Simulation output analysis for local area computer networks

Iglehart, Donald L.; Shedler, Gerald S.

doi:10.1007/bf00264614

Cited by 8 publications

(3 citation statements)

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“…As an application, consider the closed network of queues discussed in this subsection and suppose we wish to estimate the limiting average delay only for those delays that start with an arrival to an empty queue. The tagging approach has been applied in the more general settings of GSMPs (Iglehart and Shedler, 1984;Shedler, 1993) and colored SPNS (Haas and Shedler, 1993b). In the setting of queueing systems, delays are sometimes referred to as "passage times" because they correspond to the time for a job to pass from a specified initial position in the network to a specified final position.…”

Section: {E24} Andmentioning

confidence: 99%

Stochastic Petri Nets

Haas¹

2002

115

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Section: {E24} Andmentioning

confidence: 99%

Stochastic Petri Nets

Haas¹

2002

115

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“…Iglehart and Shedler [22] study abstract passage times in the setting of GSMP's with unique trigger events. The simulation methods given in [22] do not require that each clock-setting distribution have a density function that is continuous and positive on (0, m ) , but permit at most one passage time to be underway simultaneously.…”

Section: Introductionmentioning

confidence: 99%

“…The simulation methods given in [22] do not require that each clock-setting distribution have a density function that is continuous and positive on (0, m ) , but permit at most one passage time to be underway simultaneously. Prisgrove and Shedler [25] consider passage times in "symmetric" stochastic Petri nets with no immediate transitions or colors and obtain a simulation method that is analogous to the one in [22].…”

Section: Introductionmentioning

confidence: 99%

Passage times in colored stochastic petri nets

Haas

Shedler

1993

Communications in Statistics. Stochastic Models

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Passage times in colored stochastic Petri nets correspond to delays in discrete-event stochastic systems. Formal definition of a sequence of passage times in a colored stochastic Petri net is in terms of the underlying general state space Markov chain of the marking process. Using symmetry of the net with respect to color, we provide conditions under which a sequence of passage times is a regenerative process in discrete time with finite cycle-length moments. The regenerative property implies time-average convergence, convergence in distribution, and a central limit theorem for sequences of passage times. It follows that strongly consistent point estimates and asymptotic confidence intervals for general characteristics of passage times can be obtained by simulating a finite portion of a single sample path of the underlying general state space Markov chain. Using regenerative structure of the marking process and a version of Little's Law given by Glynn and Whitt, we also obtain conditions under which a sequence of passage times converges in a time-average sense and the limit can be expressed as a ratio of expected values. The resulting estimation procedure for the limiting average passage time requires no measurement of individual passage times and is valid even if there are no regeneration points for the sequence of passage times.In practice, the most difficult part of the argument required to establish the applicability of regenerative methods for simulation of passage times in colored stochastic Petri nets is to show that certain fixed sets of markings are recurrent. We show that representations for certain conditional distributions of clock readings can be combined with a "geometric trials" criterion to establish recurrence.

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Estimation methods for passage times using one-dependent cycles

Haas

Shedler

1996

Discrete Event Dyn Syst

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Abetraet. The lengths of certain passage-time intervals (random time intervals) in discrete-event stochastic systems correspond to delays in computer, communication, manufacturing, and transportation systems. Simulation is often the only available means for analyzing a sequence of such lengths. It is sometimes possible to obtain meaningful estimates for the limiting average delay indirectly, that is, without measuring lengths of individual passage-time intervals. For general time-average limits of a sequence of delays, however, it is necessary to measure individual lengths and combine them to form point and interval estimates. We consider sequences of delays determined by state transitions of a generalized semi-Markov process and introduce a recursively-generated sequence of realvalued random vectors, called start vectors, to provide the link between the starts and terminations of passage-time intervals. This method of start vectors for measuring delays avoids the need to "tag" entities in the system. We show that if the generalized semi-Markov process has a recurrent single-state, then the sample paths of any sequence of delays can be decomposed into one-dependent, identically distributed cycles. We then show that an extension of the regenerative method for analysis of simulation output can be used to obtain meaningful point estimates and confidence intervals for time-average limits. This estimation procedure is valid not only when there are no ongoing passage times at any regeneration point but, unlike previous methods, also when the sequence of delays does not inherit regenerative structure. Application of these methods to a manufacturing cell with robots is discussed.Keywords: discrete-event stochastic systems, stochastic simulation, regenerative processes, regenerative simulation, generalized semi-Markov processes, passage times, Little's Law, networks of queues 1, IntroductionAnalysis of delay phenomena is often necessary for assessment of the performance of computer, communication, manufacturing, and transportation systems. Examples of delays in such systems include , the time to produce an item in a flexible manufacturing system; ® the time to compute the answer to a query in a database management system; and the time to transmit a message from one node to another in a communication network.This paper deals with simulation methods that are applicable to delays when the system under study is modeled as a discrete-event stochastic system. We suppose that the delays of interest correspond to lengths of certain passage-time intervals (random time intervals) determined by state transitions of the system. Simulation is often the only available means for analyzing a sequence of such lengths. A discrete-event stochastic system makes state transitions when events associated with the occupied state occur; events occur only at an increasing sequence of random times. The underlying stochastic process of a discrete-event stochastic system records the state of the

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Simulation output analysis for local area computer networks

Cited by 8 publications

References 10 publications

Stochastic Petri Nets

Stochastic Petri Nets

Passage times in colored stochastic petri nets

Estimation methods for passage times using one-dependent cycles

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