### Summary

This paper presents new results concerning the use of information theoretic inference techniques in system modeling and concerning the widespread applicability of certain simple queuing theory formulas. For the case when an *M/G*/1 queue provides a reasonable system model but when information about the service time probability density is limited to knowledge of a few moments, entropy maximization and cross-entropy minimization are used to derive information theoretic approximations for various performance distributions such as queue length, waiting time, residence time, busy period, etc. Some of these approximations are shown to reduce to exact *M/M*/1 results when *G = M*. For the case when a *G/G*/1 queue provides a reasonable system model, but when information about the arrival and service distributions is limited to the average arrival and service rates, it is shown that various well known *M/M*/1 formulas are information theoretic approximations. These results not only provide a new method for approximating the performance distributions, but they help to explain the widespread applicability of the *M/M*/1 formulas.