Scheduling and Caching Strategies for Correlated Data in Push-based Information Systems 3 Etsuko Yajimay Takahiro Haraz Masahiko Tsukamotoz Shojiro Nishioz ysales Department, Tokyo Oce, FM Osaka Co., Ltd. yajima@fmosaka.net zdept. of Information Systems Eng., Graduate School of Engineering, Osaka University fhara,tuka,nishiog@ise.eng.osaka-u.ac.jp ABSTRACT Recently, there has been increasing interest in information systems that deliver data using broadcast in both wired and wireless environments. The strategy in which a server repeatedly broadcasts data to clients can result in a larger throughput, and various methods have been studied to reduce the average response time to data requests in such systems. In this paper, we propose a strategy for scheduling the broadcast program which takes into account the correlation among data items. This strategy puts data items with strong correlation side by side in the broadcast program in order to reduce the average response time. We also propose a caching strategy which extends a conventional caching strategy so that it can take advantage of correlation among broadcast data items for greater eciency. Finally, we use simulation studies to evaluate the performance of our proposed strategies. Keywords: data broadcast, data correlation, scheduling strategy, caching strategy 1 INTRODUCTION Recently, there has been increasing interest in data delivery mechanisms in which a server repetitively broadcasts various data to clients using a broad bandwidth, called \pushbased" data delivery mechanisms. As shown in Figure 1, in a system that uses a \push-based" mechanism, each client can access a piece of data by waiting for its data broadcast period. In contrast, when conventional \pull-based" mechanisms are used, servers deliver data by separately responding to every request message sent by each client. One remarkable advantage of the \push-based" delivery mechanism is higher throughput for data access in distributed systems with a large number of clients, since the absence of commu- 3 This research was supported in part by Research for the Future Program of Japan Society for the Promotion of Science under the Project \Advanced Multimedia Content Processing" (Project No. JSPS-RFTF97P00501) and Grant-in-Aid for Scientic Research numbered 12480095 from Japan Society for the Promotion of Science. Server Broadcast Data1 Data Stream....... 2 3 Clients Figure 1: Information system based on message broadcast. nication contention among the clients requesting data means that they can eciently share the bandwidth[6, 8, 12, 18]. Information broadcast systems are good applications of \push-based" mechanisms. In these systems, the server's clients are typically portable computers, desktop computers, or electrical household appliances. The following are some scenarios in which information broadcast systems could be useful: In a shopping center, store directories could be broadcast, enabling customers with portable computers to view them to select which shops to enter. In a train station, up-to-date schedules could be broadcast. Passengers with portable computers could receive and store the information. At home, PCs could automatically receive digital data of various media (image, audio, text) through satellite communication, ground communication, or cable TV communication. The data could include news, online shopping, hit charts, commercial advertisements, sports, automatic software updates and video-on-demand. User-customizable machines would be capable of ltering the necessary information before storage. 5 4 Several strategies have been proposed to improve the performance of these information systems. These strategies are categorized into the following research elds:
1. Scheduling strategies at servers This research eld includes two notable research areas. One area concentrates on strategies to shorten the response time[1, 14, 16, 17, 22, 24, 25, 26, 29, 30]. If the global access probability diers for each data item, additional bandwidth should be allocated for data with a higher access probability. Hence, the broadcast period of the data becomes shorter, and therefore, the average response time is expected to be shorter. In relation to these strategies, a statistical estimation model of access frequencies in \push-based" systems has been proposed in [31]. The other area concentrates on strategies to save the power of mobile hosts[9, 19, 20, 21]. Since mobile hosts such as palmtop computers are not connected to a direct power source, power conservation is one of the most important issues in mobile computing environments. This research area aims to conserve the power of mobile hosts by indexing the broadcast program and hence reducing the monitoring time of broadcast data. 2. Caching strategies at clients This research eld aims to shorten the response by caching parts of the broadcast data at the client[1, 2, 15, 28]. 3. Combination of \push-based" and \pull-based" data delivery mechanisms Only data with high access probabilities from clients are broadcast, while the rest are transferred using a \pull-based" data delivery mechanism[5, 21]. This strategy shortens the broadcast periods for data with high access probabilities; therefore, its response time is expected to be shorter. Moreover, the response time is also expected to be shorter for data with low access probabilities since in a pure \push-based" strategy, their broadcast periods are very long. 4. Dissemination of Updates In an application such as a weather service, the information from a server often changes. In this case, updated information should be disseminated to clients at some periodic rate. Several strategies to disseminate information updates have been proposed [3, 5, 10, 13, 27]. Although correlation generally exists among broadcast data (e.g., clients request accesses to certain sets of data at the same time), these conventional strategies do not take it into account. When clients frequently access a set of correlated data, the scheduling and caching strategies which take the correlation into account can reduce the response time for data accesses. In this