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On a modified counter with prolonging dead time

Published online by Cambridge University Press:  14 July 2016

A. Dvurečenskij  and
G. A. Ososkov
A. Dvurečenskij*
Affiliation:
JINR, Dubna
G. A. Ososkov*
Affiliation:
JINR, Dubna
*
∗ Postal address: Joint Institute for Nuclear Research, LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
∗ Postal address: Joint Institute for Nuclear Research, LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
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Abstract

Emitted particles arrive at the counter with prolonging dead time so that the interarrival times and the lengths of impulses in any dead time are independent but not necessarily identically distributed random variables, and whenever the counter is idle then the following evolution starts from the beginning. For this class of counters we derive the probability laws of the numbers of particles arriving at the counters during their dead times, and the Laplace transform of the cycle, respectively.

Keywords

CYCLELAPLACE TRANSFORMTYPE II COUNTER

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 678 - 687
Copyright
Copyright © Applied Probability Trust 1985 

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References

Afanas'Eva, L. G. and Mikhailova, I. V. (1978) On the number of demands served during the busy period. Izv. Akad. Nauk SSSR Tech. Kiber. no. 6, 88–96 (in Russian).Google Scholar
Barlow, R. (1962) Applications of semi-Markov processes to counter problems. In Studies in Applied Probability and Management Science, Stanford University Press, Stanford, Ca., 33–62.Google Scholar
Dvurecenskij, A. et al. (1982) On application of queueing systems with infinitely many servers to some problems of high energies physics. JINR P5–82–682, Dubna (in Russian).Google Scholar
Dvurecenskij, A. and Ososkov, G. A. (1984) Note on a type II counter problem. Apl. Mat. 29 (4), 237–249.Google Scholar
Dvurecenskij, A. Kuljukina, A. and Ososkov, G. A. (1984) On a problem of the busy-period determination in queues with infinitely many servers. J. Appl. Prob. 21, 201–206.Google Scholar
Feller, W. (1967) An Introduction to Probability Theory and its Applications. Vol. 1. Wiley, New York.Google Scholar
Kuczek, T. (1983) On the GA/G/8 queue. Adv. Appl. Prob. 15, 444–459.Google Scholar
Pollaczek, F. (1954) Sur la théorie stochastique des compteurs électroniques. C. R. Acad. Sci. Paris 238, 322–324.Google Scholar
Pyke, R. (1958) On renewal processes related to Type I and Type II counter models. Ann. Math. Statist. 29, 737–754.Google Scholar
Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243–284.Google Scholar
Takács, L. (1956) On the sequence of events, selected by a counter from a recurrent process of events. Teorija Verojat. i primenen. 1, 90–102.Google Scholar