TY - BOOK

T1 - A queueing/inventory and an insurance risk model

AU - Boxma, O.J.

AU - Essifi, R.

AU - Janssen, A.J.E.M.

PY - 2015

Y1 - 2015

N2 - We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted as negative workload. At random times, with an intensity {\omega}(x) when the inventory is at level x > 0, the present inventory is removed, instantaneously reducing the inventory to zero. We study the steady-state distribution of the (positive and negative) workload levels for the cases {\omega}(x) is constant and {\omega}(x) = ax. The key tool is the Wiener-Hopf factorisation technique. When {\omega}(x) is constant, no specific assumptions will be made on the service requirement distribution. However, in the linear case, we need some algebraic hypotheses concerning the Laplace-Stieltjes transform of the service requirement distribution. Throughout the paper, we also study a closely related model coming from insurance risk theory.
Keywords: M/G/1 queue, Cramer-Lundberg insurance risk model, workload, inventory, ruin probability, Wiener-Hopf technique.

AB - We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted as negative workload. At random times, with an intensity {\omega}(x) when the inventory is at level x > 0, the present inventory is removed, instantaneously reducing the inventory to zero. We study the steady-state distribution of the (positive and negative) workload levels for the cases {\omega}(x) is constant and {\omega}(x) = ax. The key tool is the Wiener-Hopf factorisation technique. When {\omega}(x) is constant, no specific assumptions will be made on the service requirement distribution. However, in the linear case, we need some algebraic hypotheses concerning the Laplace-Stieltjes transform of the service requirement distribution. Throughout the paper, we also study a closely related model coming from insurance risk theory.
Keywords: M/G/1 queue, Cramer-Lundberg insurance risk model, workload, inventory, ruin probability, Wiener-Hopf technique.

M3 - Report

T3 - arXiv

BT - A queueing/inventory and an insurance risk model

PB - s.n.

ER -