Stability of queueing-inventory systems with customers of different priorities

Sonja Otten () and Hans Daduna ()
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Sonja Otten: Hamburg University of Technology
Hans Daduna: Universität Hamburg

Annals of Operations Research, 2023, vol. 331, issue 2, No 14, 963-983

Abstract: Abstract We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well.

Keywords: Queueing networks; Inventory control; Priority customer; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-05140-1

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