Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant.

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Queueing Systems
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Mathijsen, B., & Zwart, B. (2017). Transient error approximation in a Lévy queue. Queueing Systems, 85, 269–304. doi:10.1007/s11134-016-9511-0