Non-Markovian Analysis

German, Reinhard

doi:10.1007/3-540-44667-2_4

Cited by 7 publications

(7 citation statements)

References 29 publications

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“…A duration of a task can be any number in a given interval (no probability assigned) and the strategy is evaluated according to the worst performance induced by an instance of the external environment. Duration probabilistic automata (DPA) have been introduced in [18] to express stochastic scheduling problems and evaluate the expected performance of schedulers by methods similar to techniques used for generalized semi-Markov processes (GSMP) [10,11,7] such as [6,2]. This approach refines the successor operator used in the verification of timed automata [9,15] from a zone transformer into a density transformer and can compute, for example, the time distribution of reaching the final state and hence the expected termination time under a given scheduler.…”

Section: Introductionmentioning

confidence: 99%

As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

Kempf

Bozga

Maler

2013

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. In this paper we continue our investigation of stochastic (and hence dynamic) variants of classical scheduling problems. Such problems can be modeled as duration probabilistic automata (DPA), a well-structured class of acyclic timed automata where temporal uncertainty is interpreted as a bounded uniform distribution of task durations [18]. In [12] we have developed a framework for computing the expected performance of a given scheduling policy. In the present paper we move from analysis to controller synthesis and develop a dynamicprogramming style procedure for automatically synthesizing (or approximating) expected time optimal schedulers, using an iterative computation of a stochastic time-to-go function over the state and clock space of the automaton.

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Section: Introductionmentioning

confidence: 99%

As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

Kempf

Bozga

Maler

2013

Tools and Algorithms for the Construction and Analysis of Systems

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“…In past years, several classes of non-Markovian approaches have been defined [BT98], such as Semi-Markov Stochastic Petri Net (SMSPN's) [CGL94], Markov Regenerative Stochastic Petri Nets (MRSPN's) [CKT94] and Deterministic and Stochastic Petri Nets (DSPN's) [AC87]. Some major methods for analytically solving the non-Markovian models are discussed in [BPTT98,MFT00,Ger01]. A short survey on State-Based Stochastic Methods and automated supporting tools for the assisted construction and solution of dependability models can be found in [BCG05].…”

Section: Stochastic Model-based Approaches For Early Prediction Of Dementioning

confidence: 99%

Dependability and Performance Assessment of Dynamic CONNECTed Systems

Bertolino

Calabrò

Giandomenico

et al. 2011

Formal Methods for Eternal Networked Software Systems

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Abstract. In this chapter we present approaches for analysis and monitoring of dependability and performance of Connected systems, and their combined usage. These approaches need to account for dynamicity and evolvability of Connected systems. In particular, the chapter covers the quantitative assessment of dependability and performance properties through a stochastic model-based approach: first an overview of dependability-related measurements and stochastic model-based approaches provides the necessary background. Then, our proposal in Connect of an automated and modular dependability analysis framework for dynamically Connected systems is described. This framework can be used off-line for system design (specifically, in Connect, for Connector synthesis), and on-line, to continuously assess system behaviour and detect possible issues arising at run-time. For the latter purpose, a generic, flexible and modular monitoring infrastructure has been developed. Monitoring is at the core of the Connect vision, in order to ensure run-time observation of specified quantitative properties and possibly trigger adequate reactions. We focus here on the interaction chain between monitoring and analysis, to allow for on-line continuous validation of specified dependability and performance properties. Illustrative examples of applications of analysis and monitoring are provided with reference to the Connect Terrorist Alert scenario.

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“…In fact, in earlier works we have observed that empirical characterizations for both task service times and task transfer times that were obtained from actual DCSs follow power-law distributions like the Pareto distribution [16], [29]. Moreover, researchers have shown that Markovian models may introduce significant errors on the calculation of performance and reliability metrics [16], [25]. In particular, in [16], we showed by means of Monte-Carlo (MC) simulations that the service reliability of a DCS calculated under the Markovian assumption can be highly inaccurate in settings where the average task-transfer delays are large compared to the average task service times.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, modeling and analysis of non-Markovian queuing systems has been conducted in terms of nonMarkovian stochastic Petri Nets [4], [24], [25], [26], [27], [28]. In these works non-Markovian stochastic Petri Nets have been developed and their capabilities have been exploited to model the performance of web server networks [26], queues of embedded systems [26], [27] and the queues of two network terminals [28] among other applications.…”

Section: Introductionmentioning

confidence: 99%

Performance and Reliability of Non-Markovian Heterogeneous Distributed Computing Systems

Pezoa

Hayat

2012

IEEE Trans. Parallel Distrib. Syst.

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Abstract-Average service time, quality-of-service (QoS), and service reliability associated with heterogeneous parallel and distributed computing systems (DCSs) are analytically characterized in a realistic setting for which tangible, stochastic communication delays are present with nonexponential distributions. The departure from the traditionally assumed exponential distributions for event times, such as task-execution times, communication arrival times and load-transfer delays, gives rise to a non-Markovian dynamical problem for which a novel age dependent, renewal-based distributed queuing model is developed. Numerical examples offered by the model shed light on the operational and system settings for which the Markovian setting, resulting from employing an exponentialdistribution assumption on the event times, yields inaccurate predictions. A key benefit of the model is that it offers a rigorous framework for devising optimal dynamic task reallocation (DTR) policies systematically in heterogeneous DCSs by optimally selecting the fraction of the excess loads that need to be exchanged among the servers, thereby controlling the degree of cooperative processing in a DCSs. Key results on performance prediction and optimization of DCSs are validated using Monte-Carlo (MC) simulation as well as experiments on a distributed computing testbed. The scalability, in the number of servers, of the age-dependent model is studied and a linearly scalable analytical approximation is derived.

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Non-Markovian Analysis

Cited by 7 publications

References 29 publications

As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty

Dependability and Performance Assessment of Dynamic CONNECTed Systems

Performance and Reliability of Non-Markovian Heterogeneous Distributed Computing Systems

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