TY - JOUR
T1 - Transient analysis of a stationary Lévy-driven queue
AU - Ivanovs, J.
AU - Mandjes, M.R.H.
PY - 2015
Y1 - 2015
N2 - In this paper we study a queue with Lévy input, without imposing any a priori assumption on the jumps being one-sided. The focus is on computing the transforms of all sorts of quantities related to the transient workload, assuming the workload is in stationarity at time 0. The results are simple expressions that are in terms of the bivariate Laplace exponents of ladder processes. In particular, we derive the transform of the minimum workload attained over an exponentially distributed interval.
Keywords: Queues; Lévy processes; Conditioned to stay positive; Splitting
AB - In this paper we study a queue with Lévy input, without imposing any a priori assumption on the jumps being one-sided. The focus is on computing the transforms of all sorts of quantities related to the transient workload, assuming the workload is in stationarity at time 0. The results are simple expressions that are in terms of the bivariate Laplace exponents of ladder processes. In particular, we derive the transform of the minimum workload attained over an exponentially distributed interval.
Keywords: Queues; Lévy processes; Conditioned to stay positive; Splitting
U2 - 10.1016/j.spl.2015.09.010
DO - 10.1016/j.spl.2015.09.010
M3 - Article
SN - 0167-7152
VL - 107
SP - 341
EP - 347
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -