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For an undirected network G = (V, E) whose arcs are subject to random failure, we present a relatively complete and comprehensive description of a general class of Monte Carlo sampling plans for estimating g = g(s, T), the probability that a specified node s is connected to all nodes in a node set T. We also provide procedures for implementing these plans. Each plan uses known lower and upper bounds [B, A] on g to produce an estimator of g that has a smaller variance (A − g)(g − B)/K on K independent replications than that obtained for crude Monte Carlo sampling (B = 0, A = 1). We describe worst-case bounds on sample sizes K, in terms of B and A, for meeting absolute and relative error criteria. We also give the worst-case bound on the amount of variance reduction that can be expected when compared with crude Monte Carlo sampling. Two plans arc studied in detail for the case T = {t}. An example illustrates the variance reductions achievable with these plans. We also show how to assess the credibility that a specified error criterion for g is met as the Monte Carlo experiment progresses, and show how confidence intervals can be computed for g. Lastly, we summarize the steps needed to implement the proposed technique.

This paper presents a method for deriving a confidence interval for a population mean from the output of a simulation run. The method groups the observations on a run into batches and uses these batches as the basic data for analysis. The technique is not new. What is new is the procedure for determining how to group the observations into batches that satisfy certain assumptions necessary for the technique to work correctly. It is inexpensive and requires a moderate knowledge of statistics. The results of testing the method on a single server queuing model with Poisson distributed arrivals of exponentially distributed service times (M/M/1), indicate that the proposed technique performs as theory suggests for moderate activity levels. However, for higher activity levels performance is below theoretical expectation for small sample sizes n. As n increases, performance converges to expectation. Moreover, two calculations of the sample sizes needed to obtain results with moderate accuracy indicate that these sample sizes are in a range where the procedure is expected to perform with small error.