Get An Introduction to the Regenerative Method for Simulation PDF

By M. A. Crane, A. J. Lemoine (eds.)

ISBN-10: 3540084088

ISBN-13: 9783540084082

ISBN-10: 3540371753

ISBN-13: 9783540371755

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15) gives the fraction of time that X Moreover, X(t) X(O) is greater is sampled from the steady-state , both these estimators are biased due to the initial conif s < t and s are highly correlated, does not change quickly. is close to t , then it is obvious Thus~ we must confront the same basic problems techniques that The bias of the "natural" estimators and the correlation of the observations of standard statistical that since the number of units in repair were present in the queueing and inventory simulations.

This section is organized as follows. We first discuss regenerative processes with a discrete time parameter~ as in the queueing and inventory examples; and then regenerative processes with a continuous time parameter, as in the repairman model. After defining regenerative processes~ we then give a technique for obtaining confidence intervals for steady-state parameters of 30 such processes and apply this technique to sample simulations of the models of Section 2. We next discuss the "tactical questions" of run length and of regeneration points~ this latter question arising in the case where a simulation may have two or more choices of regeneration points.

T if the repair facility be- For the simulation~ we put be the time of the {X(t)~ t ~ O} for We estimate • k = i, e, . . Also~ we let 7k (k + l)st We then let . X(O) = 0 3 entrance to 71 = R 2 - R 1 3 - • • 3 We refer to Tk as the dura- be the number of failures over the cycle. 3 gives simulation results for the repairman model based on a run of 500 observed cycles. are given for the parameters PCx= 0} , E[71) , Theoretical values and 95~ confidence intervals E[X] and E~Tl) 2 . 325] P[X > 5} o.

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An Introduction to the Regenerative Method for Simulation Analysis by M. A. Crane, A. J. Lemoine (eds.)

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