W.Whitt. Continuity of generalized semi markov processes. Mathematics of Operation Research, 5(4):494-- 501, 1980. 10  Home/Search   Document Not in Database   Summary   Related Articles   Check

....inversion of Laplace transforms. More general classes of SPNs have been considered by Haas and Shedler. They introduced regenerative SPNs and showed how this class of SPN can be analyzed by means of regenerative simulation [15] They showed that, for each generalized semi Markov process (GSMP) [16], there exists an equivalent SPN with generally distributed firing times [17] and proposed to analyze them by discrete event simulation. In this paper, we explore various subclasses of SPNs, obtained by imposing restrictions on the combinations of firing distributions types allowed or on the ....

W. Whitt, "Continuity of generalized semi-Markov processes", Mathematics of Operations Research, vol. 5, no. 4, pp. 494--501, Nov. 1980.

....the author of this article has been involved in the development of a general model of this kind. The stochastic automata model [17, 16] is a variant of the automata # Supported by the STW PROGRESS project TES 4999 (HaaST) model inspired by the so called generalised semi Markov processes (GSMPs) [39, 21] and timed automata [5, 6] Stochastic automata are intended to describe timed systems in which the occurrence time of an event is a random variable. Moreover, they provide an adequate framework for composition and it serves as the underlying semantic model for the process algebra [17, 16] In ....

.... the compositionality problem present in many existing models for performance analysis, specially in those in which time depends on arbitrary distribution functions (in contrast to the so called Markov models) Stochastic automata have been inspired by generalised semi Markov processes (GSMPs) [39, 21] and timed automata [5, 6] They provide a symbolic representation of timed probabilistic transition systems. In order to encode the passage of time, stochastic automata resort to the so called clock variables,orclocks for short. Like a chronometer, a clock can be reset to 0 and inspected at any ....

W. Whitt. Continuity of generalized semi-Markov processes. Math. Oper. Res., 5:494--501, 1980.

....we have actually assumed that P[t t f t Deltat] is independent of system history and also of the time at which f becomes enabled, but depends only upon t, the length of time since f became enabled. This assumption simplifies the model, and defines a so called semi Markov process (see e.g. [Whi80]) The untimed behaviour of the system in Figure 1 can be described by transition sequences such as fr, frf , frfr, etc. In order to represent real time system behaviour, we use transition sequences with time stamps, which record transition delay time. We write, for example, f; t 1 ) r; t 2 ) to ....

Whitt, W.: Continuity of generalized semi-Markov processes, Math. Oper. Res. 5, 1980.

....the association of events with exponentially distributed and deterministic delays. Subsequently, we show how to map these time enhanced UML system specifications onto a discrete event stochastic system. We identify a particular stochastic process, the generalized semi Markov process (GSMP) 21] [24], as the appropriate vehicle on which quantitative analysis is performed. Second, we present an efficient algorithm for the direct and automated state space generation out of these UML diagrams that removes vanishing states, i.e. states with no timed events active, and considers branching ....

....process and every configuration change in the state transition graph corresponds to a state change in the stochastic process. The most general form of the stochastic process underlying a state diagram is the generalized semi Markov process (GSMP) A generalized semi Markov process [21] [24] is a continuous time stochastic process that makes a state transition when one or more events associated with the occupied state occur. Events associated with a state compete to trigger the next state transition, and each set of trigger events has its own distribution for determining the next ....

[Article contains additional citation context not shown here]

W. Whitt, Continuity of Generalized Semi-Markov Processes, Mathematics of Operations Research, 5, 494-501, 1980.

....author of this article has been involved in the development of a general model of this kind. The stochastic automata model [17, 16] is a variant of the automata # Supported by the STW PROGRESS project TES 4999 (HaaST) 1 model inspired by the so called generalised semi Markov processes (GSMPs) [39, 21] and timed automata [5, 6] Stochastic automata are intended to describe timed systems in which the occurrence time of an event is a random variable. Moreover, they provide an adequate framework for composition and it serves as the underlying semantic model for the process algebra [17, 16] In its ....

.... the compositionality problem present in many existing models for performance analysis, specially in those in which time depends on arbitrary distribution functions (in contrast to the so called Markov models) Stochastic automata have been inspired by generalised semi Markov processes (GSMPs) [39, 21] and timed automata [5, 6] They provide a symbolic representation of timed probabilistic transition systems. In order to encode the passage of time, stochastic automata resort to the so called clock variables, or clocks for short. Like a chronometer, a clock can be reset to 0 and inspected at any ....

