Adaptive Load Shedding for Data Stream Using PI Feedback Controller

Journal of Computational Information Systems3:5(2007) 1827-1832Available at Adaptive Load Shedding for Data Stream Using PI FeedbackControllerChongzheng HUANG1,2*, Shaojiang CAI1,Ｚhijun XIE1,2,Yuanyu ZHANG3, Hong CHEN1,21School of Information, Renmin University of China, Beijing 100872, China2Key Laboratory of Data Engineering and Knowledge Engineering, MOE3 School of Electronics and Information Engineering, Xi’an Jiaotong UniversityAbstractL oad shedding has been widely used in data stream management systems (DSMSs) to keep DSMSs running steadily. One key problem in load shedding is determining how much system load to shed. Existing works tend to adapt coarse algorithm (CA) to solve this problem. In this paper, we present an adaptive PI controller-based load shedding framework for data stream. The main contribution of this paper is our use of feedback control theory to design the load shedding scheme. In contrast to the existing approaches, we firstly apply system identification to establish a dynamic model to describe DSMS, which enables us analyze DSMS quantitatively. Then, based on the model, we use the Root Locus method to design the PI controller with proven performance guarantees. The adaptive framework has been implemented by modifying Borealis system. Theoretic analysis and experimental results demonstrate that our approach is robust even when system load changes frequently. Comparing to existing strategies, our approach also achieves significantly better performanceKeywords: Data Stream; Load Shedding; PI Controller1.IntroductionThe data in typical data stream are usually unbounded, continuous, huge amount, fast arriving and time various. Under this circumstance, the huge amount of data arriving in DSMS may exceed the total processing ability of DSMS. To insure that DSMS could run steadily in this situation, DSMS has to find a way to depress the system load, so come forth the load shedding problem.One key problem in load shedding research is deciding how much to shed. If DSMS discards too much data input, query accuracy is downgraded unnecessarily, on the other hand, DSMS could not keep running steadily if excessive input load is not shed enough. Currently, there have been many works on load shedding issue [1,2,4,5] etc. However, to solve how much problem, these methods employ simple and intuitive strategies, which we call Coarse Algorithm (CA). Fig.1 shows a typical Coarse Algorithm utilized in many DSMSs.CA works well when input load changes infrequently. However, in practice, input load may fluctuate* Corresponding author.Email addresses: huangchongzhengruc@(Chongzheng HUANG)1553-9105/ Copyright © 2007 Binary Information PressSeptember, 20071828 C.Huang et al. /Journal of Computational Information Systems 3:5 (2007) 1827-1832within a wide range. Under this situation, CA may suffer from poor performance. For example, in Fig.2(a), the incoming data rate keep increasing, which is very typical in data stream. In this case, CA will not shed enough load: At the period T, CA computes the load shedding fraction F t+1 for the next period T+1 through the current system load L t , yet the incoming load at the period T+1 is greater than L t . As a result, more and more tuples are accumulated in the DSMS, until the DSMS is blocked. As the same reason, CA may shed too much tuples when the input load is decreasing (Fig.2(b)), causing unnecessary data loss. The above examples are just two of many cases that the CA cannot handle. Things become more serious when we consider the fact that the incoming data pattern and per-tuple processing cost keep changing over time.Fig.1 Coarse AlgorithmIn this paper, to solve the problem, we introduce feedback control into load management of data stream. We formulate the load shedding of DSMS as a feedback control problem and apply feedback control theory to develop a adaptive load shedder.The rest of the paper is organized as follows. In Section 2 we give a overview of the feedback PI controller-based framework. In section 3, we use system identification to model DSMS; In Section 4, we apply feedback theory to systematically design a PI controller. Experiments results are show in Section 5. Finally, we conclude the paper in Section 6.Fig 2. Two Cases of Load Input VarietyFig.3 the Framework of Load Shedding Model2. PI Controller-based Load Shedding FrameworkIn this section, we introduce the framework of adaptive load shedding using feedback PI controller. Various resources including CPU, memory, and network bandwidth may become the bottleneck in DSMS queryC.Huang et al. /Journal of Computational Information Systems 3:5 (2007) 1827-1832 1829processing. In this paper, we focus on the situation where CPU resource is limited, which is the typical case in data stream environment. In order to present, we need to define some system variables as follow: Processing delay is the time elapsed since a tuple arrives at the DSMS till it leaves. Because of the limit of CPU