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On the excursions of reflected local time processes and stochastic fluid queues


Reference:

Konstantopoulos, T., Kyprianou, A. E. and Salminen, P., 2011. On the excursions of reflected local time processes and stochastic fluid queues. Journal of Applied Probability, 48A, pp. 79-98.

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Official URL:

http://dx.doi.org/10.1239/jap/1318940457

Abstract

In this paper we extend our previous work. We consider the local-time process L of a strong Markov process X, add negative drift to L, and reflect it à la Skorokhod to obtain a process Q. The reflection of X, together with Q, is, in some sense, a macroscopic model for a service system with two priorities. We derive an expression for the joint law of the duration of an excursion, the maximum value of the process on it, and the time between successive excursions. We work with a properly constructed stationary version of the process. Examples are also given in the paper.

Details

Item Type Articles
CreatorsKonstantopoulos, T., Kyprianou, A. E. and Salminen, P.
DOI10.1239/jap/1318940457
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code24229

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