W. Whitt. Continuity of generalized semi-Markov processes. Math. Oper. Res., 5:494--501, 1980.

....logic (PCTL ) HJ89,ASB 95] where PTL formulae can be quantified by probability measures, yielding state formulae which can in turn be used to build path formulae. In the real time case, our system description formalism is essentially the model of generalized semi Markov processes [She87,Whi80] This is again a statetransition based model, where events are associated with fixed or random time delays. A random delay can be bounded or unbounded. In the first case, it must have a fixed uniform distribution in a bounded interval of the reals. In the second case, it can have an arbitrary ....

W. Whitt. Continuity of generalized semi-markov processes. Math. Oper. Res., 5, 1980.

....much more challenging. We add probabilities to our model of timed state transition graphs by associating fixed distributions with the delays. This extension makes our processes generalized semi markov processes , which have been studied by researchers in the field of stochastic modeling ( Sh87] [W80]) The process has uncountably many states, so we define a projection process over a finite state space. Unfortunately the projection process is not Markovian. In general, the properties of such processes are hard to analyze. However, we show that it can be used to check TCTL properties. The paper ....

....2 I . The model checking algorithm needs only a trivial modification when the distributions have support of more than 1 interval. To model concurrent delays we need to introduce several clocks running concurrently. Our notation is borrowed from the literature on generalized semi Markov processes ([W80], Sh87] A (finite state) real time probabilistic process has the following components: ffl A finite set S of states. ffl A labeling function : S 7 2 AP giving the assignment of truth values to atomic propositions in each state. ffl Associated with each state s is a finite set of events ....

W. Whitt, "Continuity of generalized semi-Markov processes," Math. Oper. Res. 5,1980.

.... method in the setting of generalized semi Markov processes (GSMPs) A GSMP is a general mathematical framework for modeling many discrete event systems, and there has been a considerable amount of work studying different aspects of this class of stochastic processes; e.g. see Shassberger (1976) Whitt (1980), Glynn (1989b) Haas and Shedler (1987) and Glasserman and Yao (1992a, 1992b) Also, because their dynamics closely follow those of event driven simulations, GSMPs have been useful in modeling systems analyzed through simulation and for studying various simulation methodologies; e.g. see Glynn ....

Whitt, W., "Continuity of Generalized Semi-Markov Processes," Math. Oper. Res. 5 (1980), 494--501.

....processes. We add probabilities to our model of state transition graphs with timing constraints by associating fixed distributions with the delays. This extension makes our processes generalized semi markov processes, which have been studied by researchers in the field of stochastic modeling [Sh87, Wh80]. In previous work [ACD91] we developed an algorithm for checking whether such a system satisfied a formula in TCTL [ACD90] an extension of the branching time temporal logic CTL [EC82] that allowed the inclusion of explicit constant upper and lower time bounds in formulas. Here, we describe a ....

....t 2 I. The model checking algorithm needs only a trivial modification when the distributions have support of more than one interval. To model concurrent delays we need to introduce several clocks running concurrently. Our notation is based upon the literature on generalized semi Markov processes [Wh80, Sh87]. A (finite state) real time probabilistic process M has the following components: ffl States: A finite set S of states. ffl Events: Associated with each state s is a finite set of events E(s) E(s) gives the set of events that are scheduled to occur when the process is in state s. Let E be the ....

W. Whitt, "Continuity of generalized semi-Markov processes," Math. Oper. Res. 5,1980.

....functionality. In this article, we have a three folded purpose: we discuss a probabilistic transition system model based on general distributions, we introduce a stochastic automata model which borrows ideas from both timed automata [2, 14] and generalised semi Markov processes (GSMP, for short) [26, 10], and finally we introduce and discuss in depth a stochastic process algebra. Probabilistic transition systems (PTS, for short) have been widely studied in the context of discrete probabilities [25, 17, 12, 19, 23, 9, However, the case with general distributions has received scant ....

....Systems 3 THE STOCHASTIC AUTOMATON MODEL In this section, we introduce a new automaton model that allows us to represent processes with stochastic information. The basic idea is borrowed from timed automata [2, 14] by combining it with ideas of discrete event systems, in particular GSMPs [10, 26]. Besides, we study two different semantic models for stochastic automata. Stochastic Automata. We first enumerate all the ingredients of a stochastic automaton and then give an example to explain the intuition behind the definition. Definition 3 A stochastic automaton is a structure (S; s 0 ; ....