capability, processing delay may arise as data input rate accelerates. Load shedding is performed to reverse the increase of processing delay due to overloading. We denote the processing delay of a tuple as D in this paper.Controlled variable is the performance metric monitored by the monitor. In our model, the average per-tuple processing delay AD(k) is used as control variable. AD(k) is defined over a time window {(k-1)W,kW}, where W is the sampling period and k is called the sampling instant. For the simplicity, time window {(k-1)W,kW} is also called time window k.Target delay time (D t) represents the desired system performance in terms of the control variable. We allow the administrator to specify the target delay time to the system. The difference between D t and the current value of the controlled variable AD(k) is called Error, .ie., E(k)= D t – AD(k).Fig.3 illustrates the framework of the feedback PI controller-based load shedding model. The monitor measures the controlled variable AD(k) and feeds the sample back to the PI controller. The controller compares the target delay time D t with AD(k) to get the current error E(k), and computes the control signal C(k). The load shedding controller receives control signal C(K) from the PI controller and uses a simple P ( proportional ) control function to compute the filter proportion of load shedder. Then, our system dynamically changes the accepted data arrive rate at each sampling instant k according to the control signal C(k). For example, if the arrive rate I(k) is supposed to be lower, we simply give the filter a high proportion, and then the filter drop the data items with this proportion.3.DSMS ModelingA dynamic model describes the mathematical relationship between the input and the output of a system. Modeling is important because it provides a basis for the analytical design of a feedback controller. To design a PI controller, we need the dynamic model for the DSMS. Intuitively, the output of DSMS depends on the input and the continuous queries registered into DSMS. Because those continuous queries keep running until the system is down, we can simply assume that the output of DSMS is only relative to the input. As described above, the input of the DSMS is I(k), and the output is AD(k).3.1.Model StructureThe DSMS is modeled as a difference equation with unknown parameters, i.e., an n th model can be described as follows:∑∑= =−+−=nj jnjj jkI bjkADakAD11) ()()((1)In an n th order model, there are 2n parameters {a j,b j | 1≤j≤n} that need to be decided by the least squares estimator.1830 C.Huang et al. /Journal of Computational Information Systems 3:5 (2007) 1827-18323.2. White Noise InputTo stimulate the dynamics of the DSMS, we use a standard pseudo-random digital white noise generator to randomly switch the process ratios between two different levels. White noise input has been commonly used for system identification. The standard white noise algorithm is not presented due to space limitations and can be found in [6].4. PI Controller-Based Load SheddingIn this section, we use Root Locus to design the PI controller. Due to space limitations, we only summarize results of the design in this paper. The details of the Root Locus design process can be found in control textbooks such as [7].A digital form of the PI control function is:))1()(()1()(−−+−=k rE k E g k uC k C (2)Where u ，g and r are design parameters called the control damping , the controller gain and the controller zero , respectively. The transfer function of the PI controller (Equation (2)) in the z-domain is:uz r z g z C −−=)()( (3) Given the dynamic model of DSMS described by Equation (1) and the controller model described by Equation (3), we can get the transfer function of the closed loop server as Equation (4):)21()211()(2b b g u z a a r g z r gz z G c +−+++−+−= (4) According to feedback control theory, the performance of a system depends on the poles of its transfer function. The location of system poles can tell how fast the system respects to and how well the response would be. In this paper, the closed-loop load shedding performance is evaluated by the speed and smoothness, or convergence rate and damping , of system’s response to the variety of input load. Short convergence rate , in most of cases, means that too much data may be shed. Damping is another import metric to evaluate the closed-loop system’s performance. Smaller damping causes more severe oscillation, which is not desirable. In this study, we set the desired convergence rate to four sampling periods. This means the system, in respond to dynamics, would converge to %75112≈−e of the desired value in four sampling period. We set system damping to 0.8 and set the desired closed-loop poles to be on the real axis, at 0.7. Thus, the desired closed-loop characteristic equation (CLCE) is:056.05.1)8.0)(7.0(2=+−=−−z z z z (5) Matching the CLCE of Equation (4), we get the following equation:)21()211(2b b g u z a a r g z +−+++−+=56.05.12+−z z (6) At the steady state, the system output AD(k) may