A Performance Model for Wormhole-Switched Interconnection Networks under Self-Similar Traffic Geyong Min, Member, IEEE Computer Society, and Mohamed Ould-Khaoua, Member, IEEE Computer Society Abstract—Many recent studies have convincingly demonstrated that network traffic exhibits a noticeable self-similar nature which has a considerable impact on queuing performance. However, the networks used in current multicomputers have been primarily designed and analyzed under the assumption of the traditional Poisson arrival process, which is inherently unable to capture traffic self-similarity. Consequently, it is crucial to reexamine the performance properties of multicomputer networks in the context of more realistic traffic models before practical implementations show their potential faults. In an effort toward this end, this paper proposes the first analytical model for wormhole-switched k-ary n-cubes in the presence of self-similar traffic. Simulation experiments demonstrate that the proposed model exhibits a good degree of accuracy for various system sizes and under different operating conditions. The analytical model is then used to investigate the implications of traffic self-similarity on network performance. This study reveals that the network suffers considerable performance degradation when subjected to self-similar traffic, stressing the great need for improving network performance to ensure efficient support for this type of traffic. Index Terms—Multicomputers, interconnection networks, traffic self-similarity, adaptive routing, virtual channels, performance modeling. æ 1 INTRODUCTION A number of recent studies [8], [13], [18], [30] by means of high quality, high time-resolution measurements have convincingly demonstrated that realistic network traffic exhibits self-similar nature and that the traditionally assumed models (e.g., the Poisson process) fail to capture the actual traffic properties. The Poisson arrival process has a characteristic burst length that tends to be smoothed by averaging over a long enough time scale. Rather, measure- ments of actual traffic indicate that noticeable bursts are present over a wide range of time scales. This fractal-like nature of network traffic can be much better modeled using statistically self-similar processes, which have significantly different theoretical properties from the conventional Poisson process [3], [8], [13], [18], [24], [27], [29], [30]. Since extreme traffic burstiness spanning over a number of time scales gives rise to extended periods of large queue build- ups and also to sustained periods of low activity [21], the phenomenon of traffic self-similarity has a considerable impact on queuing performance and has received signifi- cant attention in the networking research community. It has been suggested that many existing theoretical protocols and systems need to be reevaluated under this different type of traffic [3], [13], [24], [27], [30]. Some researchers have argued that an essential reason for self-similarity in network traffic is due to the fact that the distribution of certain network-related variables is heavy-tailed [8], [30]. In general, a random variable obeying a heavy-tailed distribution exhibits a high or even infinite variance, which could result in traffic burstiness over many time scales [24]. Another significant cause of traffic self- similarity is attributed to the explosive growth in multi- media applications, typically exemplified by Variable Bit Rate (VBR) video [4]. The domain of multicomputers has been expanded to encompass multimedia applications. For instance, multicomputers are accepted as candidates for large-scale parallel multimedia servers as they can meet the high computation and communication requirements of multimedia applications, offering high-processing power, reliability, and high-bandwidth I/O [16]. In order to efficiently support these emerging multimedia applications, multicomputer networks have to cope with their traffic, which could possess self-similar characteristics. It is worth noting that several more recent studies [25], [28] have demonstrated that job arrival patterns and traffic loads generated by many parallel applications exhibit a self-similar or heavy-tailed nature. For instance, Squillante et al. [28] have conducted an extensive analysis of the workload collected from a real-world parallel computation environment—the 512-node IBM SP2 multicomputer system at the Cornell Theory Center—obtained over the period from July 1996 through May 1997. Their results have shown that the job arrival patterns follow heavy-tailed distributions and traffic load is bursty over different time scales. Sahuquillo et al. [25] IEEE TRANSACTIONS ON COMPUTERS, VOL. 53, NO. 5, MAY 2004 601 . G. Min is with the Department of Computing, School of Informatics, University of Bradford, Bradford, BD7 1DP, UK. E-mail: g.min@brad.ac.uk. . M. Ould-Khaoua is with the Department of Computer Science, University of Glasgow, Glasgow, G12 8RZ, UK. E-mail: mohamed@dcs.gla.ac.uk. Manuscript received 3 May 2002; revised 13 Feb. 2003; accepted 17 Sept. 2003. For information on obtaining reprints of this article, please send e-mail to: tc@computer.org, and reference IEEECS Log Number 116474. 0018-9340/04/$20.00 ß 2004 IEEE Published by the IEEE Computer Society