Asymptotics of the area under the graph of a Levy-driven workload process

作者：Blanchet J^*; Mandjes M

来源：Operations Research Letters, 2013, 41(6): 730-736.

DOI：10.1016/j.orl.2013.10.004

• Queues
• Workload process
• Area
• Large deviations
• Levy processes

Let (Q(t))(t is an element of R) be the stationary workload process of a Levy-driven queue, where the driving Levy process is light-tailed. For various functions T(u), we analyze %26lt;br%26gt;P (integral(T(u))(0) Q(s)ds %26gt; u) %26lt;br%26gt;for u large. For T(u) = o(root u) the asymptotics resemble those of the steady-state workload being larger than u/T(u). If T(u) is proportional to root u they look like e(-alpha root u) for some alpha %26gt; 0. Interestingly, the asymptotics are still valid when root u = o(T(u)), T(u) = o(u), and T(u) = beta u for beta suitably small.

• 出版日期2013-11