be exactly as same as the target value D t. This meansC.Huang et al. /Journal of Computational Information Systems 3:5 (2007) 1827-1832 1831that1|)21()211(12=+−+++−+−=z b b g u z a a r g z r gz (7)By solving Equation (6) and Equation (7), we can determine u, g, r .5. Performance Evaluation5.1. Experiment Setup To validate our idea, we modified the source code of Borealis and added a new module that implements PI controller-based load shedding. In order to compare with other approaches, we evaluate our method with a real-world stream data set, which is the traces of requests to a cluster of web servers and widely used in data stream experiments.We compare our PI controller-based load shedding framework (referred as PILS hereafter) with the following approach: 1) Coarse Algorithm (CA): the algorithm utilized in the current AURORA/Borealis system (Fig.1); 2) CTRL: the simple feedback control-based method presented in [4]. It models the DSMS in a simple way and design controller by poles assignment method.In all the experiments, we set target delay Dt to 2000 milliseconds and run all tests for 400 seconds.We consider the following metrics in evaluating the adaptation strategy: 1) Delay Violations: the primary control goal. Specifically, we record both the accumulated delay violations (i.e.,∑D－D t for all data tuples whose processing delay D > D t ), and total delayed tuples, which is the total number of tuples whose delays are longer than D t ; 2) Maximal Overshoot: the longest delay violation recorded. This metric captures transient state performance; and 3) Data Loss Ratio: the percentage of data tuples discarded. This can be viewed as the cost of performing load shedding.5.2. Performance ResultWe first compare the long-term performance of PILS with two another approaches. In Fig.7, we plot the ratios of all four metrics measured (i.e, totals in the 400-second period) from the CA and CTRL experiments to that of PILS. Fig. 4A shows that CA rendered 205 times more total delay violations than PILS and CTRL had 23 times. Similar results were obtained in total delayed tuples (Fig.4B) and maximal overshoot (Fig. 4C). The data loss ratios for all methods are almost the same.To better understand the above long-term results, we show the transient performance of all three methods by plotting D(k) values measured at all control periods in Fig. 5. We can see that, as expected, almost all output in PILS is very close to the target value of two seconds. For CTRL and CA, we can observe peaks that are large in both height and width. Such peaks are the results of either fluctuations of arrival rate or changes of c (e.g., those at about 50th second and 125th second, and the high terrace starting from the 230th second). Note the first two peaks of c also have impact on the PILS system: average delay increases beyond two seconds. However, with the design goal of fast convergence and high damping, the controller1832 C.Huang et al. /Journal of Computational Information Systems 3:5 (2007) 1827-1832in the PILS system can quickly bring the system back to a stable state thus large peaks of y are avoided. The high terrace has almost no effect on PILS. This is because the value of c increases gradually before the terrace. Our controller can capture and compensate for this kind of gradual change while the CAs cannot.Fig. 4 Long-term Performance Comparison Fig.5 Short-term Performance ComparisonFrom the above experiments, we see that PILS is the winner in all delay-related metrics. The use of feedback signal provides big advantages over the open-loop AURORA method. A thorough understanding of system dynamics is also extremely useful. By applying simple rules derived from the system model, the CTRL method achieves far better performance than CA. Decisions based on rigorous controller design is another plus for our method. With guaranteed convergence, our controller avoids large and long-time deviations from the desired output while the CTRL method suffers from such deviations.6. ConclusionIn this paper, we study the problem of quality adaptation in data stream systems from a new angle. Our approach takes advantage of proven techniques from the field of feedback control theory. Compared to current solutions, our approach is designed to maintain tuple delays more effectively under dynamic incoming load and variable data processing costs. We have implemented our design in the Borealis data stream manager and experimental results support our expectations on the performance of our solution. AcknowledgementThis research is partly supported by the National Science Foundation of China (60673138, 60603046), Key Program of Science Technology Research of MOE(106006), Program for New Century Excellent Talents in University and Chinese National Programs for Science and Technology Development(2005BA112A02). References[1] Daniel J. Abadi.,Yanif Ahmad. M. Balazinska,etc. The Design of the Borealis Stream Processing Engine. InProcs. of 2nd CiDR Corlfererice. 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