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

ISBN-10: 3540084088

ISBN-13: 9783540084082

ISBN-10: 3540371753

ISBN-13: 9783540371755

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

**Example text**

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. E(X3 and Now 3 a natural question for the simulator to ask is how the lengths of the confidence intervals vary for the different return states 7 and ~ . Indeed, the same question arises in the simulation of any positive recurrent irreducible Markov chain, since each state can serve as a return state.

With customer we set , ~I = I WI = 0 3 and let ~k+ i customer whose waiting time is zero, for 51 = S2 - 81' " " " ' ~k = 8 k + l length of the kth cycle. served in the kth busy period. n ) if % = 0 For the simulation 2 be the index of the k = I, 23 . . - ~k' . . 1 presents simulation results for the queueing model based on a run of 1500 observed cycles. 3. 208. Thus, we might regard as a '~penalty" for long waiting times, a long waiting time~ and P{~ > 6} P[W > 24} E[{W - ~ ) + } as the likelihood of as the likelihood of a long busy period.

Thus, we might regard as a '~penalty" for long waiting times, a long waiting time~ and P{~ > 6} P[W > 24} E[{W - ~ ) + } as the likelihood of as the likelihood of a long busy period. 128] [~99. 700, 885. 399] 49 We next consider the inventory model. In this system, the demand for an item in a period has a binomial distribution with parameters 9 and 1/5. The inventory level of the item is checked at the beginning of each period. If fewer than 5 units are on hand, an order is placed which immediately raises the inventory level to 7 units; otherwise• no order is placed.

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

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