Teaching performance evaluation of ... - Semantic Scholar

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002

231

Teaching Performance Evaluation of Multiprocessor Architectures with Mathcad and MathConnex Andreas A. Veglis, Member, IEEE, Constantine A. Barbargires, Member, IEEE, and Andrew S. Pombortsis, Member, IEEE

Abstract—This paper presents the development of an interactive environment that facilitates the performance evaluation of multiprocessor architectures with Mathcad and MathConnex. This environment was primarily designed for utilization as an interactive computer laboratory exercise for teaching undergraduate students of the Computer Science Department at the Aristotle University of Thessaloniki, Greece. Index Terms—Computer-aided instruction, computer architecture, interactive learning, interconnection networks, Mathcad, MathConnex. Fig. 1.

Typical crossbar network diagram.

I. INTRODUCTION

T

HE RAPID and continuing advances in very large-scale integration (VLSI) technology, coupled with the ever increasing need for higher computing power, have motivated a large body of research activities in the field of parallel computers. Shared-memory multiprocessors are very attractive for building large parallel machines because of their ease in programming and implementation [1]. The interconnection network (IN) [2]–[4] plays a very important role in the operation of parallel multiprocessor systems. It is the mechanism needed for the information transfer between processors and memory modules. The performance of a multiprocessor system depends significantly on the efficiency of its interconnection network. As the number of processors and memory modules increases, the characteristics of the IN can become critical to the overall system performance and cost. The IN design involves a tradeoff between cost and performance. Many types of INs have been proposed in the past few years [1], [5]. Generally, an IN can be classified into 1) crossbar (CBN) (Fig. 1), 2) shared-bus (SBN) (Fig. 2), or 3) multistage interconnection network (MIN) (Fig. 3) [5]. A special case of MINs is the Clos IN that incorporates multiple communication paths between every processor–memory pair [6]. Recently, such networks have also been considered for constructing the interconnection fabric of the next-generation switching systems for the asynchronous transfer mode (ATM) technology in telecommunication networks [7], [8] and optical communications networks [9] as well. Manuscript received January 22, 2002. A. A. Veglis and C. A. Barbargires are with the Media Informatics Laboratory, Department of Journalism and Mass Communication, Aristotle University of Thessaloniki, 540 06 Thessaloniki, Greece (e-mail: [email protected]; [email protected]). A. S. Pombortsis is with the Department of Computer Science, Aristotle University of Thessaloniki, 540 06 Thessaloniki, Greece (e-mail: [email protected]). Publisher Item Identifier S 0018-9359(02)05065-3.

Fig. 2. Typical shared-bus network diagram.

Fig. 3.

Typical omega network diagram for

N = M = 8 and b = 2.

All of these topics are included in the Computer Architecture II course in the Computer Science Department of the Aristotle University of Thessaloniki, Greece. The course is taught in the sixth semester with the traditional method that primarily uses lectures. The growing need of the students to experiment interactively, through suitably designed laboratory exercises, with the new cognitive material they are offered during the lecture classes has been the main motivation for this work.

0018-9359/02$17.00 © 2002 IEEE

232

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002

Fig. 4. Performance evaluation under uniform traffic pattern.

This paper presents the development of an interactive computational environment based on the combined use of Mathcad [10], and MathConnex [11] to serve as a laboratory exercise.1 The MathConnex environment facilitates the integration and linking of visual components that describe the behavior of the aforementioned INs (developed with Mathcad) and the computation of various performance metrics for uniform and nonuniform traffic patterns. More specifically, the environment is based on well-known performance analyses of multiprocessor systems [2]–[4]. The Mathcad files contain relations that calculate, using statistical simulation, the bandwidth of multiprocessor systems that employ the three aforementioned networks under various traffic patterns. The environment seamlessly handles all the data passing and processes execution, allowing the students to focus on the system as a whole. The students can change several parameters of the system configuration and, consequently, observe the results on the overall performance in the form of tables and diagrams. They are also able to access and modify the Mathcad files directly, thus deeply understanding the performance analysis mechanism of the aforementioned INs. II. INTERCONNECTION NETWORKS The performance of the three main types of INs has been studied thoroughly [3], [4], [6]. The CBN is found to be the most efficient but also the most expensive. On the other hand, the SBN has lower cost but also exhibits lower performance. MINs provide a compromise between the above networks. The 1Mathcad is a registered trademark and MathConnex is a trademark of MathSoft, Inc.

