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The use of an efficient stopping rule can assist in the achievement of accurate simulation results at a reduced cost of computation. Conversely, with an inefficient stopping rule, either in-accurate results or excessive costs can occur. The problem of deciding when to stop a simulation model of a computer system is further complicated by the fact that a key parameter, response time at a service center, is not an independent random variable. In spite of this complication, procedures for determining the number of observations of response time variables required to achieve statistically valid results have been developed. This paper presents, via the case-study approach, the effects of using an insufficient number of observations of response time and the improved accuracy which is obtained when an efficient stopping rule is used. While these results are not new, they are perhaps not widely known in the field of simulation of computer systems. We therefore view the contribution of this paper as that of demonstrating the application of such results in this field, so that other researchers can make use of them. An appendix includes a brief description of the algorithms used.