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On a functional equation arising from two processors with coupled inputs

机译：关于由两个具有耦合输入的处理器产生的函数方程

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During the last few decades, a certain interesting class of functional equations arises when obtaining the generating functions of many system distributions. Such a class of equations has numerous applications in many modern disciplines like wireless networks and communications. This paper has been motivated by an issue considered by Paul E. Wright in [Advances in applied probability, (1992), 986 ?? 1007]. The functional equation obtained there has been solved using elliptic functions and analytic continuation, which in turn lead to the determination of the main unknown. Unfortunately that solution seems to be a bit too general with many technical assumptions. In this paper on one hand, we introduce a solution in the symmetric case using boundary value problem approach. On the other hand, we investigate the potential singularities of the unknowns of the functional equation giving one possible application, and we compute some expectation of interest using the corresponding generating function.
机译：在过去的几十年中，当获得许多系统分布的生成函数时，会出现一类有趣的函数方程。这样的一类方程式在许多现代学科（如无线网络和通信）中具有大量应用。这篇论文的动机是保罗·赖特（Paul E. Wright）在[应用概率的进步，（1992），986？ 1007]。使用椭圆函数和解析连续性求解了在此获得的泛函，进而确定了主要未知数。不幸的是，在许多技术假设下，该解决方案似乎过于笼统。一方面，本文使用边界值问题方法介绍了对称情况下的解决方案。另一方面，我们研究给出了一个可能应用的函数方程的未知数的潜在奇点，并使用相应的生成函数来计算感兴趣的期望值。

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