paper, we propose new scheduling and caching strategies which do just that. We then evaluate the performances of our proposed strategies. The following system environment is assumed: The system has a single server. Data is handled in clusters called data items. All data items are the same size. The server creates a broadcast program consisting of data items (ID: 1; 111;M). The program is repeatedly broadcast. Neither the data items nor the broadcast program is updated. All clients know the broadcast program precisely. This may be accomplished by broadcasting program information when the program is created. The access probabilities and the correlation of data items dier for each client, and each client knows its own access probabilities and the correlation. The remainder of the paper is organized as follows: In section 2, correlation among broadcast data items is described. New scheduling and caching strategies are proposed in section 3 and 4, respectively. Simulation results are shown in section 5. Finally, in section 6, we summarize this paper. 2 CORRELATION AMONG DATA ITEMS In a real environment, clients often access certain sets of data collectively. We dene the term \correlation" as the probability that the client sequentially accesses a certain set of data items. As the correlation increases, so does the probability that a particular set of data items will be accessed together. The correlation diers for each set of data items. A client may access a set of correlated data items in two ways. Firstly, the client submits multiple access requests at the same time. This includes the case where the intervals between successive requests are smaller enough than the broadcast period of one program cycle so that they can be ignored. For example, if a server broadcasts HTML les and images of various home pages separately as data items, a client often issues simultaneous requests for data items of an HTML le and image les that form a single page. Secondly, the client accesses a set of correlated data items by submitting access requests at some intervals. For example, if a server broadcasts various home pages as data items, a user (client) often refers to a certain page for a while and then refers to one of the pages linked from the rst page. Moreover, if binary les of various tools are broadcast, a user often uses a word processor for a while in order to produce a document and then uses a drawing tool in order to create some gures in the document. In this paper, we assume the rst way { i.e., the client submits multiple access requests at the same time. Moreover, for the purpose of simplicity, we assume that each client issues access requests for two correlated data items at the same time. In general, correlation among data items is complex so that a graph consisting of vertices representing individual data items and edges linking to correlated data items does not become a tree but a network topology. Thus, in order to reduce the response time to access sets of correlated data items, it seems wise to employ scheduling and caching strategies which consider this complex correlation. 3 SCHEDULING STRATEGIES FOR CORRELAT- ED DATA ITEMS In this section, rst we describe the conventional scheduling strategies. Then, we propose a new strategy that takes into account the correlation among data items. 3.1 Conventional Scheduling Strategies Generally, the probability that a data item will be accessed depends on the client. It has been reported that each client
M a D ij i j b W ab f Time Time Figure 2: A broadcast program. c d e a c e f b d Program issues data accesses to 20% of data items with 80% probability[1]. As for the access pattern of the global system, it is generally skewed. Thus, in the conventional scheduling strategies, the server frequently broadcasts data items with high access probabilities. In [1], it is mentioned that the broadcast order of data items does not inuence the average response time when the broadcast period of each item is properly chosen and remains unchanged in every broadcast cycle. An exception to this case occurs when the clients have caches and use prefetching-based caching strategies. However, in [1], the correlation among data items is not taken into account. Because it seems to be quite general that there is correlation among data items, scheduling strategies which take into account that correlation are expected to shorten the average response time for data accesses. 3.2 CBS (Correlation-Based Scheduling) Strategy In this subsection, we propose the CBS (Correlation-Based Scheduling) strategy, which takes into account the correlation among data items. For the purpose of simplicity, we assume that each data item is broadcast only once in a cycle of a program. In this case, the problem of scheduling a periodic broadcast program is equivalent to the problem of selecting a Hamiltonian circuit from a complete graph consisting of vertices representing each data item and ordering the data items along the circuit. Here, a Hamiltonian circuit means a circuit in which each vertex in the given graph appears exactly once. Let M denote the total number of data items that the server broadcasts in a program. Let L denote the time required to broadcast a single data item, and let D ij denote the number of data items that are broadcast between items i (j) and j (i) in a program (0 D ij M 0 2, and D ij = D ji) (see Figure 2). If a client does not have a cache, the average response time, avg ij, when a client requests two arbitrary items i and j at the same time is represented by the following equation: avg ij = Dij M 1fDij +(M 0 Dij 0 1)gL 2 + M 0 Dij 0 2 M + 2 M 1 (M 0 1 2 )L 1f M 0 Dij 0 2 2 +(D ij +1)gL = L M fdij(m 0 Dij 0 2)g + L(M 2 +2M 0 2) 2M The rst term of the center member in equation (1) represents the average response time to data access requests which are issued after i is broadcast and before j is broadcast in the cycle of the program. Similarly, the second term (1) Figure 3: An example of executing the CBS strategy. represents the average response time to requests which are issued after j is broadcast and before i is broadcast