Open AccessRELATIONS FOR CHARACTERISTICS OF MULTI-CHANNEL SYSTEMS WITH POISSON ACCIDENTS
Author(s) -
Georgiy Aleksandrovich Popov
Publication year - 2017
Publication title -
vestnik astrahanskogo gosudarstvennogo tehničeskogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2687-1076
pISSN - 1812-9498
DOI - 10.24143/1812-9498-2017-2-29-36
Subject(s) - queue , poisson distribution , moment (physics) , laplace transform , channel (broadcasting) , computer science , joint (building) , residual , order (exchange) , service (business) , mathematics , computer network , mathematical analysis , algorithm , engineering , statistics , physics , structural engineering , economy , finance , classical mechanics , economics
The article describes a special class of multichannel systems with Poisson incoming flows. The assumption of poissonity of the incoming flow is typical for many models. For these systems there are found recurrent relations for Laplace-Styltjes transformations of joint distribution of the queue lengths, residual time of services and a busy period, which allow to express these characteristics through their marginal values: joint distribution of residual services and a busy period at the moment of the beginning of services and in the moments of calling-in, when the system has no queue, or rather, not all devices are busy. Thus, the problem of analysis of multi-channel systems with Poisson incoming flows is reduced to the problem of finding marginal characteristics of the specified system. All other system characteristics can be expressed through the described characteristics of the system. For every moment of the service beginning there is introduced a parameter: the vector of the numbers of servicing devices, components of which are arranged in the increasing order of residual duration of service on the respective devices - the vector of order release devices. The obtained system of integral relations, linking the system characteristics of all vectors of the order of release of the devices among themselves.