The Solution Method for Lindley Integral Equation

Abstract

Research subject. This article considers the problem of solving the Lindley integral equation for esti-mating the average waiting time of a request in a queue in the general type queueing system. Method. Here we obtain a solution of the Lindley integral equation using selective functions. Core results. The proposed solution is based on the “degeneration” of the kernel of the Lindley integral equation where the kernel is factorized by its variables. Practical relevance. The considered procedure allows to obtain a solution of the integral equation for any statistical characteristics of the served traffic.