1. University of Toronto, Joseph L. Rotman School of Management, 105 St. George Street, Toronto, M5S 3E6, Canada;2. Sabanc? University, Faculty of Engineering and Natural Sciences, Orhanl?-Tuzla, 34956 Istanbul, Turkey
Abstract:
We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1 queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies.