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

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

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Additional resources for An Introduction to the Regenerative Method for Simulation Analysis, 1st Edition

Example text

We then found~ however, that these problems could he overcome (at least for the examples) in a very simple way if the stochastic simulation had the property of "regenerating itself" probabilistically from time to time. We now go on from here to set down a simple framework in Section 3 for analyzing the output of any stochastic simulation having a "regenerative" property of the sort we observed in the examples of this section. of simulations is very broad indeed. We will see that this class Moreover~ we will give a simple procedure for constructing a confidence interval (from the simulation output) for a wide variety of steady-state parameters of interest in a "regenerative" simulation.

Ii 0 II II t4. J oi 46 32 ~ : 14 Y4 = ~ W i = 150 i = 87 i=19 4O (~5 8 : Y5 = ~w i=33 5 ~Yj 3. 5 = j=l s $. 2 ^ ~2 s__£± - 2rs__£m + r s22 = 21 = . 81~8 ~ and reducing this width by a factor of two (at 90% confidence) would require about 20 cycles. ~ Sample Simulation Results for Models of Section 2 We now present sample simulation results for the queueing 3 inventory 3 and repairman models of Section 2. ~. We first present results for the queueing model. 1) in which the interarrival times are constant with value 60 and the service times are uniformly distributed on We are interested in estimate E{W] E[W] W is the steady-state waiting time.

1 Regenerative Processes in Discrete Time A sequence [~n ~ n ~ 13 of random vectors in a regenerative process if there is an increasing sequence K dimensions is 1 ~ ~i < ~2 < " " " of random discrete times~ called regeneration epochs; such that at each of these epochs the process starts afresh prohahilistically according to the same probabilistic structure governing it at epoch secutive regeneration epochs ~j and 81 . That is, between any two con- ~j + 1 ~ say~ the portion [~n ; ~j S n < ~j +i of the process is an independent and identically distributed replicate of the portion between any other two consecutive regeneration epochs.

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