A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue
Sarhangian, Vahid and Balcıoğlu, Ahmet Barış (2013) A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue. Operations Research Letters, 41 (6). pp. 659-663. ISSN 0167-6377
Official URL: http://dx.doi.org/10.1016/j.orl.2013.09.008
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.
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