M/M/1 Queueing systems with inventory

Authors:
Maike Schwarz;Cornelia Sauer;Hans Daduna;Rafal Kulik;Ryszard Szekli
Affiliations:
Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes, University of Hamburg, Hamburg, Germany 20146;Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes, University of Hamburg, Hamburg, Germany 20146;Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes, University of Hamburg, Hamburg, Germany 20146;University of Wroclaw, Mathematical Institute, Wroclaw, Poland 50-384;University of Wroclaw, Mathematical Institute, Wroclaw, Poland 50-384
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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Abstract

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/驴-system.