W. Whitt. Continuity of generalized semi-Markov processes. Math. Oper. Res., 5:494--501, 1980.

....they assume the existence of a generalized semi Markov process, whereas we construct it from a given set of pdfs. The completed probabilistic duration automaton constructed by our algorithm can be used as input to their model checking algorithm. Much closer to our work is the work of Whitt [17], who has investigated the convergence of the construction of generalized semi Markov processes. Probabilistic Duration Automata 131 8 Conclusion We have described a novel methodology and tools for analyzing probabilistic timing properties of real time systems. In our methodology, clocks are ....

W. Whitt, "Continuity of generalized semi-Markov processes," Mathematics of Operations Research 5, 4 (November 1980), pp. 494-501.

....the inversion of Laplace transforms. More general classes of SPNs have been considered by Haas and Shedler. They introduced regenerative SPNs and showed how this class of SPN can be analyzed by means of regenerative simulation [15] They showed that, for each generalized semi Markov process (GSMP) [16], there exists an equivalent SPN with generally distributed firing times [17] and proposed to analyze them by discrete event simulation. In this paper, we explore various subclasses of SPNs, obtained by imposing restrictions on the combinations of firing distributions types allowed or on the ....

W. Whitt, "Continuity of generalized semi-Markov processes", Mathematics of Operations Research, vol. 5, no. 4, pp. 494--501, Nov. 1980.

....we have actually assumed that P[t t f t Deltat] is independent of system history and also of the time at which f becomes enabled, but depends only upon t, the length of time since f became enabled. This assumption simplifies the model, and defines a so called semi Markov process (see e.g. [Whi80]) The untimed behaviour of the system in Figure 1 can be described by transition sequences such as fr, frf , frfr, etc. In order to represent real time system behaviour, we use transition sequences with time stamps, which record transition delay time. We write, for example, f; t 1 ) r; t 2 ) to ....

Whitt, W.: Continuity of generalized semi-Markov processes, Math. Oper. Res. 5, 1980.

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WHITT, W. 1980b. Continuity of generalized semi-Markov processes. Math. Opns. Res. 5, 494-501.

.... B(t) In our simulation experiments we actually considered combination and linear control estimators based on BS (t) as well as BN (t) but as in our previous paper we found that BS (t) and BN (t) tend to be interchangeable, so we only report results for BN (t) As in Srikant and Whitt, we find that the performance of the estimators in GI GI s 0 model depends on the loading. Roughly speaking, the loading can be regarded as light, normal or heavy when ff s Gamma 2 p ff, s Gamma 2 p ff ff s 2 p ff, or ff s 2 p ff. A starting point is the result from our previous ....

....exact blocking probabilities are B = 0:07570 for = 100 and B = 0:30124 for = 140. From Table 3 we see that there is no discernible bias in the estimators BN (t) and BC (t) The standard deviations of the estimators BN (t) and B I (t) are also consistent with the predictions in Srikant and Whitt, which justifies our choice of run length. Note that the standard deviation of the blocking probability is about 1 of the estimated value, whereas the standard deviations of the standard deviation estimates are larger (relatively) e.g. for the natural estimator they are about 15 . Similarly, the ....

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Whitt, W. 1980b. Continuity of generalized semi-Markov processes. Math. Opns. Res. 5, 494--501.

....be with the original interarrival time and service time distributions. Fortunately, such robustness, stability or continuity properties have been established for performance models, e.g. see Section VIII.5 of Asmussen [5] Section 21 of Borovkov [13] Kalashnikov and Rachev [32] and Whitt [52] [53]. Even though robustness results have been established, care is needed because the robustness results do not hold unconditionally. The robustness depends upon what we mean by close and upon regularity conditions. For probability distributions on the real line (or, more generally, on a metric ....

W. Whitt, Continuity of generalized semi-Markov processes, Math. Oper. Res. 5 (1980) 494--501.

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W.Whitt. Continuity of generalized semi markov processes. Mathematics of Operation Research, 5(4):494-- 501, 1980. 10

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W. Whitt. Continuity of generalized semi-Markov processes. Mathematics of Operations Research, 5:494--501, 1980.

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Whitt, W. (1980). Continuity of Generalized Semi-Markov Processes. Mathematics of Operations Research 5, 494--501.

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W. Whitt, "Continuity of generalized semi-Markov processes," Mathematics of Operations Research, vol. 5, no. 4, pp. 494--501, November 1980.

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Whitt, W. (1980). Continuity of generalized semi-Markov processes. Math. Oper. Res. 5 494--501.

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