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Stochastic Simulation by Brian D. Ripley

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CHAPTER 6

Output Analysis

The analysis of simulation experiments that give one observation per run is relatively straightforward unless, as in Chapter 5, deliberate dependence was introduced in the experimental design. However, for simulations of systems evolving through time we may take many correlated observations per run. Suppose we are interested in the distribution of customer waiting time in a queueing system. Then the waits of each customer will be relevant data. Furthermore, we will expect the waiting times of successive arrivals to be correlated.

These problems arise also with the observation of actual queueing systems. However, because of the expense of observation, real systems are usually observed by sparse sampling (if at all), so the development of appropriate statistical analyses has been triggered by simulation experiments relatively recently.

The problems only arise for quantities defined on a system “in equilibrium” or in “steady state.” That is, we have a strictly stationary process Xt on (−∞, ∞) or all the integers, and we are interested in aspects of the distribution of Xt for any fixed t. Alternatively, we can consider Xt starting at t = 0 and converging to an equilibrium process as t → ∞. (The two ideas are equivalent in most examples, since the equilibrium process must be strictly stationary, and if a stationary process exists, there is usually a convergence theorem.) If we are interested in the transient behavior of the process, as in estimating ω =

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