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M/M/1 Queueing systems with inventory

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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/∞-system.

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Authors and Affiliations

  1. Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes, University of Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Maike Schwarz, Cornelia Sauer & Hans Daduna

  2. University of Wroclaw, Mathematical Institute, Pl. Grunwaldzki 2/4, 50-384, Wroclaw, Poland

    Rafal Kulik & Ryszard Szekli

Authors
  1. Maike Schwarz
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  2. Cornelia Sauer
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  3. Hans Daduna
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  4. Rafal Kulik
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  5. Ryszard Szekli
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Corresponding author

Correspondence to Cornelia Sauer.

Additional information

All authors were supported by DAAD/KBN grant number D/02/32206.

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Schwarz, M., Sauer, C., Daduna, H. et al. M/M/1 Queueing systems with inventory. Queueing Syst 54, 55–78 (2006). https://doi.org/10.1007/s11134-006-8710-5

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  • DOI: https://doi.org/10.1007/s11134-006-8710-5

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