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On a buffer problem for packetized voice with an N-periodic strongly interchangeable input process

Published online by Cambridge University Press:  14 July 2016

Teunis J. Ott  and
J. George Shanthikumar
Teunis J. Ott*
Affiliation:
Bellcore
J. George Shanthikumar*
Affiliation:
University of California at Berkeley
*
∗ Postal address: Bell Communications Research, 445 South Street, P.O. Box 1910, Morristown. NJ 07960–1910, USA.
∗∗ Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
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Abstract

Consider a slotted communication channel which carries packetized voice and which can transmit exactly one packet every timeslot. Assume that every conversation routed over this channel generates exactly one packet every N timeslots. We study, for the case of an infinite buffer and an N-periodic strongly interchangeable input process, buffer behavior and packet delays as functions of the number of calls routed over the channel, as long as that number is less than or equal to N. Among our results are a simple algorithm which computes the marginal distribution of the buffer content and an algorithm with complexity of order N4 which computes the distribution of the maximal buffer content (over a period of N timeslots).

Keywords

SLOTTED CHANNELN-PERIODICITYSTRONG INTERCHANGEABILITYALGORITHMIC PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 630 - 646
Copyright
Copyright © Applied Probability Trust 1991 

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References

Daigle, J. and Langford, J. (1986) Models for analysis of packet voice communication systems. IEEE J. SAC 4, 847–855.Google Scholar
Eckberg, A. E. Jr. (1979) The single server queue with periodic arrival process and deterministic service times. IEEE Trans. Comm. 27, 556–562.Google Scholar
Eckberg, A. E. Jr. (1981) Response time analysis for pipelining jobs in a tree network of processors. Applied Probability–Computer Science: The Interface, ed. Dishey, R. L. and Ott, T. J.; pp. 387–413, Birkhauser, Boston.Google Scholar
Heffes, H. and Lucantoni, D. (1986) A Markov modulated characterization of packetized voice and data traffic and related statistical multiplex performance. IEEE J. SAC 4, 856–868.Google Scholar
Latouche, G. (1990) Sample path analysis of packet queues subject to periodic traffic. Comp. Networks ISDN Syst. 20, 409–413.Google Scholar
Latouche, G. and Ramaswami, V. (1991) A unified stochastic model for the arrival of packets from periodic sources. Performance Eval. To appear.Google Scholar
Li, S. Q. (1987) A new performance measurement for voice transmission in burst and packet switching. IEEE Trans. Comm. 35, 1083–1094.Google Scholar
Ott, T. J. and Shanthikumar, J. G. (1990) On maxima and minima of partial sums of strongly interchangeable random variables. Prob. Eng. Inf. Sci. 3, 319–332.Google Scholar
Ramamurthy, G. and Sengupta, B. (1988) Delay analysis of a packet voice multiplexer by the S Di/D/1 queue. IEEE Trans. Comm. To appear.Google Scholar
Sriram, K. and Whitt, W. (1986) Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. SAC 4, 833–846.Google Scholar