Observable augmented systems for sensitivity analysis of Markov and semi-Markov processes

Cassandras, C.G.; Strickland, Stephen G.

doi:10.1109/9.35272

Cited by 45 publications

(10 citation statements)

References 9 publications

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“…This question was addressed in Cassandras andStrickland (1989b, 1989c), and the constructability condition presented in Cassandras and Strickland (1989c) is briefly reviewed next. Suppose we are constructing a sample path {e{, t{}, k = 1, 2,..., and the current state is z~.…”

Section: The Sample Path Constructability Problemmentioning

confidence: 97%

“…This is always true for Markovian events, or it may be true in special cases where one can exploit the structure of the system (see Chapter 9 in Cassandras 1993 for some such examples). It was shown in Cassandras and Strickland (1989c) that a variant of the algorithm above, termed the "Age Matching Algorithm", allows the use of ASA in all DES with at most one non-Markovian event process. More recently (see Chapter 9 in Cassandras 1993) ASA was further extended to general stochastic models at the expense of additional information storage.…”

Section: If P[(x J)] C R[(xl)'] Update a To Include J;mentioning

confidence: 99%

“…., are directly observable, the problem is to construct a sample path {eL, t~}, k = 1, 2,..., for any 0j, j = 2,...,m, as shown in Figure 1. We refer to this as the sample path constructability problem (Cassandras and Strickland 1989c). Ideally, we would like this construction to take place on line, i.e.…”

Section: The Sample Path Constructability Problemmentioning

confidence: 99%

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Parallel sample path generation for discrete event systems and the traffic smoothing problem

Cassandras

1995

Discrete Event Dyn Syst

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Abstract. We review two approaches, the Standard Clock (SC) technique and Augmented System Analysis (ASA), that have been proposed for generating sample paths of Discrete Event Systems (DES) in parallel. These are placed in the unifying framework of the fundamental sample path constructability problem: for a finite discrete parameter set O --{01,..., Om }, given a sample path under 01, the problem is to simultaneously construct sample paths under all remaining parameter values. Using the ASA approach we then consider the problem of smoothing arbitrary, generally bursty, and possibly nonstationary traffic processes which are encountered in many applications, especially in the area of flow control for integrated-service, high-speed networks. We derive some basic structural properties of a smoothing scheme known as the Leaky Bucket (LB) mechanism through which it is seen that the variability of a traffic process can be monotonically decreased by decreasing an integer-valued parameter of this scheme. Finally, we show that a sample path under any value of this parameter is constructable with respect to an observed sample path under any other value. Therefore, by controlling this parameter on line, we show how simple iterative optimization schemes can be used to achieve typical design objectives such as keeping both the mean packet delay due to smoothing and the variability of the traffic process low.

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Section: The Sample Path Constructability Problemmentioning

confidence: 97%

Section: If P[(x J)] C R[(xl)'] Update a To Include J;mentioning

confidence: 99%

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Parallel sample path generation for discrete event systems and the traffic smoothing problem

Cassandras

1995

Discrete Event Dyn Syst

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“…By "alternative" systems, we mean systems that are different in structure but are driven by the same primitive events and associated timing properties. The above problem, often called the sample path constructibility problem (see Cassandras 1993), was considered by Cassandras and Strickland (1989a, 1989b, 1989c, as an avenue of extending ideas from perturbation analysis (Ho and Cao 1991) to discrete perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…Cassandras and Strickland considered the sample path constructibility problem by introducing a technique called Augmented System Analysis (Cassandras and Strickland 1989a, 1989b, 1989c). This technique is based on augmenting the state-space of a given system such that the "augmented system" incorporates the dynamics of both the given and an alternative system.…”

Section: Introductionmentioning

confidence: 99%

Distributed inversion in timed discrete event systems

Park

Chong

1995

Discrete Event Dyn Syst

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Abstract. We consider a discrete event system (DES) modeled by a timed automaton with partial state and event observations. We view the system as an input-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transition epochs. We consider the problem of extracting event lifetimes (input) from observations of the output trajectory, which we call inversion. We give necessary and sufficient conditions for invertibility, and an algorithm that extracts event lifetimes from any given output observation of an invertible system. We describe a distributed timed DES model based on the prioritized synchronous product of subsystems, and study the inversion problem in this framework. We show that invertibility in the subsystems implies invertibility in the global system. To illustrate our results, we provide an example of a tandem network.

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Discrete Event Systems

Cristea

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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Observable augmented systems for sensitivity analysis of Markov and semi-Markov processes

Cited by 45 publications

References 9 publications

Parallel sample path generation for discrete event systems and the traffic smoothing problem

Parallel sample path generation for discrete event systems and the traffic smoothing problem

Distributed inversion in timed discrete event systems

Discrete Event Systems

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