TY - JOUR
T1 - A queuing model with a randomized depletion of inventory
AU - Albrecher, H.
AU - Boxma, O.J.
AU - Essifi, R.
AU - Kuijstermans, A.C.M.
PY - 2017
Y1 - 2017
N2 - In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.
AB - In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.
KW - applied probability
KW - inventory theory
KW - queueing theory
KW - stochastic modelling
UR - http://www.scopus.com/inward/record.url?scp=84987662367&partnerID=8YFLogxK
U2 - 10.1017/S0269964816000322
DO - 10.1017/S0269964816000322
M3 - Article
AN - SCOPUS:84987662367
SN - 0269-9648
VL - 31
SP - 43
EP - 59
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 1
ER -