Abstract
This paper presents transient analyses for a Markovian loss system with heterogeneous inputs. Results are applied to the analysis of the measured time congestion of this system. Transient analyses show the properties of system recovery and covariance functions. The measured time congestion is analyzed and approximations are proposed using these properties. These results are significant for management and control in the Integrated Services Digital Network.
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References
E. Arthurs and J.S. Kaufman, Sizing a message store subject of blocking store, in:Performance of Computer Systems (North-Holland, 1979) pp. 547–564.
V.E. Benes, The covariance function of a simple trunk group with applications to traffic measurement, Bell Sys. Tech. J. 40 (1961) 117–148.
R.B. Cooper,Introduction to Queueing Theory (Edward Arnold, London, 1981).
A. Descloux, On the accuracy of loss estimates, Bell Sys. Tech. J. 44 (1965) 1139–1164.
A. Descloux, Variance of load measurements in Markovian service systems, Bell Sys. Tech. J. 54 (1975) 1277–1300.
L.A. Gimpelson, ISDN and value-added services in public and private network,Proc. 11th Int. Teletraffic Congress, Kyoto (1985).
H. Heffes, A class of data traffic processes — covariance function characterization and related queueing results, Bell Sys. Tech. J. 59 (1980) 897–929.
J.S. Kaufman, Blocking in a shared resource environment, IEEE Trans. Commun. COM-29 (1981) 1474–1481.
J. Keilson,Markov Chain Models, Rarity and Exponentiality (Springer, New-York, 1979).
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, Chichester, 1979).
L. Kosten, J.R. Manning and F. Garwood, On the accuracy of measurements of probabilities of loss in telephone systems, J. Roy. Soc., Ser. B, 11 (1949) 54–67.
B. Kraimeche and M. Schwartz, Analysis of traffic access control strategies in integrated service networks, IEEE Trans. Commun. COM-33 (1985) 1085–1093.
A. Kuczura and S.R. Neal, The accuracy of call congestion measurements for loss systems with renewal input, Bell Sys. Tech. J. 51 (1972) 2197–2208.
F. Machihara, Measurement accuracy for a loss system, Rev. Electrical Communication Laboratories 29 (1981) 155–169.
F. Machihara, Transition probabilities of Markovian service system and their application, Rev. Electrical Communication Laboratories 29 (1981) 170–188.
S. Nakajima, A design method of control parameters for a code blocking control system on a telephone network, Trans. IECE Japan, J66-B, 7 (1983) 837–844.
S.R. Neal and A. Kuczura, A theory of traffic-measurement errors for loss systems with renewal input, Bell Sys. Tech. J. 52 (1973) 967–990.
Y. Nunotani, Call connection control in telephone network, J. Institute of Electronics and Communication Engineers of Japan 69 (1986) 339–344.
J. Riordan,Stochastic Service Systems (Wiley, New York, 1962).
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Saito, H., Machihara, F. Transient analysis of a Markovian loss system with heterogeneous inputs for time congestion measurement. Queueing Syst 8, 81–96 (1991). https://doi.org/10.1007/BF02412242
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DOI: https://doi.org/10.1007/BF02412242