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

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

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Example text

Let [%s J ~ I} ~j = ~j + 1 - ~j for j ~ 1 . Note that the "sojourn times" between consecutive epochs of regeneration are independent and identically distributed. We will assume henceforth that E{~ I) < ~ not a restrictive assumption. This is For example; it holds in almost any queueing system of practical interest s and it certainly holds for the queueing and inventory examples of Section 2 s as well as for any positive recurrent irreducible Markov chain. The regenerative property is an extremely powerful tool for obtaining analytical results for the process [~n s n ~ I} Under very mild conditions the process has a limiting or steady-state distribution.

These assumptions certainly hold in the repair model of Section 23 and are 3 in general 3 very mild 37 assumptions for discrete-event simulations. Just as in the case of regenerative processes in discrete time, it is true that regenerative processes in continuous time have limiting or steadystate distributions under very mild conditions. discussed in Section 3-7. The exact conditions will be Once again; however, the point is that virtually all regenerative processes of practical interest for simulation applications have steady-state distributions; and most often in the following sense.

5. J = n ii n n j=l j=l n-I ^ = n Sll - 2 r s 1 2 " ^2 + r s22 Form the confidence interval ^ r± where z 5 = ~-i(i - 5) z~ s TNand is the standard normal distribution function. Note that in the case where the first cycle does not begin immediately at the start of the simulation s the above procedure indicates that the data prior to the first cycle is to be discarded. In order to clarify the procedure that has just been summarized~ let us follow through this procedure for a numerical example. Example.

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