Abstract
Here considered a model of the kernel of the Lindley integral equation for a queuing system G/G/1. An exact solution of Lindley equation can be obtained using the Fourier transform under analytic continuation to the half-plane of the complex function originally defined on the real axis. However, it is quite difficult to obtain such solution, therefore, one resorts to finding approximate solutions based on the procedure of “degeneration” of the kernel when the kernel is factorized according to its variables. The method based on the use of selective functions is used. As an example, a special case is considered when the arrival time intervals have a gamma distribution, and the service time is constant. The result is shown for the kernel with the exponential form.
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