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

ISBN-10: 3540084088

ISBN-13: 9783540084082

ISBN-10: 3540371753

ISBN-13: 9783540371755

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**Additional resources for An Introduction to the Regenerative Method for Simulation Analysis**

**Sample text**

A). 11) we have which may be rewritten as $ is the standard normal distribution function. < ~ is not restrictive for simulation applications. 12) since the value of estimate the value of ¢ Let 2 = E{(Y I s22 Sll , ~ as follows. - r~l )2} and s12 = - ~[~ n - 1 n l I CoV(Yl, 51) + r 2 Var(~ I} and t h e sample c o v a r i a n c e o f t h e n (Yj . 's 3 j=l s22 is unknown. 12) holds with s lim P ~-i(I % n . ~ = ~ x ®(x) . - % B ®(~)=i- nl/2[ r . for large 2 . 13) we have . 1~) then w ^ for large n 2z5~ ~ with high probability.

Cycle. 3) and (3-~)- The sequence [(Yj, ~j), j > I} consists of independent and identically distributed random vectors. h) Note that we demonstrated the validity of and inventory examples. those examples. 3) holds since the vectors ((Yj, ~j) , j > I } are defined in successive regeneration cycles~ and these cycles are independent and exhibit the same probabilistie behavior. ~)~ it is known that under quite general conditions f ( X l ) + . . 5) N as N -+ ~ ~ with probability one. Now suppose that ~I = i so that the first regeneration cycle starts at the very beginning of the simulation.

Are given for the parameters ~ 3 = F{X= j) for Theoretical values and 95~ confidence intervals E{X} ~ E[min(X~ D)} , E[~ I) • and ~j where J = 3, 4, 5, 6, 7 • Finallyj we consider the repairman model. Recall that we have a system as depicted in Figure 2. 3 with I0 operating units• 5 spare units, and h servers at the repair facility. lifetime" of an operating unit is exponentially distributed with mean 5, and the time required to repair a unit is exponentially distributed with mean 2. 514] 51 P[X > 5] where X is the number of units at the repair facility (waiting for and undergoing repair) under steady-state conditions.

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

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