A queueing model with randomized depletion of inventory

H.-J. Albrecher, O.J. Boxma, R. Essifi, A.C.M. Kuijstermans

Research output: Book/ReportReportAcademic

149 Downloads (Pure)


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 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.
Original languageEnglish
Place of PublicationEindhoven
Number of pages19
Publication statusPublished - 2015

Publication series

NameReport Eurandom
ISSN (Print)1389-2355


Dive into the research topics of 'A queueing model with randomized depletion of inventory'. Together they form a unique fingerprint.

Cite this