Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T08:03:23.084Z Has data issue: false hasContentIssue false
  • English
  • Français

Markov chains governed by complicated renewal processes

Published online by Cambridge University Press:  01 July 2016

T. Gergely ,
I. N. Tsukanow  and
I. I. Yezhow
T. Gergely
Affiliation:
Central Research Institute for Physics, Hungarian Academy of Sciences, Budapest
I. N. Tsukanow
Affiliation:
University of Kiev
I. I. Yezhow
Affiliation:
University of Kiev
Get access Rights & Permissions [Opens in a new window]

Extract

In this work Markov chains governed by complicated processes are introduced and investigated (Section 1). In Section 2 an ergodic theorem for these processes is formulated, while in Section 3 the sojourn time of the process in a fixed region is studied; in Section 4 some examples are considered. The processes studied are of practical importance in the description of mass service systems and the theory of reliability for which the time intervals between successive demands cannot be assumed to be mutually independent random variables. It is shown that the dependence parameter r of these processes, if it is sufficiently large, allows us to formulate a relationship between the time intervals in question.

Type
Research Article
Information
Advances in Applied Probability , Volume 2 , Issue 2 , Autumn 1970 , pp. 287 - 322
Copyright
Copyright © Applied Probability Trust 1970 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] (1955) .Google Scholar
[2] Kendall, D. G. (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Ann. Math, Statist, 24, 338–354.CrossRefGoogle Scholar
[3] Howard, R. A. (1964) System analysis of semi-Markov processes. IEEE Trans, Milit, Electron, MII-8, 2.CrossRefGoogle Scholar
[4] Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.CrossRefGoogle Scholar
[5] Feller, W. (1964) On semi-Markov processes. Proc. Nat. Acad. Sci. U.S.A. 51, 653–659.Google Scholar
[6] (1966) .Google Scholar
[7] (1966) 18, 48–65.Google Scholar
[8] (1966) , 79–81.Google Scholar
[9] (1967) , 58–65.Google Scholar
[10] (1969) .Google Scholar
[11] (1962) , 309–323.Google Scholar
[12] (1966) .Google Scholar
[13] (1968) , 20, 384–388.Google Scholar
[14] Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243–302.Google Scholar
[15] Takács, L. (1958) A telefon-forgalom elméletének néhány valószinüségszámitási kérdéséröl. MTA III. Oszt. Közleményei 8, 151–210.Google Scholar
[16] (1963) .Google Scholar
[17] (1967) , 123–126.Google Scholar
[18] (1968) , 720–723.Google Scholar
[19] (1965) , 865–868.Google Scholar
[20] (1965) Google Scholar
[21] (1953) .Google Scholar
[22] (1962) .Google Scholar
[23] (1967) .Google Scholar