Abstract
A class of open queueing networks with packet switching is discussed. The configuration graph of the network may be finite or infinite. The external messages are divided into standard pieces (packets) each of which is transmitted as a single message. The messages are addressed, as a rule, to nearest neighbours and thereby the network may be treated as a small perturbation of the collection of isolated servers.
The switching rule adopted admits overtaking: packets which appeared later may reach the delivery node earlier. The transmission of a message is completed when its last packet reaches the destination node.
The main result of this paper is that the network possesses a unique stationary working regime. Weak dependence properties of this regime are established as well as the continuity with respect to the parameters of the external message flows.
References
M.Ya Kelbert and Yu.M. Suhov, Mathematical problems in the queueing theory, in:Probability Theory, Mathematical Statistics, Theoretical Cybernetics, vol. 26 (Itogi nauki i tehniki, VINITI AN SSSR, Moscow, 1988) pp. 3–97 (in Russian).
M.Ya, Kelbert, R.P. Kopeika, R.N. Shamsiev and Yu.M. Suhov, Perforation theory approach for a class of hybrid switching networks with small transit flows, to appear in Appl. Prob. (1989).
M.Ya. Kelbert and Yu.M. Sukhov, Conditions for existence and uniqueness of a random field describing the state of a switching network, Probl. Inf. Transmission 19, no. 4 (1983) 50–71.
M.Ya. Kelbert and Yu.M. Sukhov, Weak dependence properties of a random field describing the state of a switching network for small transit flows, Probl. Inf. Transmission 21, no. 3 (1985) 89–98.
M.Ya, Kelbert and Yu.M. Sukhov, Circuit-switching networks with (FIFO plus justifying blockout) service on infinite graphs, to appear in Queueing Systems (1989).
V.A. Malyshev and S.A. Berezner, On a class of circuit-switching networks, to appear in Appl. Prob. (1989).
V.A. Malyshev and I.A. Ignatjuk, Processes with local interaction and communication networks, to appear in Probl. Inf. Transmission (1989).
N.U. Prabhu,Queues and Inventories (Wiley, New York, 1965).
R.N. Shamsiev, Circuit switching networks with priorities on a one-dimensional lattice, to appear in J. Appl. Prob. (1989).
Y.M. Sukhov and R.N. Shamsiev, Hybrid switched networks on a one-dimensional lattice, Probl. Inf. Transmission 23, no. 4 (1987) 75–86.
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Kelbert, M.Y., Suhov, Y.M. On a class of packet-switching networks on an infinite graph. Queueing Syst 6, 391–403 (1990). https://doi.org/10.1007/BF02411485
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DOI: https://doi.org/10.1007/BF02411485