Large deviations and long-time behavior of stochastic fluid queues with generalized fractional Brownian motion input

Sumith Reddy Anugu () and Guodong Pang ()
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Sumith Reddy Anugu: Rice University
Guodong Pang: Rice University

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 1, No 4, 47-98

Abstract: Abstract We study the large deviation behaviors of a stochastic fluid queue with an input being a generalized Riemann–Liouville (R–L) fractional Brownian motion (FBM), referred to as GFBM. The GFBM is a continuous mean-zero Gaussian process with non-stationary increments, extending the standard FBM with stationary increments. We first derive the large deviation principle for the GFBM by using the weak convergence approach. We then obtain the large deviation principle for the stochastic fluid queue with the GFBM as the input process as well as for an associated running maximum process. Finally, we study the long-time behavior of these two processes; in particular, we show that a steady-state distribution exists and derives the exact tail asymptotics using the aforementioned large deviation principle together with some maximal inequality and modulus of continuity estimates for the GFBM.

Keywords: Stochastic fluid queue; Generalized Riemann–Liouville fractional Brownian motion; (Sample path) large deviation; Running maximum process; Self-similar process; Long-range dependence; Long-time behavior (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09889-5

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