G-Networks: Development of the Theory of Multiplicative Networks

This is a review on G-networks, which are the generalization of the Jackson and BCMP networks, for which the multi-dimensional stationary distribution of the network state probabilities is also represented in product form. The G-networks primarily differ from the Jackson and BCMP networks in that they additionally contain a flow of the so-called negative customers and/ or triggers. Negative customers and triggers are not served. When a negative customer arrives at a network node, one or a batch of positive (ordinary) customers is killed (annihilated, displaced), whereas a trigger displaces a positive customer from the node to some other node. For applied mathematicians, G-networks are of great interest for extending the multiplicative theory of queueing networks and for practical specialists in modeling computing systems and networks and biophysical neural networks for solving pattern recognition and other problems.

Авторы
Bocharov P.P. 1 , Vishnevskii V.M.2
Редакторы
-
Издательство
Maik Nauka Publishing / Springer SBM
Номер выпуска
5
Язык
Английский
Страницы
714-739
Статус
Опубликовано
Подразделение
-
Номер
-
Том
64
Год
2003
Организации
  • 1 Peoples Friendship University, Moscow, Russian Federation
  • 2 Inst. for Info. Transmiss. Problems, Russian Academy of Sciences, Moscow, Russian Federation
Ключевые слова
Algebra; Computer networks; Markov processes; Neural networks; Nonlinear equations; Numerical methods; Optimization; Packet networks; Pattern recognition; Poisson distribution; Problem solving; Queueing theory; Multiplicative networks; Network nodes; Queueing networks
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/108/