Resumen
En este artículo se describen algunos de los modelos marcovianos de redes de colas más interesantes, como los de Jackson, Gordon y Newell, Reiser y Kobayashi y otros, estudiando las relaciones existentes entre ellos. Se demuestra que la solución conocida como “forma de producto” es válida para todos ellos con las modificaciones apropiadas en cada caso.
Abstract
In this paper are described some of the more interesting markovian models of queueing networks as the Jackson, Gordon and Newell, Reiser and Kobayashi, and other. We study the relations among them. It’s proved that solution we know as “Product form” is valid for all, with the appropiate modifications for every case.
This is a preview of subscription content, log in via an institution to check access.
Bibliografia
BARBOUR, A.D.: “Networks of queues and the method of stades”. Adv. Appl. Prob. Vol. 8 (1976) pp. 584–591.
BENSON, F., GREGORY, G.: “Closed queueing systems: A generalization of the Machine interference Model”. J. Royal Stat. Soc. B, 23 (1961) pp. 385–395.
BURKE, P.J.: “The output of a queueing system”. Oper. Res. 4 (1956) pp. 699–704.
FINCH, P.D.: “Cyclic queues with feedback”. J. Roy. Stat. Soc. B 21 (1959) pp. 153–157.
GORDON, W.J. NEWELL, G.F.: “Closed queueing systems with restricted queue lengths” Oper. Res. 15 (1967) pp. 254–265.
GORDON, W.J. NEWELL, G.F.: “Closed queueing systems with restricted queue lengths” Oper. Res. 15 (1967) pp. 266–277.
HILLIER, F.S. BOLING, R.W.: “Finite queues in series with exponential or Erlang services times. A numerical approach” Oper. Res. 15 (1967) pp. 286–303.
HUNT, G.C.: “Sequential arrays of waiting lines”. Oper. Res. 4 (1956) pp. 674–683.
JACKSON, J.R.: “Networks of waiting lines”. Oper. Res. 5 (1957) 518–521.
JACKSON, J.E.: “Jobshop-like queueing systems”. Manag. Science 10, 1 (1963) pp. 131–142.
JACKSON, R.R.P.: “Queueing processes with phase-type service”. J. Roy. Sts. Sc. B 18,1 (1956) pp. 129–132.
KELLY, F.P.: “Networks of queues with customers of different classes”. J. Appl. Pro. 12 (1975) pp. 542–544.
KOENISBERG, E.: “Cyclic queues”. Oper. Res. Quat. 9 (1958) pp. 22–35.
POSNER, M. BERNHOLTZ, B.: “Closed finite queueing systems with time lags” Oper. Res. 16 (1968) pp. 962–976.
POSNER, M. BERNHOLTZ, B.: “Closed finite queueing systems with time lags and with several classes of units”. Oper. Res. 16 (1968) pp. 977–985.
REICH, E.: “Waiting times when queues are in tandem” Ann. Math. St. 28 (1957) 768–773.
REISER, M.; KOBAYASHI, H.: “Queueing networks with multiple close chains: Theory and computational algorithm” IBM J. Res. Dev. 19 (1975) 283–294.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gallego, J.A. Algunas relaciones entre modelos Marcovianos de redes de colas. Trabajos de Estadistica y de Investigacion Operativa 33, 3–29 (1982). https://doi.org/10.1007/BF02888431
Issue Date:
DOI: https://doi.org/10.1007/BF02888431