performance evaluation studies of such multiprocessor systems are usually based on analytical models and rely on the bandwidth (BW) as the basic performance metric [2], [6], [8], [12]. The BW is defined as the number of successful requests per memory cycle. In some cases, a variation of the above metrics is employed, namely, the probability of request acceptance. The performance analysis is usually performed under the assumption that there is a uniform traffic load. This assumption simplifies the analysis, but in real conditions users seldom encounter such traffic loads. Thus, the case of the nonuniform traffic patterns is also included in the performance evaluation. The main parameter that defines the traffic pattern is the probability with which each processor generates a request ( ) [4]. In the case of the nonuniform traffic pattern, two additional parameters are defined: the favorite rate ( ) and the hot rate ( ). The jobs that are executed in a multiprocessor system usually involve a set of communication tasks. Each processor has a favorite memory module for storing the tasks that are being assigned. Thus, each processor issues requests for its favorite memory module with probability . Furthermore, some memory modules can be characterized as hot memory modules, because all processors issue requests for the specific memory modules with probability . The above model is usually employed for modeling the nonuniform traffic pattern [4] , [6], [12]. III. MATHCAD AND MATHCONNEX Mathcad is a rich problem-solving environment that provides a wide choice of tools and supports a variety of analysis and visualization techniques. It combines the live document interface of a spreadsheet with the “what you see is what you get”

VEGLIS et al.: TEACHING PERFORMANCE EVALUATION OF MULTIPROCESSOR ARCHITECTURES

233

Fig. 5. Performance evaluation of the crossbar network under uniform and nonuniform traffic pattern.

interface of a word processor. Equations, text, and graphics can be placed anywhere in the Mathcad worksheet, making it easy to keep track of the most complex calculations and represent the results in two- or three-dimensional plots. The creation of a presentation-quality document can be shared with others by printing the worksheet exactly as it appears on the screen, e-mailing it, or posting it on the World Wide Web [13], [14]. Mathcad has been extensively utilized before, not only for research computations [15] but also for the development of educational environments in a diverse variety of scientific and engineering fields, such as materials [16], electromagnetics [17], [18], signal processing [19]–[22], communications systems [23], [24], electrical engineering [25]–[27], and civil engineering [28]. It has been recently selected by the U.K. Open University as the tool for teaching and training its technical students through the distance learning curriculum. The MathConnex layer in Mathcad 7 Professional (and newer versions) provides a powerful programming mode, a visual block diagramming language that allows the connection of Mathcad modules, data sources, and other computational engines into a single computation flow. Thus, it forms an environment for visually integrating applications and data sources to control projects involving a variety of applications and data sources. By providing a choice of 16 visual components for each data source or application in a system—such as a Mathcad

component, an Excel component, and a File Read/Write component—MathConnex lets one manage the flow of data from one application or data source to another. In this way, one can easily create a system consisting of Mathcad worksheets, other applications, and data sources by simply: 1) dragging components from a component palette and dropping them into the worksheet; 2) wiring the components together to indicate data flow; 3) simulating the system using toolbar controls to run through the system. Given the variety of components available for integration into a system, MathConnex can be used to design an endless number of different systems involving different applications and data sources. In this way, Mathcad worksheets can be chained together, and data can pass from one to the next, thus enabling the breaking of a large Mathcad worksheet into several smaller worksheets and their connection through MathConnex, so as to visualize the calculation of complex mathematical expressions. IV. PERFORMANCE EVALUATION ENVIRONMENT The performance evaluation environment for the advanced computer architectures mentioned above consists of a series of MathConnex projects that cover various INs for the uniform and the nonuniform traffic pattern cases. More specifically, there

234

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002

Fig. 6. Performance evaluation of the shared-bus network under uniform and nonuniform traffic pattern.

TABLE I BASIC MATHCONNEX COMPONENTS

is one project with the filename that covers the bandwidth computation for CBNs (Fig. 1), SBNs (Fig. 2) and omega networks (Fig. 3) under a uniform traffic pattern. A MathConnex project can include 20 different types of comproject incorporates five different ponents. The

types of components: the input component, the Mathcad programmable component, the Excel component, the graph component, and the stop/pause component. A brief description of the above components is presented in Table I. These components were created and wired in order to create computation flows.

VEGLIS et al.: TEACHING PERFORMANCE EVALUATION OF MULTIPROCESSOR ARCHITECTURES

235

Fig. 7. Performance evaluation of the omega network under uniform and nonuniform traffic pattern.

