Abstract
We consider the ordinary M/M/1 queue with the FIFO queueing discipline. It seems that the sum of service times of the customers in the system (or the required work, as we call it briefly) is a random variable that is not considered before. In this paper we derive the equilibrium distribution of this variable. The task is not quite trivial because of the dependencies between the elapsed service time and the number of customers in the system. Our motivation for this problem comes from the performance analysis of a dynamic memory allocation scheme of a packet buffer.
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References
D. Bertsekas and R. Gallager, Data Networks, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1992).
J. Keilson and A. Kooharian, On time dependent queueing processes, The Annals of Mathematical Statistics 31 (1960) 104-112.
L. Kleinrock, Queueing Systems, Vol. 1: Theory (Wiley, 1975).
K. Kvols, S. Manthorpe and I. Norros, Engineering guidelines for the design of an interworking unit, in: Interoperability in Broadband Networks, ed. S. Rao (IOS Press, 1994) pp. 341-350.
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Aalto, S. Required Work in the M/M/1 Queue, with Application in IP Packet Processing. Telecommunication Systems 16, 555–560 (2001). https://doi.org/10.1023/A:1016679303045
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DOI: https://doi.org/10.1023/A:1016679303045