechanism is quite simple, which deploys subsystems at different locations based on daily statistics. For example, in a Theme Park, popular districts with more user demand will have more

4 A Scalable Multiprocessor Architecture for Pervasive Computing 45 Fig. 2. The scalable multiprocessor architecture subsystems deployed. Less popular places may only require one subsystem to satisfy the requirement of service coverage. Thus, the Deploy as Needed is a static mechanism to satisfy user demand. The real situation is more complicated. Take the Theme Park as example again; visitors are crowded in the district that has amusement rides in the daytime, but in the performance hall in the nighttime. Furthermore, when the animal march performance ends and 4D Cinema is about to start a stunning movie, lots of visitor move from the performance ground to the 4D cinema. Although we can put the appropriate amount of subsystems according to the statistical information, we also need a dynamic mechanism to handle peak loads. Share with Neighbors. We focus on the Share with Neighbors mechanism that can deal with the peak load and use idle or under-loaded subsystems effectively. Specifically, we organize subsystems into a ring topology. The Share Degree represents the number of neighbor subsystems that an RR can use, including its own subsystem. Take Fig. 2 as an example, where the ring direction is clockwise. When SD is set to three, the neighbors of Subsystem IV are subsystem IV, V, VI. When SD is one, subsystems cannot share their PEs with any other subsystems. When SD is equal to the number of subsystems in the ring topology, all subsystems can share their PEs. When the Share with Neighbors mechanism is enabled, the PEs in the neighbors become a larger virtual subsystem, with RRs in the neighbors synchronized to each other. We propose Scalable Dynamic Allocation (SDA) algorithm to support the Share with Neighbors mechanism (See Algorithm 1). Note that the notation RRs specifies the RRs in its neighbor subsystems and PE1 means a PE in task phase 1. PE2, PE3, till PE6 refer to PEs in the subsequent phases. A task has six phases.

5 46 L. Zheng et al. Algorithm 1. Scalable Dynamic Allocation (SDA) Algorithm 1: RR receives a new task from a CT. 2: RR finds an idle PE1 from its subsystem and then transfers the task to this PE1. 3: After getting the task RR, this PE1 sends a busy status message to RRs. 4: After processing the task, this PE1 sends an idle status message to RRs and asks RRs for the next PE. 5: RRs finds idle PE2 in each subsystem, and then tells the PE1. 6: PE1 accepts the message of the nearest RR, ignores others. If there is no response from RRs, which means there is no available PE at this moment, PE1 waits a particular time, then asks again. 7: PE2 sends the status busy to RRs; PE1 transfers the task to PE2, and sends idle status message to RRs. 8: PE2, PE3, PE4, and PE5 act in the same manner. 9: After PE6 has processed the task, PE6 transfers the processed task back to the RR that originally owns this task. 10: RR sends back the processed task to the CT. 3 Performance Model and Analysis In our system, the tasks sent by users should be processed as soon as possible for good user experience. Therefore, our goal is to shorten the system response time, i.e., the time between sending a task to RR and getting the response. The average response time T of all tasks in s phases during time interval Δ can be expressed as T = s i=1 g(δ,i) j=1 / s g(δ, i), (1) where is the response time of the j-th task in the i-th phase, and g(δ, i) is the number of tasks of the i-th phase during the time interval Δ. Our performance model can be reasonably simplified with the following two assumptions on time interval Δ: 1. The time interval Δ is any interval after system initialization and before system halt; 2. Except for the beginning and end time, our system time is composed of many Δ in which each subsystem has for each phase no more than one task requesting a PE for the next phase. With the above assumption, it is easy to know that g(δ, i) is equal to the number of subsystems n. Furthermore, since each subsystem has the same number of phases s, so Equation (1) also can be simplified as: T = s i=1 j=1 i=1 n /(n s) (2)

