Abstract
In Chapter 3 the focus is on the steady-state workload Q. For spectrally positive input this is done by explicitly establishing its Laplace transform (the generalized Pollaczek–Khintchine formula). The spectrally negative case can be dealt with explicitly, resulting in an exponentially distributed stationary workload. To deal with the case that jumps in both directions are allowed (i.e. the spectrally two-sided case), we provide a brief introduction to Wiener–Hopf theory, leading to an expression for the transform of Q albeit in a rather implicit form. We conclude this chapter by presenting (semi-) explicit results for two specific classes of spectrally two-sided processes, that is, the class in which the jumps have a phase-type distribution, and the class of meromorphic processes.
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Dębicki, K., Mandjes, M. (2015). Steady-State Workload. In: Queues and Lévy Fluctuation Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-20693-6_3
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DOI: https://doi.org/10.1007/978-3-319-20693-6_3
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