Abstract
Consider an M/G/1 queue where each customer (independently of others) has a space requirement which may depend on its service time. We find the steady state distribution of the total space required by all customers present in the system. An application of the model is in the field of message switching where the memory space required by a message is (usually) a monotonic function of the service time. By using the processor sharing version of the M/G/1 queue, another application may be in the design of storage space required for time sharing computers.
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References
L. Kosten, "Stochastic Theory of Service Systems," Pergamon Press, 1973.
M. Sakata, S. Noguchi, J. Oizumi, "Analysis of a Processor Shared Queuing Model for Time Sharing Systems," Proceedings of the Second Hawaii International Conference on Systems Sciences, 625–528, January, 1969.
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© 1984 Springer-Verlag
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Sengupta, B. (1984). The spatial requirement of an M/G/1 queue, or: How to design for buffer space. In: Baccelli, F., Fayolle, G. (eds) Modelling and Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005191
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DOI: https://doi.org/10.1007/BFb0005191
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