Open AccessSpectral expansion method for analysis of a system with shifted Erlang and hyper-Erlang distributions
Author(s) -
В. Н. Тарасов,
В. Н. Тарасов,
Н. Ф. Бахарева,
Н. Ф. Бахарева
Publication year - 2021
Publication title -
fizika volnovyh processov i radiotehničeskie sistemy
Language(s) - English
Resource type - Journals
eISSN - 2782-294X
pISSN - 1810-3189
DOI - 10.18469/1810-3189.2021.24.2.55-61
Subject(s) - erlang (programming language) , queueing theory , computer science , queue , erlang distribution , queue management system , mathematics , mathematical optimization , theoretical computer science , exponential distribution , computer network , statistics , functional programming
In this paper, we obtained a spectral expansion of the solution to the Lindley integral equation for a queuing system with a shifted Erlang input flow of customers and a hyper-Erlang distribution of the service time. On its basis, a calculation formula is derived for the average waiting time in the queue for this system in a closed form. As you know, all other characteristics of the queuing system are derivatives of the average waiting time. The resulting calculation formula complements and expands the well-known unfinished formula for the average waiting time in queue in queuing theory for G/G/1 systems. In the theory of queuing, studies of private systems of the G/G/1 type are relevant due to the fact that they are actively used in the modern theory of teletraffic, as well as in the design and modeling of various data transmission systems.