TY - JOUR
T1 - Analysis of stochastic fluid queues driven by local-time processes
AU - Konstantopoulos, Panagiotis Takis
AU - Kyprianou, Andreas E.
AU - Salminen, Paavo
AU - Sirviö, Marina
PY - 2008
Y1 - 2008
N2 - We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically(but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator). hence making the theory of Lévy processes applicable. Another important ingredient in our approach the use of Palm calculus for stationary random point processes and measures. © Applied Probability Trust 2008.
AB - We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically(but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator). hence making the theory of Lévy processes applicable. Another important ingredient in our approach the use of Palm calculus for stationary random point processes and measures. © Applied Probability Trust 2008.
KW - Fluid queue
KW - Inspection paradox
KW - Lévy process
KW - Local time
KW - Palm calculus
KW - Performance analysis
KW - Skorokhod reflection
UR - http://www.scopus.com/inward/record.url?scp=59549087373&partnerID=8YFLogxK
U2 - 10.1239/aap/1231340165
DO - 10.1239/aap/1231340165
M3 - Article
SN - 0001-8678
VL - 40
SP - 1072
EP - 1103
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 4
ER -