Asymptotic Analysis of RQ-System with Feedback and Batch Poisson Arrival Under the Condition of Increasing Average Waiting Time in Orbit

Asymptotic diffusion analysis of the retrial queuing system with feedback and batch Poisson arrival

“…Table 1 presents Kolmogorov distances Δ 1 calculated by formula (23), table 2 presents Kolmogorov distances Δ 2 calculated for the Gaussian approximation obtained in [6]. Bold in the tables are the values that correspond to a satisfactory approximation accuracy.…”

“…A diffusion approximation of the probability distribution of the number of customers in orbit is constructed. It is shown that the accuracy of the diffusion approximation is higher then the accuracy of Gaussian approximation obtained in [6].…”

“…Solution we find in the form Here 𝐶 ⋅ 𝑅 𝑛 (𝑥) is the general solution of the homogeneous equation due to (6), 𝑔 𝑛 is the solution of the equation…”

“…The application of asymptotic analysis methods makes it possible to obtain the asymptotic characteristics of the system under various limiting conditions. For example, in [6], a stationary probability distribution of the number of customers in orbit was obtained under conditions of a large delay of customers in orbit. To perform more detailed and accurate analysis of the model a method of asymptotic diffusion analysis is applied [7].…”