In real-time systems with highly variable task execution times simplistic task models are insufficient to accurately model and to analyze the system. Variability can be tackled using distributions rather than a single value, but the proper charac- terization depends on the degree of variability. Self-similarity is one of the deep- est kinds of variability. It characterizes the fact that a workload is not only highly variable, but it is also bursty on many time-scales. This paper identifies in which situations this source of indeterminism can appear in a real-time system: the com- bination of variability in task inter-arrival times and execution times. Although self- similarity is not a claim for all systems with variable execution times, it is not unusual in some applications with real-time requirements, like video processing, networking and gaming.
The paper shows how to properly model and to analyze self-similar task sets and how improper modeling can mask deadline misses. The paper derives an analyti- cal expression for the dependence of the deadline miss ratio on the degree of self- similarity and proofs its negative impact on real-time systems performance through system¿s modeling and simulation. This study about the nature and impact of self- similarity on soft real-time systems can help to reduce its effects, to choose the proper scheduling policies, and to avoid its causes at system design time.This work was developed under a grant from the European Union (FRESCOR-FP6/2005/IST/5-03402).Enrique Hernández-Orallo; Vila Carbó, JA. (2012). On the nature and impact of self-similarity in real-time systems. Real-Time Systems. 48(3):294-319. doi:10.1007/s11241-012-9146-0S294319483Abdelzaher TF, Sharma V, Lu C (2004) A utilization bound for aperiodic tasks and priority driven scheduling. IEEE Trans Comput 53(3):334–350Abeni L, Buttazzo G (1999) QoS guarantee using probabilistic deadlines. In: Proc of the Euromicro confererence on real-time systemsAbeni L, Buttazzo G (2004) Resource reservation in dynamic real-time systems. Real-Time Syst 37(2):123–167Anantharam V (1999) Scheduling strategies and long-range dependence. Queueing Syst 33(1–3):73–89Beran J (1994) Statistics for long-memory processes. Chapman and Hall, LondonBeran J, Sherman R, Taqqu M, Willinger W (1995) Long-range dependence in variable-bit-rate video traffic. IEEE Trans Commun 43(2):1566–1579Boxma O, Zwart B (2007) Tails in scheduling. SIGMETRICS Perform Eval Rev 34(4):13–20Brichet F, Roberts J, Simonian A, Veitch D (1996) Heavy traffic analysis of a storage model with long range dependent on/off sources. Queueing Syst 23(1):197–215Crovella M, Bestavros A (1997) Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Trans Netw 5(6):835–846Dìaz J, Garcìa D, Kim K, Lee C, Bello LL, López J, Min LS, Mirabella O (2002) Stochastic analysis of periodic real-time systems. In: Proc of the 23rd IEEE real-time systems symposium, pp 289–300Erramilli A, Narayan O, Willinger W (1996) Experimental queueing analysis with long-range dependent packet traffic. IEEE/ACM Trans Netw 4(2):209–223Erramilli A, Roughan M, Veitch D, Willinger W (2002) Self-similar traffic and network dynamics. Proc IEEE 90(5):800–819Gardner M (1999) Probabilistic analysis and scheduling of critical soft real-time systems. Phd thesis, University of Illinois, Urbana-ChampaignGarrett MW, Willinger W (1994) Analysis, modeling and generation of self-similar vbr video traffic. In: ACM SIGCOMMHarchol-Balter M (2002) Task assignment with unknown duration. J ACM 49(2):260–288Harchol-Balter M (2007) Foreword: Special issue on new perspective in scheduling. SIGMETRICS Perform Eval Rev 34(4):2–3Harchol-Balter M, Downey AB (1997) Exploiting process lifetime distributions for dynamic load balancing. ACM Trans Comput Syst 15(3):253–285Hernandez-Orallo E, Vila-Carbo J (2007) Network performance analysis based on histogram workload models. In: Proceedings of the 15th international symposium on modeling, analysis, and simulation of computer and telecommunication systems (MASCOTS), pp 331–336Hernandez-Orallo E, Vila-Carbo J (2010) Analysis of self-similar workload on real-time systems. In: IEEE real-time and embedded technology and applications symposium (RTAS). IEEE Computer Society, Washington, pp 343–352Hernández-Orallo E, Vila-Carbó J (2010) Network queue and loss analysis using histogram-based traffic models. Comput Commun 33(2):190–201Hughes CJ, Kaul P, Adve SV, Jain R, Park C, Srinivasan J (2001) Variability in the execution of multimedia applications and implications for architecture. SIGARCH Comput Archit News 29(2):254–265Leland W, Ott TJ (1986) Load-balancing heuristics and process behavior. SIGMETRICS Perform Eval Rev 14(1):54–69Leland WE, Taqqu MS, Willinger W, Wilson DV (1994) On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Trans Netw 2(1):1–15Liu CL, Layland JW (1973) Scheduling algorithms for multiprogramming in a hard-real-time environment. J ACM 20(1):46–61Mandelbrot B (1965) Self-similar error clusters in communication systems and the concept of conditional stationarity. IEEE Trans Commun 13(1):71–90Mandelbrot BB (1969) Long run linearity, locally Gaussian processes, h-spectra and infinite variances. Int Econ Rev 10:82–113Norros I (1994) A storage model with self-similar input. Queueing Syst 16(3):387–396Norros I (2000) Queueing behavior under fractional Brownian traffic. In: Park K, Willinger W (eds) Self-similar network traffic and performance evaluation. Willey, New York, Chap 4Park K, Willinger W (2000) Self-similar network traffic: An overview. In: Park K, Willinger W (eds) Self-similar network traffic and performance evaluation. Willey, New York, Chap 1Paxson V, Floyd S (1995) Wide area traffic: the failure of Poisson modeling. IEEE/ACM Trans Netw 3(3):226–244Rolls DA, Michailidis G, Hernández-Campos F (2005) Queueing analysis of network traffic: methodology and visualization tools. Comput Netw 48(3):447–473Rose O (1995) Statistical properties of mpeg video traffic and their impact on traffic modeling in atm systems. In: Conference on local computer networksRoy N, Hamm N, Madhukar M, Schmidt DC, Dowdy L (2009) The impact of variability on soft real-time system scheduling. In: RTCSA ’09: Proceedings of the 2009 15th IEEE international conference on embedded and real-time computing systems and applications. IEEE Computer Society, Washington, pp 527–532Sha L, Abdelzaher T, Årzén KE, Cervin A, Baker T, Burns A, Buttazzo G, Caccamo M, Lehoczky J, Mok AK (2004) Real time scheduling theory: A historical perspective. Real-Time Syst 28(2):101–155Taqqu MS, Willinger W, Sherman R (1997) Proof of a fundamental result in self-similar traffic modeling. SIGCOMM Comput Commun Rev 27(2):5–23Tia T, Deng Z, Shankar M, Storch M, Sun J, Wu L, Liu J (1995) Probabilistic performance guarantee for real-time tasks with varying computation times. In: Proc of the real-time technology and applications symposium, pp 164–173Vila-Carbó J, Hernández-Orallo E (2008) An analysis method for variable execution time tasks based on histograms. Real-Time Syst 38(1):1–37Willinger W, Taqqu M, Erramilli A (1996) A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. In: Stochastic networks: Theory and applications, pp 339–366Willinger W, Taqqu MS, Sherman R, Wilson DV (1997) Self-similarity through high-variability: statistical analysis of ethernet lan traffic at the source level. IEEE/ACM Trans Netw 5(1):71–8
