Queueing Networks with ``Transparent'' Calls¹

Rykov, Vladimir (Moscow, Russia)
rykov@rykov.ins.ru

In some applications of the queueing networks the situations arrive when all calls of the same type can be served simultaneously as only one of them. One of the main applications of the these types models is the queueing networks with the multicasting protocols [1], which are used in TV-broadcasting, video-on-demand, whiteboard teleconferencing etc.

Analogous service principles are probably realised in neuron networks, where an impuls caused by some irritater is delivered to all executive for it organs simultaneously, being each kind of eritater during the whole neuron fibre occupate some specific for it resourse without doplicate for each executive organ.

Traditional approach to analysis of a complex telecommunication network id based on its modelling with the help of stochastic networks and reversible Markov processes (see for example [2]--[4]), which permit to obtain the steady state probabilities in product form. In [5], [6] an alternative approach to decomposition of complex hierarhical nets was proposed. In [7] the model of networks with multycast connection was proposed which was analyse in assumption allowed to consider it as a reversible Markov process. In the talk this model is generalised for the case of general servise times. It is shown that the product for also takes place in this case

References

1

C. Diot et all. Multipoint communication: a survey of protocols, functions and mechanisms. IEEE Jounal on Selected Areas of Communications, 1997, N0. 15 (3), pp. 227-290.

2

F.P. Kelly. Reversibility and stochastic network. Wiley, Chichester, 1979.

3

K.W. Ross. Multyservice loss models for broadband telecommunication networks. Springer-Verlag, Lnd, 1995

4

R. Serfozo. Introduction to stochastic networks. Springer-Verlag, N.-Y., 1999

5

V.V. Rykov. Two approact to decomposition of complex hierarhical systems. Continuously interacting systems. Autom. and Remote Control, 1997, No. 10, стр. 91-104.

6

V.V. Rykov. Two approact to decomposition of complex hierarhical systems. Agregative systems. Autom. and Remote Control, 1997, No. 12, стр. 140-149.

7

V.V. Rykov, K.E. Samouylov. Product form solution for stochastic model of dynamic multicast connectiions. Proceedings of The Internztional conference on Distributed Computer Communication Networks (DCCN-99), November 9-13, 1999, Tel-Aviv (Israel), IITP RAS, Moscow, 1999.