in the next cycle, and the third term represents the average response time to access requests which are issued while item i or j is being broadcast. The right-hand side of equation (1) shows that avg ij is a function of D ij and that the rst term has to be minimized in order to minimize avg ij. IfD ij is either 0 or M 0 2, avg ij becomes minimum, since D ij takes an integer value from 0 to M 02. In both the case where D ij is 0 and the case where D ij is M 0 2, the items i and j are broadcast side by side in the program. However, as the number of data items which have the correlation with other items increases, it becomes very dicult to compose the optimal program by deciding which data items should be broadcast side by side, since the number of items which can be broadcast side by side is limited. Thus, we propose the following heuristic strategy, called CBS strategy, which composes a program by putting data items with stronger correlation side by side in the broadcast program. The CBS strategy: 1. A complete graph consisting of vertices representing all data items and edges is created such that an edge between items i and j is weighted W ij =10P ij. Here, P ij denotes the probability P that the clients request two items i and j at the same time { i.e., the correlation M between i and j ( j=i+1p M Pij =1,and Pij = i=1 P ji ). 2. A Hamiltonian circuit which gives the minimum total weight is selected. This is done by solving the traveling salesman problem (TSP) on the given graph. 3. Along the selected circuit, all items are put in a broadcast program. Figure 3 shows an example of composing a program using the CBS strategy. First, the graph shown in the left part of Figure 3 is created for the items represented by the letters a to f. Then, a Hamiltonian circuit which gives the minimum total weight is selected. By putting the data items in the same order as the circuit, a broadcast program can be composed as in the right part of the gure. Because the CBS strategy only considers the strength of correlation among data items which are put side by side, the program constructed by this strategy is not always optimal. Even so, the CBS strategy seems to greatly shorten the average response time.
Though the CBS strategy is much easier than the problem of composing the optimal program, the second step of this strategy is equal to the TSP. Ifthenumber of broadcast data items increases, the CBS strategy cannot be practically solved, since the TSP is an NP-complete problem. Algorithms which can solve the TSP heuristically and quickly have already been proposed and used in various elds of engineering[7, 11, 23]. Thus, we use a heuristic TSP algorithm when the number of broadcast data items is large. 4 CACHING STRATEGIES FOR CORRELATED DA- TA ITEMS Since both the correlation among data items and the data items' access probabilities depend on each client, the average response time of some clients may be very large because only the global access probabilities and correlation were taken into consideration. In this case, if the client has a cache, a suitable caching strategy for each client can improve its performance. In this section, rst, we describe the PT strategy [4] which is a typical conventional caching strategy. Then, we propose a new strategy which extends the PT strategy to consider the correlation among data items. 4.1 Conventional Prefetching-Based Caching Strategy Several caching strategies have been proposed so far to improve the average response time of information systems which use a \push-based" data delivery mechanism. These strategies can be classied into two categories: prefetching-based and non-prefetching-based, which are distinguished by the time when each data is replaced. In prefetching-based strategies, data items which seem to be important are prefetched into a cache in advance. It is generally supposed that prefetching-based strategies are more suitable for \push-based" information systems, since these strategies can reduce the average response time almost without any additional cost. The PT strategy is a typical prefetching-based strategy, and it gives the best performance among the conventional strategies proposed so far. Here is a brief explanation of the PT strategy. The PT strategy: 1. Every time a new item is broadcast, a PT value is assigned to each item that is in the cache and is currently broadcast. Here, let P 0 i denote the probability that item i will be requested, T i denote the broadcast period of item i, i denote the time that has passed since item i has been cached, and i denote the time remaining until i is broadcast next. The PT value X i which is assigned to item i is expressed as follows: X i = P 0 i 1 T i 0 P 0 i 1 i (= P 0 i 1 i) (2) The PT value takes a maximum value P 0 i 1 T i upon insertion into the cache and takes a minimum value 0 when it is broadcast next. 2. X j, which is the PT value of the newly broadcast item j, is compared with the lowest PT value, X min, inthe cache. 3. If X j is larger than X min, the item with the lowest PT value is removed from the cache and j is inserted. Otherwise, no cache replacement occurs. Time b e f a b c d e f g h Currently Broadcasting Cache 1cycle a b... Figure 4: Item sets C and Q i for item e. The PT value, X i, represents the average response time when a client accesses item i if it is not stored in the cache. Therefore, for a given item set in the cache, the replacement based on the PT value is optimal at the moment when each item is broadcast. Although this replacement is not always optimal in the long term, this strategy gives the best performance out of all of the conventional strategies. C Q 4.2 CBPT (Correlation-Based PT) Strategy When the correlation among data items is considered, it is also eective to remove from the cache the item which requires the shortest response time. Based on this fact, we propose the following caching strategy, called the CBPT (Correlation-Based PT) strategy, which extends the PT strategy to consider the correlation among data items. The CBPT strategy: 1. Every time a new item is broadcast, a CBPT value is assigned to each item that is in the cache and is currently broadcast. Here, let i denote the time remaining until the item i is broadcast next and P ij denote the probability that items i and j will be requested at the same time { i.e., the correlation between i and j. Moreover, let C denote the set of items which are in the cache and Q i denote the set of data items which will be broadcast before item i is broadcast next and which are not contained in C. The CBPT value of item i, Y i, is represented by the following equation: Y i = i 1 X X P ik + ( i 0 k) 1 P ik (3) k2q i k2c 2. Y j, which is the CBPT value of the newly broadcast item j, is compared with the lowest CBPT value, Y min, in the cache. 