A QUEUEING MODEL WITH RANDOMIZED DEPLETION OF INVENTORY. Issue 1 (13th September 2016)

• Record Type: Journal Article
• Authors: Albrecher, Hansjörg; Boxma, Onno; Essifi, Rim; Kuijstermans, Richard
• Is Part Of: Probability in the engineering and informational sciences. Volume 31:Issue 1(2017)
• Page Start: 43
• Page End: 59
• Publication Date: 2016-09-13
• Subjects: applied probability, -- inventory theory, -- queueing theory, -- stochastic modelling; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964816000322
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : 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.