Abstract
Workloads generated by the real-world parallel applications that are executed on a multicomputer have a strong effect on the performance of its interconnection network—the hardware fabric supporting communication among individual processors. Existing multicomputer networks have been primarily designed and analysed under the assumption that the workload follows the non-bursty Poisson arrival process. As a step towards obtaining a clear understanding of network performance under various workloads, this paper presents a new analytical model for computing message latency in wormhole switched torus networks in the presence of bursty traffic, based on the well-known Markov-Modulated Poisson Process (MMPP). In order to derive the model, the approach for accurately capturing the properties of the composite MMPPs is applied to characterize traffic on network channels. Moreover, a general method has been proposed for calculating the probability of virtual channel occupancy when the traffic on network channels follows a multi-state MMPP process. Simulation experiments reveal that the model exhibits a good degree of accuracy.
Similar content being viewed by others
References
A. Agarwal. Limits on interconnection network performance. IEEE Trans. Parallel and Distributed Systems, 2(4):398–412, 1991.
E. C. Anderson, J. P. Brooks, C. M. Grassl, and S. L. Scott. Performance of the Cray T3E multiprocessor. Proc. ACM/IEEE Supercomputing Conf. (SC97), CD-ROM, ACM Press, 1997.
A. Baiocchi, N. B. Melazzi, M. Listanti, A. Roveri, and R. Winkler. Loss performance analysis of an ATM multiplexer loaded with high-speed On-Off processes. IEEE J. Selected Areas Commun., 9(3):388–393, 1991.
Y. M. Boura, C. R. Das, and T. M. Jacob. A performance model for adaptive routing in hypercubes. Proc. 1st Int. Workshop on Parallel Processing, pp. 11–16, 1994.
R. Buck. nCUBE corporation-The Oracle media server for nCube massively parallel system. Proc. 8th Int. Parallel Processing Symp. (IPPS'94), pp. 670–673, IEEE Computer Society Press, 1994.
W. J. Dally. Performance analysis of k-ary n-cubes interconnection networks. IEEE Trans. Computers, 39(6):775–785 1990
W. J. Dally. Virtual channel flow control. IEEE Trans. Parallel and Distributed Systems, 3(2):194–205, 1992.
W. J. Dally, L. R. Dennison, D. Harris, and K. Kan. The reliable router: A reliable and highperformance communication substrate for parallel computers. Proc. 1st Workshop on Parallel Computer Routing and Communication, LNCS 853, pp. 241–255, Springer-Verlag, 1994.
J. Duato. A new theory of deadlock-free adaptive routing in wormhole routing networks. IEEE Trans. Parallel and Distributed Systems, 4(12):1320–1331, 1993.
J. Duato, S. Yalamanchili, and L. Ni. Interconnection networks: An engineering approach, IEEE Computer Society Press. Los Alamitos, CA, 1997.
J. Duato, S. Yalamanchili, M. B. Caminero, D. Love, and F. Quiles. MMR: A high-performance multimedia router: Architecture and design trade-offs. Proc. 5th Int. Symp. High Performance Computer Architecture (HPCA-5), pp. 300–309, IEEE Computer Society Press, 1999.
M. Escheikh, K. Barkaoui, and A. Bouallegue, Performance analysis of an N x N ATM switch with Markov modulated Poisson process under back-pressure mechanism. Proc. 8th Int. Symp. on Modeling, Analysis and Simulation of Computer and Telecomm. Systems (MASCOTS'2000), pp. 416–423, IEEE Computer Society Press, 2000.
W. Fischer and K. Meier-Hellstern. The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation, 18(2):149–171, 1993.
T. Gross and D. R. O'Hallaron. iWarp: Anatomy of a Parallel Computing System, MIT Press, 1998.
H. Heffes and D. M. Lucantoni. A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance. IEEE Journal Selected Areas Communications, 4(6):856–868, 1986.
S. H. Kang, D. K. Sung, and B. D. Choi, An empirical real-time approximation of waiting time distribution in MMPP(2)/D/1. IEEE Communications Letters, 2(1):17–19, 1998.
S. H. Kang, D. K. Sung, and B. D. Choi, CAC scheme based on real-time cell loss estimation for ATM multiplexers. IEEE Trans. Communications, 48(2):252–258, 2000.
R. E. Kessler and J. L. Schwarzmeier. CRAY T3D: A new dimension for Cray research. Proc. 38th Int. Computer Conf. (COMPCON'93), pp. 176–182, IEEE Computer Society Press, 1993.
J. Kim and C. R. Das. Hypercube communication delay with wormhole routing. IEEE Trans. Computers, 43(7):806–814, 1994.
L. Kleinrock. Queueing Systems: Theory, Vol. 1, John Wiley & Sons, New York, 1975.
S. Konstantinidou and L. Snyder. Chaos router: architecture and performance. Proc. ACM/IEEE 24th Int. Symp. on Computer Architecture (ISCA-24), pp. 212–221, ACM Press, 1991.
G. Min and M. Ould-Khaoua. A comparative study of switching methods in multicomputer networks. The Journal of Supercomputing, 21(3):227–238, 2002.
G. Min and M. Ould-khaoua. Performance analysis of wormhole switching in k-ary n-cubes under multimedia traffic. Proc. 15th IEEE & ACM Int. Parallel & Distributed Processing Symp. (IPDPS'2001), San Francisco, USA. CD-ROM, IEEE Computer Society Press, 2001.
G. Min and M. Ould-Khaoua. Performance modeling of pipelined circuit switching under MMPP traffic. Journal of Interconnection Networks, 2(4):471–484, 2001.
T. Olivares, P. Cuenca, F. Quiles, and A. Garrido. Parallelisation of the MPEG algorithm over a multicomputer, a proposal to evaluate its interconnection network. Proc. Pacific Rim Conf. Comm. Computer Science (RACRIM'97), pp. 113–116, IEEE Computer Society Press, 1997.
M. Ould-Khaoua. A performance model for Duato's fully adaptive routing algorithm in k-ary n-cubes. IEEE Trans. Computers, 48(12):1–8, 1999.
S. Rai and Y. C. Oh. Analysing packetized voice and video traffic in an ATM multiplexer. Int. Journal of communication systems, 11(4):225–235, 1998.
S. S. Wang and J. A. Silvester. An approximate model for performance evaluation of real-time multimedia communication system. Performance Evaluation, 22(3):239–256, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Min, G., Ould-Khaoua, M. Communication Delay in Wormhole-Switched Tori Networks under Bursty Workloads. The Journal of Supercomputing 26, 77–94 (2003). https://doi.org/10.1023/A:1024468119020
Issue Date:
DOI: https://doi.org/10.1023/A:1024468119020