3. If Y j is larger than Y min, the item with the lowest CBPT value is removed from the cache and j is inserted into the cache. Otherwise, no cache replacement occurs. Figure 4 shows the sets C and Q i for computing the CBPT value of the item e when the item a is currently being broadcast in the program consisting of data items represented by the letters a to h and when the items b, e, and f are in the cache. The CBPT value, Y i, represents the average response time to a client's simultaneous requests for two items, i and one other arbitrary item, assuming that the item i is not e
stored in the cache. Therefore, for the given item set in the cache, the replacement based on the CBPT strategy is optimal at the moment when each item is broadcast. Similar to the PT strategy, although the replacement based on the CBPT strategy is not always optimal in the long term, this strategy seems to give a good performance for the same reasons. If we let P ii denote the probability that a client requests only one item i in equation (3), the CBPT strategy can still be used even if there is no correlation among the data items. The conventional PT strategy is a special case of the CBPT strategy where there is no correlation among data items. 5 PERFORMANCE EVALUATION In this section, we show the performance results from simulations of the CBS and CBPT strategies. The following assumptions were made for the simulation experiments: There exist 120 data items (item identiers: 1, 111, 120) which are each broadcast once according to the broadcast program. It takes 10 units of time to broadcast one item in the program. Although this value proportionally aects the response time, it has relatively little eect on the simulation results, so we choose this value arbitrarily. The probability that a client issues simultaneous requests for two items is 0.1 at each unit time. This value does not aect the response time, since the system's access frequency does not aect our proposed scheduling and caching strategies. Hence, this value is also chosen arbitrarily. The probability that two items i and j (i =1; 111; 120, j = 1; 111; 120) will be requested at the same time is expressed by an i-j element, P ij (P ij = P ji), in the access probability matrix (a 120 dimensional matrix). For the purpose of simplicity, it is assumed that P ii = 0 for each item i (i =1; 111; 120). The remaining elements are assigned either 0 or some positive value. In the simulations, the following two access probability matrices are used. MATRIX 1: All elements except for the diagonal ones (P ii, i =1; 111; 120) are assigned 0 or a constant value. The percentage of the elements which are not assigned 0 is a variable in the simulations in section 5.1.1 and section 5.2. As the percentage of the elements which are not assigned 0 gets lower, the correlation between each two items becomes stronger. MATRIX 2: The data items are divided into several groups. The elements for every combination of two items in a group are assigned a positive value, and the rest of the elements are assigned 0. This means that the correlation exists only among data items which are in a same group. The positive value assigned to each element is selected randomly from three values: `large', `medium', and `small'. The ratio `large':`medium':`small' is 8:5:2. The number of groups is a variable in the simulation in section 5.1.2. As the number of groups gets larger, the correlation range becomes smaller and each correlation becomes more conspicuous. Average Response Time 440 420 400 380 360 340 320 Figure 5: 300 20 30 40 50 60 70 80 90 100 Percent (%) CBS SCATTER Average response time of the CBS strategy (Simulation 1). 5.1 Evaluation of the CBS Strategy In this subsection, we evaluate the interval between the responses to two access requests which are issued at the same time. Evaluating the interval between two responses is suf- cient because the response time to the rst access does not depend on the employed scheduling strategy. Here, we call this interval the `response time' for simplicity. For comparison, we also evaluate the average response time of the random scheduling strategy which does not consider the correlation among data items. 5.1.1 Simulation 1 The average response times of the two strategies, the CBS strategy and the random scheduling strategy, using MA- TRIX 1 are compared, varying the ratio (%) of elements which are not 0 in the matrix. Figure 5 shows the result of this simulation. The horizontal axis indicates the percentage of elements which are not 0. In the graph, the random scheduling strategy is shown as `SCATTER'. The result shows that the CBS strategy gives shorter response times than the random scheduling strategy. Moreover, it also shows that the dierence in response time between two strategies increases as the percentage of elements which are not 0 gets smaller { i.e., as the correlation gets stronger. 5.1.2 Simulation 2 The average response times of the two strategies using MA- TRIX 2 is compared, varying the number of the item groups. Figure 6 shows the result of this simulation. The horizontal axis indicates the number of groups. The result shows that the CBS strategy gives shorter response times than the random scheduling strategy. Moreover, it also shows that the dierence in the performance between two strategies becomes larger as the number of groups becomes larger { i.e., as the correlation among data items becomes more conspicuous.
