A new variance reduction technique is introduced called internal control variables, to be used in the context of regeneration simulations. The idea is to identify a sequence of control random variables, each one defined within a regenerative cycle, whose mean can be calculated analytically. These controls should be highly correlated with the usual quantities observed in a regenerative simulation. This correlation reduces the variance of the estimate for the parameter of interest. Numerical examples are included for the waiting time process of an M/M/1 queue and for several Markov chains. (Author)

A technique ~s presented for the estmaatton by simulation of response time characteristics of queuemg network models of multlprogrammed computer systems The techmque is based on the regenerative method for the simulation of stochastic systems and the ~dea of trackmg a marked job m the network Illustrative numencal results m part obtained from a simulation of a queuemg model of a database management system are reported KEY WORDS AND PHRASES, queuemg

In this paper the author continues his study of the regenerative method for analyzing simulations of stable stochastic systems. The principal concern is to estimate the quantiles of the stationary distribution of a regenerative process. Markov chains in discrete or continuous time and multiple server queues in light traffic provide concrete examples of regenerative processes to which this technique applies. Approximate confidence intervals for these quantiles are derived from appropriate central limit theorems. The method has been applied to three stochastic simulations, and the numerical results are presented.

A technique is introduced for analyzing simulations of stochastic systems in the steady state. From the viewpoint of classical statistics, questions of simulation run duration and of starting and stopping simulations are addressed. This is possible because of the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation. The analysis is presented in the context of the general multiserver queue, with arbitrarily distributed interarrival and service times. In this case, it is the busy period structure of the system which produces the grouping mentioned above. Numerical illustrations are given for the M/M/1 queue. Statistical methods are employed so as to obtain confidence intervals for a variety of parameters of interest, such as the expected value of the stationary customer waiting time, the expected value of a function of the stationary waiting time, the expected number of customers served and length of a busy cycle, the tail of the stationary waiting time distribution, and the standard deviation of the stationary waiting time. Consideration is also given to determining system sensitivity to errors and uncertainty in the input parameters.

A technique for simulating GI/G/s queues is shown to apply to simulations of discrete and continuous-time Markov chains. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation. This grouping allows confidence intervals to be obtained for a general function of the steady-state distribution of the Markov chain. The technique is illustrated with simulation of an ( s, S ) inventory model in discrete time and the classical repairman problem in continuous time. Consideration is also given to determining system sensitivity to errors and uncertainty in the input parameters.