TABLE II VARIABLES FOR THE UNIFORM TRAFFIC PATTERN CASE

The most important role of the Mathcad component includes the worksheet that calculates the performance of the systems. , the student can For all these cases, and for see the values of the bandwidth in both a tabular (Excel component) and a diagram (graph component) form (Fig. 4). The input variables (input components) that the student can change for each case, without explicitly editing the corresponding Mathcad components, are given in Table II. Thus, the student can directly compare the performance of the three systems in all cases of input load.

For the nonuniform traffic pattern case, there are three (Fig. 5), projects with the filenames (Fig. 6), and (Fig. 7). The above projects include similar components as those described in Table I. Each project gives the student the opportunity to study both the uniform and the nonuniform traffic pattern case for the IN under consideration. The additional input parameters and the favorite rate (input components) are the hot rate (Table III). The student can vary the values of the above parameters and observe how the increase of the hot rate decreases the

236

IEEE TRANSACTIONS ON EDUCATION, VOL. 45, NO. 3, AUGUST 2002

TABLE III TRAFFIC LOAD PARAMETERS FOR THE NONUNIFORM CASE

bandwidth of the system. Similarly, he/she can discover how the increase of the favorite rate peaks the performance of the system. Although there was no formal feedback from the students (for example, in the form of questionnaires), some observations can be made on the reaction of the students after using the MathConnex projects. The Computer Architecture course is usually taught in the traditional way, that is, classroom lectures. The addition of the MathConnex projects, which allowed the students to interact with the multiprocessor architectures, helped them to understand the performance issues more easily. It is also worth noting that some students experimented by altering crucial parameters of the multistage network. The students expressed their desire to employ more MathConnex projects in teaching other issues of computer architectures.

V. CONCLUSION A novel, interactive, computational environment for teaching performance evaluation of advanced computer architectures was presented. This environment was developed with the use of Mathcad and MathConnex and gives a student the opportunity to experiment with various interconnection networks, such as the crossbar network, the shared-bus network, and multistage IN’s (Omega networks) under uniform and nonuniform traffic patterns, thus estimating their relative usefulness in terms of performance and cost. Furthermore, the student can also investigate the underlying computational mechanism for the evaluation of the various performance metrics, thus accomplishing a thorough study on the interconnection networks. Future extensions of this work will include MathConnex projects that will evaluate the performance of multiprocessor architectures that employ packet switching INs.

REFERENCES [1] K. Hwang and F. A. Briggs, Computer Architecture and Parallel Processing. New York: McGraw-Hill, 1984. [2] J. H. Patel, “Performance of processor memory interconnections for multiprocessors,” IEEE Trans. Comput., vol. C-30, pp. 771–780, Oct. 1981. [3] C. R. Das and L. N. Bhuyan, “Bandwidth availability of multiple-bus multiprocessor,” IEEE Trans. Comput., vol. C-34, pp. 918–926, Oct. 1985. [4] K. Hwang, Advanced Computer Architecture. New York: McGrawHill, 1993. [5] R. Sahner, K. S. Trivedi, and A. Puliafito, Performance and Reliability Analysis of Computer Systems: An Example-Based Approach Using the Sharpe Software Package: Kluwer Academic, 1995.

