Abstract
Real-time analysis methods are usually based on worst-case execution times (WCET). This leads to pessimistic results and poor resource utilisation when applied to highly variable execution time tasks. This paper proposes a discrete statistical description of task execution times, known as histograms. The proposed characterisation facilitates a powerful analytical method which offers a statistical distribution of task response times. The analysis enables workloads to be studied with a utilisation higher than 1 during transient overloads. System behaviour is shown to be a stochastic process that converges to steady state probability distribution when the average utilisation is lower or equal to 1. The paper shows that workload isolation is a desirable property of scheduling algorithms which greatly aids analysis and makes it algorithm independent. The alternative, when workload isolation cannot be assumed, is the so-called interference method, which is also introduced for the case of GPS (Generalised Processor Sharing) algorithms. As an example, the proposed method is evaluated using network routers and real traffic traces. The obtained results are compared to alternative analysis methods based on solving queueing systems (M/D/1/N) analytically.
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References
Abeni L, Buttazzo G (1999) QoS guarantee using probabilistic deadlines. In: Proc of the euromicro conference on real-time systems
Addie RG, Zukerman M, Neame TD (1998) Broadband traffic modeling: simple solutions to hard problems. IEEE Commun Mag 88–95
Bennett J, Zhang H (1996) WF2Q: worst-case fair weighted fair queueing. In: Proc IEEE INFOCOM, pp 120–128
Cho K et al (2000) Traffic data repository at the WIDE project. In: USENIX 2000 FREENIX track
Díaz J (2003) Tecnicas estocasticas para el calculo del tiempo de respuesta en sistemas de tiempo real. Phd thesis, Universidad de Oviedo, Spain
Díaz J, Garcìa D, Kim K, Lee C, Bello LL, López J, Min SL, Mirabella O (2002) Stochastic analysis of periodic real-time systems. In: Proc of the 23rd IEEE real-time systems symposium, pp 289–300
Ferrari D, Verma D (1990) A scheme for real-time channel establishment in wide-area networks. IEEE J Sel Areas Commun 8(2):368–379
Gardner M (1999) Probabilistic analysis and scheduling of critical soft real-time systems. Phd thesis, University of Illinois, Urbana-Champaign
Kleinrock L (1976) Queueing systems. Computer applications, vol 2. Wiley–Interscience, New York
Kweon S-K, Shin KG (2001) Real-time transport of mpeg video with a statistically guaranteed loss ratio in ATM networks. IEEE Trans Parallel Distrib Comput 12(4):387–403
Lehoczky J (1997) Real-time queueing network theory. In: Proc of the 18th IEEE real-time systems symposium, pp 58–67
Leland WE, Taqqu MS, Willinger W, Wilson DV (1994) On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans Netw 2(1):1–15
Liu JW (2000) Real-time systems, vol 1. Pearson
Manolache S, Eles P, Peng Z (2001) Memory and time-efficient schedulability analysis of task sets with stochastic execution time. In: Proc of the 13th euromicro conference on real-time systems, pp 19–26
Parekh AK, Gallager RG (1993) A generalized processor sharing approach to flow control in integrated services networks: the single node case. IEEE/ACM Trans Netw 1(3):344–357
Shroff NB, Schwartz M (1994) Video modeling withing networks using deterministic smoothing at the source. In: IEEE Infocom, pp 342–349
Shroff NB, Schwartz M (1998) Improved loss calculations at an ATM multiplexer. IEEE/ACM Trans Netw 6(4):411–421
Skelly P, Schwartz M, Dixit S (1993) A histogram-based model for video traffic behavior in an ATM multiplexer. IEEE/ACM Trans Netw 1(4):446–459
Spuri M, Buttazzo GC (1996) Scheduling aperiodic tasks in dynamic priority systems. Real-Time Syst 10(2):179–210
Tia 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 164–173
Zhang ZL, Towsley D, Kurose J (1995) Statistical analysis of the generalized processor sharing scheduling discipline. IEEE J Sel Areas Commun 14(6):1071–1080
Zukerman M, Neame TD, Addie RG (2003) Internet traffic modeling and future technology implications. In: IEEE Infocom
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This work was developed under a grant from the Spanish Government CICYT TIC2005-08665-C03 and E.U. FRESCOR-FP6/2005/IST/5-034026.
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Vila-Carbó, J., Hernández-Orallo, E. An analysis method for variable execution time tasks based on histograms. Real-Time Syst 38, 1–37 (2008). https://doi.org/10.1007/s11241-007-9033-2
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DOI: https://doi.org/10.1007/s11241-007-9033-2