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In this paper we study a queue with L\'evy input, without imposing any apriori assumption on the jumps being one-sided. The focus is on computing thetransforms of all sorts of quantities related to the transient workload,assuming the workload is in stationarity at time 0. The results are simpleexpressions that are in terms of the bivariate Laplace exponents of ladderprocesses. In particular, we derive the transform of the minimum workloadattained over an exponentially distributed interval.

Transient analysis of a stationary L\'evy-driven queue