6 A Scalable Multiprocessor Architecture for Pervasive Computing 47 In order to get T,wefirstanalyze, which can be divided into: = EXE + MSG + DATA +, (3) where EXE is the time PE needs to execute the task in i-th phase and in j-th subsystem; MSG is the time that the PE needs to send messages to RRs and other PEs; DATA is the time needed to transmit the task in i-th phase and in j-th subsystem among users, RRs and PEs; and is the total delay time RRs need to response requests from PEs that executes the task in i-th phase and in j-th subsystem. Since i,j EXE and TDATA is determined by the size of tasks, we can consider them as a constant values C. Hence, (3) can be rewritten to = MSG + + C (4) So Equation (2) can be transformed into i=1 j=1 s n T = c + i=1 j=1 MSG s n /(n s) + i=1 j=1 /(n s), (5) where c is a constant, equal to C/(n s). Let the average time of sending messages be T MSG and the average time of RRs response time be T, i.e., T MSG = s n MSG /(n s), and T = s n /(n s). i=1 j=1 Thus, the system performance is decided by T MSG and T. When SD increases, PEs have higher probability to find a free PE in the next phase, which leads to improved system performance. However, as SD increases, RRs will receive more requests from PEs and the response time of RRs will be longer, which leads to decreased system performance. In other words, the system performance is a function of SD and is a tradeoff between T MSG and T. Specifically, MSG can be calculated as: MSG (d) =( P i,j (d) ρ + ( 1 P i,j (d) )) θ(i), (6) where i,j MSG (d) isthevalueoftmsg when SD is d, P i,j (d) is the probability that a PE that executes a task in i-th phase j-th subsystem cannot find any free PE in next phase, θ(i) is the time that a PE in the i-th phase need to find a free PE in the next phase by sending messages when there is at least one free PE in the next phase, and ρ indicates the average times a PE can find a free PE in the next phase after it fails to find a free PE in the next phase. P i,j (d) can be calculated as P i,j (d) = U α N(i,j,d) S(U α ) S max, (7) where U α represents a particular PE, function N(i, j, d) returns a set that includes all neighbor PEs of the j-th subsystem in the i-th phase when SD is d,

7 48 L. Zheng et al. S(U α ) is the task size of U α,ands max is the maximal size of tasks. With Equation (7), we can get the probability that when SD is d, PE executing the task in i-th phase j-th subsystem cannot find any free PEs in the next phase in the worst case. NowwegettheexpressionofT MSG. Based on the analysis above, the average of RRs response time T is relative to the workload of each RR, so we first calculate W i,j (d), the workload of RR of the j-th subsystem in the i-th phase when SD is d. W i,j (d) =( P i,j (d) ρ + ( 1 P i,j (d) )) ω(i), (8) where ω(i) is the workload that the PE executing the task in i-th phase j-th subsystem causes to find the free PE in the next phase if there is at least one free PE in the next phase. In our architecture, there aren subsystems in the system, that is, n RRs exist. The workload of RR in the j-th subsystem, R j can be calculated as follows: R j = k+d 1 k=j s i=1 W i,k (d). (9) Because k + d 1maybegreaterthann, we define W i,j = W i,j+n for (j <n). Hence, if μ, the processing capacity of RR during Δ is known, the average of response time of RRs, T can be calculated as T = 1 2 μ n n R j (10) Finally, we re-organize the expressions above. The average of response time of each task T is expressed as follows. T = T MSG + T + c j=1 T MSG = 1 s n n s i=1 j=1 MSG (d) T = 1 2 μ n n j=1 k+d 1 s k=j i=1 W i,k (d) MSG (d) =( P i,j (d) ρ + ( 1 P i,j (d) )) θ(i) (11) W i,j (d) =( P i,j (d) ρ + ( 1 P i,j (d) )) ω(i) P i,j (d) = U α N(i,j,d) S(U α ) S max In Equation (11), the variables s, n, ρ, μ, θ(i) andω(i) areknown.inthese variables, s, n, ρ, andμ are system parameters; θ(i) andω(i) are decided by the SDA algorithm in the system. From the analysis of SDA algorithm, it is easy to

