On a functional equation arising from two processors with coupled inputs

20150619 https://doi.org/10.14419/ijbas.v4i3.4760 
Functional Equation, Complex Analysis, Queueing Theory, Boundary Value Problem, Singularity, Generating Function. 
Abstract
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 ô€€€ 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.

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How to Cite
ElHady, E.S., & ForgRob, W. (2015). On a functional equation arising from two processors with coupled inputs. International Journal of Basic and Applied Sciences, 4(3), 264276. https://doi.org/10.14419/ijbas.v4i3.4760Received date: 20150513
Accepted date: 20150608
Published date: 20150619