[6] A. A. Veglis and A. S. Pombortsis, “Performability analysis of clos multiprocessor systems,” Inform. Sci. J., vol. 88, pp. 95–112, 1996. [7] J. M. Pitts and J. A. Schormans, Introduction to ATM: Design and Performance. New York: Wiley, 1996. [8] A. A. Veglis and A. S. Pombortsis, “Cell availability of multiple path ATM switch,” in Proc. 9th Mediterranean Electrotechnology Conf. (MELECON ’98), Tel-Aviv, Israel, May 1998, pp. 1313–1317. [9] Y. Pan, C. Qiao, and Y. Yang, “Optical multistage interconnection networks: New challenges and approaches,” IEEE Commun. Mag., vol. 37, pp. 50–56, Feb. 1999. [10] MathSoft, Inc., Mathcad, User’s Guide. Cambridge, MA: Mathcad 7 Professional, 1997. [11] MathSoft, Inc., MathConnex: Getting Started Guide Cambridge, MA, 1997. [12] C. R. Das, J. T. Kreulen, M. J. Thazhuthaveetil, and L. N. Bhuyan, “Dependability modeling for multiprocessors,” IEEE Comput. Mag., vol. 23, pp. 7–19, Oct. 1990. [13] F. Purcell, “Mathcad and the Collaboratory: A web-based environment for interactive learning and curriculum development,” in Proc. Frontiers in Education 26th Annu. Conf. (FIE ’96), vol. 29, pp. 1031–1034. [14] M. James, “Collaboration features in new maths release,” Sci. Comput. World, pp. 39–40, Nov. 1997. [15] A. Riddle, “Mathematical power tools,” IEEE Spectrum, vol. 31, pp. 35–47, Nov. 1994. [16] R. E. Desrosiers, “Electronic books as teaching supplements,” in Proc. Frontiers in Education 26th Annual Conf. (FIE ’96), vol. 29, pp. 1419–1421. [17] R. R. DeLyser, “Using Mathcad in electromagnetics education,” IEEE Trans. Educ., vol. 39, pp. 198–210, May 1996. [18] K. W. Whites, “Visual electromagnetics for Mathcad: A computer-assisted learning tool for undergraduate electromagnetics education,” in Proc. 1998 IEEE Antennas and Propagation Society Int. Symp., vol. 4, 1998, pp. 2288–2291. [19] J. M. Ramirez and D. Baez-Lopez, “An experimental simulation lab in MathCAD for teaching signal processing,” in Proc. 6th IEEE Digital Signal Processing Workshop, 1994, pp. 123–126. [20] W. J. Ebel and N. Younan, “Counting on computers in DSP education,” IEEE Spectrum, vol. 12, pp. 38–43, Nov. 1995. [21] R. O. Harger, “Introducing DSP with an electronic book in a computer classroom,” IEEE Trans. Educ., vol. 39, pp. 173–179, May 1996. , “Teaching in a computer classroom with a hyperlinked, interactive [22] book,” IEEE Trans. Educ., vol. 39, pp. 327–335, Aug. 1996. [23] J. T. F. Schubert, “The use of a simple computer math package to demonstrate complex communication systems principles,” in Proc. Frontiers in Education 24th Annual Conf. (FIE ’94), San Jose, CA, Nov. 1994, pp. 34–38. [24] P. Yum, K. Ake, and T.-W. Kao, “The application of readily available software packages in communication and radar system simulations,” in Proc. Frontiers in Education 26th Annual Conf. (FIE ’96), vol. 29, pp. 254–257. [25] V. G. Agelidis, “Incorporating software tools in electrical engineering laboratory experiments—An example,” in Proc. IEEE 1st Int. Conf. Multi-Media Engineering Education, July 1994, pp. 319–328. [26] D. Y. Northam, “Introducing computer tools into a first course in electrical engineering,” IEEE Trans. Educ., vol. 38, pp. 13–16, Feb. 1995. [27] M. Lightner and J. Avery, “A paperless circuits laboratory: Vision and reality,” in Proc. Frontiers in Education 26th Annu. Conf. (FIE ’96), vol. 29, pp. 1186–1190. [28] T. A. Lenox, S. J. Ressler, R. J. O’Neil, and C. H. Conley, “Computers in the integrated civil engineering curriculum: A time of transition,” in Proc. 1997 Amer. Soc. Engineering Education Conf., Milwaukee, WI, June 1997. [29] Proc. Frontiers in Education 26th Annual Conf. (FIE ’96), San Juan, Puerto Rico, Nov. 1996.

Andreas Veglis (S’91–A’95–M’99) received the B.S. degree in physics, the M.S. degree in electronics and communications, and the Ph.D. degree in computer science from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1988, 1992, and 1995, respectively. He is an Assistant Professor in the Department of Journalism and Mass Communication, University of Thessaloniki. His research interests include multiprocessor architectures, distance learning, and course support environments.

VEGLIS et al.: TEACHING PERFORMANCE EVALUATION OF MULTIPROCESSOR ARCHITECTURES

Constantine A. Barbargires (S’88–M’99) was born in Veria, Greece, on May 1, 1966. He received the B.Sc. degree in physics, the M.Sc. degree in electronics and telecommunications, and the Ph.D. degree in computer controlled systems (all with highest honors) from the Aristotle University of Thessaloniki (AUTh), Thessaloniki, Greece, in 1988, 1991, and 1995, respectively. Since 1999, he has been a part-time Lecturer in the Department of Journalism and Mass Communication, AUTh, teaching computer science courses. His research interests focus on discrete-time control systems, computer-aided design of control systems, and educational technology. Dr. Barbargires is a member of the Greek Physical Society.

237

Andrew S. Pombortsis (M’87) received the B.S. degree in physics, the M.S. degree in electronics and communications, and the Ph.D. degree in computer science from the University of Thessaloniki, Thessaloniki, Greece, and the Dipl.-Ing. degree in electrical engineering from the Technical University of Thessaloniki. Currently, he is a Professor in the Department of Informatics, University of Thessaloniki. His research interests include computer architecture, parallel and distributed computer systems, and multimedia systems.