8 A Scalable Multiprocessor Architecture for Pervasive Computing 49 Table 1. θ(i) andi i θ(i) 2τ 3τ 3τ 3τ 3τ 2τ Table 2. ω(i) andi i ω(i) define a map between θ(i) andi; so is the one between ω(i) andi. The maps are listed in Table 1 and Table 2. Therefore, we find out that T is decided by d, the value of SD. With the performance model expressed by Equation (11), we can find the optimal value of SD, such that the system response time is the minimal. Table 3. Parameters of Practical Environment Symbols Values Descriptions s 6 The number of phases. n 10 The number of subsystems. μ req/s The process capacity of RR. (Gigabit Router using 266MHz embedded processor. τ 0.5 ms The message transmission delay. d [1,n] The range of values of SD. S(U α )/S max [0.8,1] The range of S(U α )/S max. Δ 0.5 ms The value that satisfies the two assumptions about the time interval in practice. 60 The number of PEs in a subsystem. This value will be used indirectly in Equation (7). 4 Performance Evaluation We evaluate the performance of our systems with simulations. The parameters for the system are listed in Table 3. Our simulation is implemented using Matlab. Fig. 3 shows the values of T MSG and T with different values of SD. When ρ increases, both T MSG and T become larger. However, the difference between values of ρ is very small, and the difference is small when SD is greater than four. When SD varies from 1 to 10, T MSG decreases but T increases, which is consistent with our analysis in Section 3. Fig. 4 depicts the values of T with different values of SD. Since there is a constant c in T, we show the value of T excluding c. We can observe that the average response time decreases first, and then increases as the value of SD varies from 1 to 10. For different values of ρ, all the average response times achieve the minimum when SD is three. Therefore, with our current system configuration, we should set SD to three to minimize the average response time.

9 50 L. Zheng et al. Fig. 3. The values of T MSG and T with different values of SD 5 Conclusion Fig. 4. The values of T with different values of SD Our previous work uses the static deployment of computing resources, which is difficult to extend for use in dynamic environment. To solve this problem, we propose a novel scalable architecture with a ring topology to connect each subsystem so that this decentralized structure makes it easier to extend the computing capacity by adding the new subsystem to any location of the system.

10 A Scalable Multiprocessor Architecture for Pervasive Computing 51 Our architecture also enables Deploy as Needed and Share with Neighbors two mechanisms that optimize the performance. We focus on the Share with Neighbors mechanism and propose a new SDA algorithm. To achieve the best performance, we formally analyze our system performance and find that the performance of our system depends on the value of SD. Experimental results show that with our current system configuration, when SD is set to three, the average response time is lowest. Acknowledgment This work was supported in part by NFSC (Grant No , ), and the National 973 Basic Research Program (No. 2007CB310900) of China. Jingyu Zhou is the corresponding author. References 1. Dong, M., Zheng, L., Ota, K., Guo, S., Guo, M., Li, L.: Improved Resource Allocation Algorithms for Practical Image Encoding in a Ubiquitous Computing Environment. Journal of Computers 4(9), (2009) 2. Dong, M., Zheng, L., Ota, K., Guo, S., Guo, M., Li, L.: A trade-off approach to optimal resource allocation algorithm with cache technology in ubiquitous computing environment. In: International Conference on Computational Science and Engineering, CSE 2009, vol. 1, pp (August 2009) 3. Dong, M., Zheng, L., Ota, K., Ma, J., Guo, S., Guo, M.: A probabilisticapproach based resource allocation algorithm in pervasive computing systems. In: International Conference on Computer Application and System Modeling (ICCASM), vol. 11, pp. V-315 V-319 (October 2010) 4. Huh, J., Kim, C., Shafi, H., Zhang, L., Burger, D., Keckler, S.W.: A nuca substrate for flexible cmp cache sharing. IEEE Transactions on Parallel and Distributed Systems 18, (2007) 5. Kubo, M., Ye, B., Shinozaki, A., Guo, M.: Ump-percomp: A ubiquitous multiprocessor network-based pipeline processing framework for pervasive computing environments. In: 21st International Conference on Advanced Information Networking and Applications, AINA 2007, pp (2007) 6. Shinozaki, A., Shima, M., Guo, M., Kubo, M.: Multiprocessor Simulator System Based on Multi-way Cluster Using Double-buffered Model. In: 21st International Conference on Advanced Information Networking and Applications, AINA 2007, pp (2007) 7. Shinozaki, A., Shima, M., Guo, M., Kubo, M.: A high performance simulator system for a multiprocessor system based on a multi-way cluster. In: Jesshope, C., Egan, C. (eds.) ACSAC LNCS, vol. 4186, pp Springer, Heidelberg (2006) 8. Zheng, L., Dong, M., Jin, H., Guo, M., Guo, S., Tu, X.: The core degree based tag reduction on chip multiprocessor to balance energy saving and performance overhead. In: Ding, C., Shao, Z., Zheng, R. (eds.) NPC LNCS, vol. 6289, pp Springer, Heidelberg (2010)