- Asymptotics of the area under the graph of a Lévy-driven workload process
- Operations Research Letters
- Volume | Issue number
- 41 | 6
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Let (Qt)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(∫T(u)0Qsds>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 View the MathML source they look like View the MathML source for some α>0. Interestingly, the asymptotics are still valid when View the MathML source, T(u)=o(u), and T(u)=βu for β suitably small.
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