450 400 CBS SCATTER 500 CBPT PT 350 480 Average Response Time 300 250 200 150 Average Response Time 460 440 420 100 50 1 2 3 4 5 6 Number of Groups 400 20 30 40 50 60 70 80 90 100 Percent(%) Figure 6: Average response time of the CBS strategy (Simulation 2). Figure 7: Average response time of the CBPT strategy. 5.2 Evaluation of the CBPT Strategy In this subsection, the average response time of our proposed CBPT strategy is evaluated in the environment where the client has a cache and the size of the cache is 40 percent of the size of one program cycle. Figure 7 shows the simulation result using MATRIX 1, varying the ratio of the elements which are not P 0. For comparison, the average response time of the PT strategy is also shown, assigning each item to the value Pi 0 M = Pij as the access probability in order to j=1 compute the PT value. The horizontal axis indicates the percentage of the elements which are not 0. The result shows that the CBPT strategy gives better performance than the PT strategy, which is considered to give the best performance among the conventional strategies. In particular, the dierence in performance between the two strategies becomes larger as the correlation among data items gets stronger. Although in this paper the access requests for two items are issued at the same time, the CBPT strategy is expected to give even better performance when the access requests for more than two items are issued at the same time. This is because the CBPT strategy replaces the items in a cache based on the correlation among data items as well as the items' access probabilities. 6 CONCLUSION In this paper, we considered \push-based" information systems in which each client issues access requests for two correlated data items at the same time, and discussed the scheduling and the caching of broadcast data items that gives careful consideration to the correlation among data items. First, we proposed a scheduling strategy which puts data items with strong correlation side by side in the broadcast program in order to reduce the average response time. Then, we proposed a caching strategy which extends the conventional PT strategy so that it can take advantage of correlation among broadcast data for greater eciency. We also showed simulation results which we did to evaluate the eectiveness of our proposed strategies. The sim- ulation results show that correlation among data items is a signicant factor in system performance. As a part of our future work, we are planning to extend the CBS strategy to consider the broadcast frequencies of data items, since in the conventional scheduling strategies, the server frequently broadcasts data items which have high access probabilities. So far, we have assumed an environment in which each client issues access requests for two data items at the same time. However, in a real environment, there are also situations in which the client accesses a set of correlated data items with some intervals. We are now studying the scheduling and caching strategies for such cases. REFERENCES [1] Acharya, S., Alonso, R., Franklin, M., and Zdonik, S.: Broadcast Disks: Data Management for Asymmetric Communication Environments, Proc. ACM SIGMOD Conference, pp.199{210 (1995) [2] Acharya, S., Franklin, M., and Zdonik, S.: Dissemination-Based Data Delivery Using Broadcast Disks, IEEE Personal Communications, Vol.2, No.6, pp.50{60 (1995) [3] Acharya, S., Franklin, M., and Zdonik, S.: Disseminating Updates on Broadcast Disks, Proc. Int'l Conf. on Very Large Data Bases (VLDB'96), pp.354{365 (1996) [4] Acharya, S., Franklin, M., and Zdonik, S.: Prefetching from a Broadcast Disks, Proc. Int'l Conf. on Data Engineering (ICDE'96), pp.276{285 (1996) [5] Acharya, S., Franklin, M., and Zdonik, S.: Balancing Push and Pull for Data Broadcast, Proc. ACM SIG- MOD Conference, pp.183{194 (1997) [6] Ammar, M.H. and Wong, J.W.: On the Optimality of Cyclic Transmissions in Teletext Systems, IEEE Transactions on Communications, Vol.35, No.1, pp.68{ 73 (1987)
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