It is a very hard task to compute an exact solution for the differential equations, with differences, system that allows the determination of the M|M|m|m system transient probabilities. The respective complexity grows with m. The computations are extremely fastidious and the length and the fact that the expressions obtained are often approximate, and not exact, will not allow the transient probabilities behavior as time functions characterization. To overcome these problems, in this work it is analyzed how that system can supply approximate values to the M|M|m|m queue system. It is also presented an asymptotic method to solve the system that becomes possible in many cases to obtain simple approximated expressions for those probabilities using the M|M|Inf transient probabilities, very well-known and very much easier to study.

翻译：精确求解用于确定 M|M|m|m 系统瞬态概率的含差微分方程组是一项非常困难的任务。其计算复杂度随 m 增大而增加。计算过程极其繁琐，且所推导表达式往往仅为近似形式而非精确解，这导致无法刻画瞬态概率随时间变化的函数特征。为克服上述问题，本研究分析了该体系如何为 M|M|m|m 排队系统提供近似值。同时提出了一种渐近求解方法，使得在许多情况下能够利用已知且易于研究的 M|M|∞ 瞬态概率，获得这些概率的简明近似表达式。