Hostname: page-component-7f64f4797f-8cpv7 Total loading time: 0 Render date: 2025-11-04T08:32:11.280Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion approximations for the cooperative service of voice and data messages

Published online by Cambridge University Press:  14 July 2016

J. P. Lehoczky  and
D. P. Gaver
J. P. Lehoczky*
Affiliation:
Carnegie–Mellon University
D. P. Gaver*
Affiliation:
Naval Postgraduate School
*
∗ Postal address: Department of Statistics, Carnegie-Mellon University, Pittsburgh, PA 15213, U.S.A.
∗∗ Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A diffusion approximation is developed for a voice and data communication system. Voice traffic operates as an M/M/v/v loss system, while data is a Markovian queueing system with a random number of channels assigned. The data process is shown to be approximated by a certain Wiener process with reflecting barrier at 0. System behavior is described using this approximation. The methodology is based on the work of Burman (1979).

Keywords

VOICE-DATA COMMUNICATION SYSTEMDIFFUSION APPROXIMATIONREFLECTED BROWNIAN MOTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 660 - 671
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Research supported by the National Science Foundation Grant ENG79–05526 and the Office of Naval Research, Contract Number N000 1480 WR00067.

References

Barbacci, M. R. and Oakley, J. D. (1976) The integration of circuit and packet switching networks towards a SENET implementation. 15th NBS-ACM Annual Technique Symposium.Google Scholar
Bhat, U. N. and Fischer, M. J. (1976) Multichannel queueing systems with heterogeneous classes of arrivals. Naval Res. Logist. Quart. 23, 271–283.Google Scholar
Burman, D. Y. (1979) An Analytic Approach to Diffusion Approximations in Queueing. Ph.D. Dissertation, Courant Institute of Mathematics, New York University.Google Scholar
Chang, L.-H. (1977) Analysis of Integrated Voice and Data Communication Network. Ph.D. Dissertation, Carnegie-Mellon University.Google Scholar
Coviello, G. and Vena, P. A. (1975) Integration of circuit/packet switching in a SENET (Slotted Envelop NETwork) concept. National Telecommunications Conference, New Orleans, December 1975, 42–12–42–17.Google Scholar
Fischer, M. J. (1977) A queueing analysis of an integrated telecommunications system with priorities. INFOR 15, 277–288.Google Scholar
Fischer, M. J. and Harris, T. C. (1976) A model for evaluating the performance of an integrated circuit- and packet-switched multiplex structure. IEEE Trans. Comm. COM-24.Google Scholar
Gaver, D. P. and Lehoczky, J. P. (1979a) Channels that cooperatively service a data stream and voice messages. Technical Report, Department of Operations Research, Naval Postgraduate School.Google Scholar
Halfin, S. (1972) Steady-state distributions for the buffer content of an M/G/1 queue with varying service rate. SIAM J. Appl. Math. 23, 356–363.Google Scholar
Halfin, S. and Segal, M. (1972) A priority queueing model for a mixture of two types of customers. SIAM J. Appl. Math. 23, 369–379.Google Scholar
Lehoczky, J. P. and Gaver, D. P. (1979b) Channels that cooperatively service a data stream and voice messages, II: Diffusion approximations. Technical Report Department of Operations Research, Naval Postgraduate School.Google Scholar
Weinstein, C. J., Malpass, M.L. and Fischer, M. J. (1980) Data traffic performance of an integrated, circuit- and packet-switched multiplex structure. IEEE Trans. Comm. COM-28, 973–978.Google Scholar