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On a modified counter with prolonging dead time

  • A. Dvurečenskij (a1) and G. A. Ososkov (a1)


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.


Corresponding author

Postal address: Joint Institute for Nuclear Research, LCTA, Head Post Office, P.O. Box 79, 101000 Moscow, USSR.
Permanent address: Institute of Measurement and Measuring Techniques EPRC of the Slovak Academy of Sciences, 885 27 Bratislava, Czechoslovakia.


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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, 8896 (in Russian).
Barlow, R. (1962) Applications of semi-Markov processes to counter problems. In Studies in Applied Probability and Management Science, Stanford University Press, Stanford, Ca., 3362.
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).
Dvurecenskij, A. and Ososkov, G. A. (1984) Note on a type II counter problem. Apl. Mat. 29 (4), 237249.
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, 201206.
Feller, W. (1967) An Introduction to Probability Theory and its Applications. Vol. 1. Wiley, New York.
Kuczek, T. (1983) On the GA/G/8 queue. Adv. Appl. Prob. 15, 444459.
Pollaczek, F. (1954) Sur la théorie stochastique des compteurs électroniques. C. R. Acad. Sci. Paris 238, 322324.
Pyke, R. (1958) On renewal processes related to Type I and Type II counter models. Ann. Math. Statist. 29, 737754.
Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243284.
Takács, L. (1956) On the sequence of events, selected by a counter from a recurrent process of events. Teorija Verojat. i primenen. 1, 90102.



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