In this paper, the cost function of a single-server queueing system with Poisson input stream and Erlang- service time will be analyzed. Treated as a function of the traffic intensity , with respect to some known constants, we will show that its stationary points are solutions of a fourth-degree polynomial equation with real coefficients. Moreover, an explicit form of these solutions is given and it is shown the function reaches a minimum value at some of these points. For illustration, a numerical analysis of the cost function is carried out by changing the values of the costs, which are changed according to the principle of arithmetic progression. Also, a statistical analysis of the relationship between optimal solutions and is done.

中文翻译：

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具有泊松输入流和 Erlang-k 服务时间的单服务器排队系统的成本函数分析

本文将分析具有泊松输入流和 Erlang 服务时间的单服务器排队系统的成本函数。将 视为交通强度的函数，对于一些已知常数，我们将证明其驻点是具有实数系数的四次多项式方程的解。此外，给出了这些解的显式形式，并且表明函数在其中一些点处达到最小值。为了说明，通过改变成本值来进行成本函数的数值分析，成本值是根据算术级数原理改变的。此外，还对最优解 和 之间的关系进行了统计分析。