By M. A. Crane, A. J. Lemoine (eds.)
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Extra resources for An Introduction to the Regenerative Method for Simulation Analysis, 1st Edition
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. of the process between epoch 1 and epoch ~i 3 while independent of the rest of the process~ is allowed to have a different distribution. portion [~ n ~ Bj ~ n < ~j + I ] In the queueing example~ [Sj, j ~ l} of the process as the X ~n = W n H ~ e v e r ; the portion We will refer to the jth cycle.
It is only through such reliability measures that the simulator can judge whether the desired precision in the estimates has been obtained or whether more lengthy simulation runs are necessary. For each of the three examples presented in this section, we observed that if a stochastic system is simulated with the goal of estimating some steady-state parameter, then the simulator faces difficult problems of a "tactical" nature in providing a convincing statistical analysis of the simulation output.
I~] and since the repair times are exponentially distrlbuted 3 each of the states can serve as a regeneration state. ) In the inventory example we chose state But the post-ordering-decision inventory levels of 3, ~, ~, 6, 7, 7 as the return state. [Xn, n ~ 13 can be any one and, owing to the nature of the demands, the times of successive returns to any one of these states can serve as regeneration points. Thus, for example, we can say that if ~ Xn= to state n is an epoch of regeneration ; group the output into blocks according to successive returns ~ E[min(X, D)} and proceed to construct confidence intervals for by the procedure given earlier.