Abstract
An inventory-queue is an inventory system controlled by a processing station with queueing. They are natural building blocks for supply chain models. An important and largely open issue for inventory queues is the characterization of their departure processes. In an inventory-queue, departures are triggered either by a job arrival when the output buffer is not empty or otherwise by a service completion. Such departures are more difficult to analyze than departures from a standard queue. The main results in this study are expressions for the probability distributions and squared coefficient of variations of inter-departure times for base-stock inventory-queues with birth–death production processes.
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References
S.L. Albin and S.R. Kai, Approximation for the departure process of a unique network, Naval Res. Logist. 33 (1986) 129–143.
F. Baccelli and P. Brémaud, Elements of Queueing Theory (Springer, New York, 1994).
P.J. Burke, The output of a queueing system, Oper. Res. 4 (1956) 699–704.
J.A. Buzacott, S.M. Price and J.G. Shanthikumar, Service level in multistage MRP and base stock controlled production systems, in: New Directions for Operations Research in Manufacturing System, eds. T. Fandel, T. Gulledge and A. Jones (Springer, 1992) pp. 445–463.
D.J. Daley, Queueing departure processes, Adv. Appl. Probab. 8 (1976) 395–415.
M. Ettl, G.E. Feigin, G.Y. Lin and D.D. Yao, A supply network model with base-stock control and service requirements, Oper. Res. 48 (2000) 216–232.
D. Gross and C.M. Harris, Fundamentals of Queueing Theory, 3rd edn. (Willey, New York, 1998).
J. Hu, The departure process of the GI/G/1 queue and its MacLaurin series, Oper. Res. 44 (1996) 810–815.
F.P. Kelly, Reversibility and Stochastic Networks (New York, 1979).
W. Kleinrock, Queueing System, Vol. 1: Theory(Wiley, 1975).
G.V. Kulkarni, Modeling and Analysis of Stochastic Systems (Chapman & Hall, 1995).
L. Liu, X. Liu and D.D. Yao, Analysis and optimization of multi-stage inventory-queues, Managm. Sci. (March 2004).
L. Liu and J.G.C. Templeton, Departures in GRXn/Gn/8, Queueing Systems 19 (1995) 399–419.
S. Ross, Introduction to Probability Models, 7th edn. (Harcourt/Academic Press, Burlington, MA, 2000).
R.F. Serfozo, Introduction to Stochastic Networks (Spinger, New York, 1999).
D.A. Stanford, Waiting and interdeparture times in priority queues with Poisson-and general-arrival streams, Oper. Res. 45 (1997) 725–735.
W. Whitt, Departures from a queue with many servers, Math. Oper. Res. 9 (1984) 534–544.
W. Whitt, Approximation for departure process and queues in series, Nav. Res. Logist. 31 (1984) 499–521.
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Bai, L., Fralix, B., Liu, L. et al. Inter-Departure Times in Base-Stock Inventory-Queues. Queueing Systems 47, 345–361 (2004). https://doi.org/10.1023/B:QUES.0000036396.19059.3b
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DOI: https://doi.org/10.1023/B:QUES.0000036396.19059.3b