Article contents
On the output theorem of queueing theory, via filtering
Published online by Cambridge University Press: 14 July 2016
Abstract
We prove and extend Burke's output theorem for queues in equilibrium with the help of a filtering formula giving the time evolution of the least square estimate of the state with respect to the output.
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1978
References
Brémaud, P. (1974) The martingale theory of point processes with an intensity. In Proc. IRIA Coll. Control Theory.
Lecture Notes in Economics and Mathematical Systems 107, Springer-Verlag, Berlin, 519–542.Google Scholar
Brémaud, P. (1975a) An extension of Watanabe's characterization of Poisson processes. J. Appl. Prob.
12, 396–399.Google Scholar
Brémaud, P. (1975b) Estimation de l'état d'une file d'attente et du temps de panne d'une machine par la méthode des semi-martingales. Adv. Appl. Prob.
7, 845–863.CrossRefGoogle Scholar
Brémaud, P. and Jacod, J. (1977) Processus ponctuels et martingales: Revue des résultats récents sur la modélisation et le filtrage. Adv. Appl. Prob.
9, 362–416.Google Scholar
Dellacherie, C. (1972) Capacités et Processus stochastiques.
Springer-Verlag, Berlin.CrossRefGoogle Scholar
Reich, E. (1965) Departure processes. In Proc. Symp. Congestion Theory, ed. Smith, and Wilkinson, , University of North Carolina Press, 439–457.Google Scholar
Watanabe, S. (1964) On discontinuous additive functionals and Lévy measures of Markov processes. Jap. J. Maths
34, 53–70.CrossRefGoogle Scholar
- 11
- Cited by