A QUEUEING MODEL WITH RANDOMIZED DEPLETION OF INVENTORY

Hansjörg Albrecher · Onno Boxma · Rim Essifi · Acm Richard Kuijstermans

13 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

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.

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2010Ruin Probabilities 2006M/M/1 Queueing systems with inventory 2011Randomized observation periods for the compound Poisson risk model: the discounted penalty function 1992Queueing and related models 2013The M/M/1 queue with inventory, lost sale, and general lead times 2011The optimal dividend barrier in the Gamma–Omega model 2006Queueing systems with inventory management with random lead times and with backordering 2001Dynamic order replenishment policy in internet-based supply chains

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