On the nature and impact of self-similarity in real-time systems

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. 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An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such a probability to that of the steady state probability of an infinite state Discrete Time Markov Chain with a periodic structure. This structure is exploited to develop an efficient numeric solution where different accuracy/computation time trade-offs can be obtained by operating on the granularity of the model. More importantly we offer a closed form conservative bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability in one real-time application of practical interest. When this bound is used for the optimisation of the overall Quality of Service for a set of tasks sharing the CPU, it produces a good sub-optimal solution in a small amount of time.Comment: IEEE Transactions on Parallel and Distributed Systems, Volume:27, Issue: 3, March 201

Performance analysis of downlink shared channels in a UMTS network

In light of the expected growth in wireless data communications and the commonly anticipated up/downlink asymmetry, we present a performance analysis of downlink data transfer over \textsc{d}ownlink \textsc{s}hared \textsc{ch}annels (\textsc{dsch}s), arguably the most efficient \textsc{umts} transport channel for medium-to-large data transfers. It is our objective to provide qualitative insight in the different aspects that influence the data \textsc{q}uality \textsc{o}f \textsc{s}ervice (\textsc{qos}). As a most principal factor, the data traffic load affects the data \textsc{qos} in two distinct manners: {\em (i)} a heavier data traffic load implies a greater competition for \textsc{dsch} resources and thus longer transfer delays; and {\em (ii)} since each data call served on a \textsc{dsch} must maintain an \textsc{a}ssociated \textsc{d}edicated \textsc{ch}annel (\textsc{a}-\textsc{dch}) for signalling purposes, a heavier data traffic load implies a higher interference level, a higher frame error rate and thus a lower effective aggregate \textsc{dsch} throughput: {\em the greater the demand for service, the smaller the aggregate service capacity.} The latter effect is further amplified in a multicellular scenario, where a \textsc{dsch} experiences additional interference from the \textsc{dsch}s and \textsc{a}-\textsc{dch}s in surrounding cells, causing a further degradation of its effective throughput. Following an insightful two-stage performance evaluation approach, which segregates the interference aspects from the traffic dynamics, a set of numerical experiments is executed in order to demonstrate these effects and obtain qualitative insight in the impact of various system aspects on the data \textsc{qos}