Blanchet, J., & Mandjes, M. (2013). Asymptotics of the area under the graph of a Lévy-driven workload process. Operations Research Letters, 41(6), 730-736. https://doi.org/10.1016/j.orl.2013.10.004
Abstract
Let (Q t) t∈ R be the stationary workload process of a Lévy-driven queue, where the driving Lévy process is light-tailed. For various functions T (u), we analyze P (∫ 0 T (u) Q s d s> u) for u large. For T (u)= o (u) the asymptotics resemble those of the steady-state workload being larger than u/T (u). If T (u) is proportional to u they look like e− α u for some α> 0. Interestingly, the asymptotics are still valid when u= o (T (u)), T (u)= o (u), and T (u)= β u for β suitably small.
Authors
J Blanchet, Michel Mandjes
Publication date
2013/11/1
Journal
Operations Research Letters
Volume
41
Issue
6
Pages
730-736
Publisher
North-Holland
