TY - JOUR
T1 - Stationarity and control of a tandem fluid network with fractional brownian motion input
AU - Lee, Chihoon
AU - Weerasinghe, Ananda
PY - 2011/9
Y1 - 2011/9
N2 - We consider a stochastic control model for a queueing system driven by a two-dimensional fractional Brownian motion with Hurst parameter 0 < H < 1. In particular, when H > 1/2 , this model serves to approximate a controlled two-station tandem queueing model with heavy-tailed ON/OFF sources in heavy traffic. We establish the weak convergence results for the distribution of the state process and construct an explicit stationary state process associated with given controls. Based on suitable coupling arguments, we show that each state process couples with its stationary counterpart and we use it to represent the long-run average cost functional in terms of the stationary process. Finally, we establish the existence result of an optimal control, which turns out to be independent of the initial data.
AB - We consider a stochastic control model for a queueing system driven by a two-dimensional fractional Brownian motion with Hurst parameter 0 < H < 1. In particular, when H > 1/2 , this model serves to approximate a controlled two-station tandem queueing model with heavy-tailed ON/OFF sources in heavy traffic. We establish the weak convergence results for the distribution of the state process and construct an explicit stationary state process associated with given controls. Based on suitable coupling arguments, we show that each state process couples with its stationary counterpart and we use it to represent the long-run average cost functional in terms of the stationary process. Finally, we establish the existence result of an optimal control, which turns out to be independent of the initial data.
KW - Controlled queueing system
KW - Fractional Brownian motion
KW - Heavy traffic theory
KW - Long-range dependence
KW - Self-similarity
KW - Stochastic control
KW - Tandem queue
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U2 - 10.1239/aap/1316792672
DO - 10.1239/aap/1316792672
M3 - Article
AN - SCOPUS:80053403644
SN - 0001-8678
VL - 43
SP - 847
EP - 874
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 3
ER -