TY - JOUR
T1 - On the excursions of reflected local time processes and stochastic fluid queues
AU - Konstantopoulos, T
AU - Kyprianou, Andreas E
AU - Salminen, P
PY - 2011/8
Y1 - 2011/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84880681960&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1239/jap/1318940457
U2 - 10.1239/jap/1318940457
DO - 10.1239/jap/1318940457
M3 - Article
SN - 0021-9002
VL - 48A
SP - 79
EP - 98
JO - Journal of Applied Probability
JF - Journal of Applied Probability
ER -