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An analytical model for torus networks in the presence of batch message arrivals with hot-spot destinations

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Abstract

Interconnection networks are hardware fabrics supporting communications between individual processors in multicomputers. The low-dimensional k-ary n-cubes (or torus) with adaptive wormhole switching have attracted significant research efforts to construct high-performance interconnection networks in contemporary multi-computers. The arrival process and destination distribution of messages have great effects on network performance. With the aim of capturing the characteristics of the realistic traffic pattern and obtaining a deep understanding of the performance behaviour of interconnection networks, this paper presents an analytical model to investigate the message latency in adaptive-routed wormhole-switched torus networks where there exists hot-spot nodes and the message arrivals follow a batch arrival process. Each generated message has a given probability to be directed to the hot-spot node. The average degree of virtual channel multiplexing is computed by the GE/G/1/V queueing system with finite buffer capacity. We compare analytical results of message latency with those obtained through the simulation experiments in order to validate the accuracy of the derived model.

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Author information

Authors and Affiliations

  1. Department of Computing, School of Informatics, University of Bradford, Bradford, BD7 1DP, UK

    Yulei Wu & Geyong Min

  2. Department of Computing Science, University of Glasgow, Glasgow, G12 8RZ, UK

    Mohamed Ould-Khaoua

  3. Department of Computer Science, Tsinghua University, Beijing, 100084, PRC

    Hao Yin

Authors
  1. Yulei Wu
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  2. Geyong Min
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  3. Mohamed Ould-Khaoua
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  4. Hao Yin
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Corresponding author

Correspondence to Geyong Min.

Additional information

This work was supported by the UK EPSRC research grant (No. EP/C525027/1) and Nuffield Foundation (No. NAL/00682/G).

Yulei Wu received the B. Sc. degree in computer science from University of Bradford, UK, in 2006. He is currently a Ph.D. candidate in the Department of Computing, School of Informatics, University of Bradford, UK.

His research interests include performance modeling and evaluation, parallel and distributed systems, cluster and grid computing, and multi-hop wireless networks.

Geyong Min received the B. Sc. degree in computer science from Huazhong University of Science and Technology, PRC, in 1995, and Ph.D. degree in computing science from the University of Glasgow, UK, in 2003. He is currently a senior lecturer in the Department of Computing at the University of Bradford, UK. He has published over 120 research papers in prestigious international journals. He serves on the editorial board of International Journal of Simulation Modeling Practice and Theory, International Journal of Wireless and Mobile Computing, International Journal of Smart Home, and International Journal of Security and Its Applications. He served as the guest editor for 12 international Journals and was the chair or vice-chair of 16 international conferences/workshops. He served on the program committees of over 100 professional conferences/workshops including IEEE Global Communications Conference (GLOBECOM), IEEE International Conference of Communications (ICC), IEEE Conference on Local Computer Networks (LCN), IEEE Vehicular Technology Society (VTC), International Conference on Parallel Processing (ICPP), and International Conference on Computer Communications and Networks (ICCCN). He is a member of the IEEE Computer Society and a member of the ACM.

His research interests include performance modelling and evaluation, computer networking, traffic engineering, mobile computing, and multimedia systems. His recent research has been supported by UK EPSRC, Royal Society, European FP6, and Nuffield Foundation.

Mohamed Ould-Khaoua worked at Glasgow University, UK, as a lecturer from 2000 to 2003, and then as a reader from 2004 to 2007. He also worked as a lecturer at Starthclyde University, UK, from 1997 to 2000 and post-doctoral research fellow at Teesside University, UK, from 1994 to 1997. He is currently a professor in the Department of Electrical & Computer Engineering, Sultan Qaboos University, Oman. He is the editor-in-chief of the Journal of Engineering Research. He serves on the editorial board of IEEE Transactions on Parallel & Distributed Systems, International Journal of Parallel, Distributed & Emergent System, International Journal of Computers & Applications, International Journal of High Performance Computing & Networking, International Review on Computers and Software, and International Journal of Computer & System Sciences. He is the guest editor of over 17 special issues on topics related to systems and networks performance evaluation and analysis in the Computation & Concurrency: Practice & Experience, IEE Proceedings of Computers & Digital Techniques, Future Generation Computing Systems, Journal of Parallel and Distributed Computing, Performance Evaluation, Supercomputing, Cluster Computing, International Journal of Computer Applications. He was a co-chair of the International Workshop Series on Performance Modeling, Evaluation, and Optimization of Parallel and Distributed Systems (PMEO-PDS), ACM International Workshop on Performance Evaluation of Wireless Ad Hoc, Sensor, and Ubiquitous Networks (PE-WASUN), ACM International Workshop on Performance Monitoring, Measurement, and Evaluation of Heterogeneous Wireless and Wired Networks (PM2HW2N), International Workshop on Performance Evaluation of Networks for Parallel, Cluster and Grid Computing Systems (PEN-PCGCS), International Workshop on Performance Modeling and Analysis of Communication in Parallel, Distributed, and Grid Networks (PMAC-PDG). He has served on the technical program committee of over 130 well-known international conferences and workshops, including International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA), IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS), IEEE Global Communications Conference (GLOBECOM), International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS), International Workshop on Modeling Analysis and Simulation of Wireless and Mobile Systems (MSWiM), International Conference on High Performance Computing (HiPC), International Conference on High Performance Computing and Communications (HPCC), International Performance Computing and Communications Conference (IPCCC), IEEE Conference on Local Computer Networks (LCN), International Conference on Parallel and Distributed Computing Systems (PDCS), The IASTED International Conference on Parallel and Distributed Computing and Networks (PDCN), IEEE International Conference on Advanced Information Networking and Applications (AINA), ASM, International Conference on Grid and Pervasive Computing (GPC), and International Conference on Computer Communications & Networks (IC3N).

His research interests include performance modelling and evaluation of wired/wireless networks and parallel/distributed systems.

Hao Yin is an associate professor with the Department of Computer Science and Technology, Tsinghua University, PRC.

His research interests include performance evaluation for Internet and wireless network, content delivery network, media streaming over P2P network, and security. He has published more than 50 papers and held several patents in above areas.

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Wu, Y., Min, G., Ould-Khaoua, M. et al. An analytical model for torus networks in the presence of batch message arrivals with hot-spot destinations. Int. J. Autom. Comput. 6, 38–47 (2009). https://doi.org/10.1007/s11633-009-0038-2

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  • DOI: https://doi.org/10.1007/s11633-009-0038-2

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