Abstract
A product form approximation, based on the principle of maximum entropy (ME), is characterised for arbitrary open discrete time queueing network models (QNMs) of shared buffer ATM switches under the departures first (DF) buffer management policy. Traffic entering and flowing in the network is assumed to be bursty and is modelled by a Compound Bernoulli Process (CBP) with geometrically distributed bulk sizes. Entropy maximisation implies decomposition of the network into individual shared buffer switches which are analysed to obtain cell loss probabilities and mean delays. The ME queue length distribution of a single shared buffer queue under DF policy, together with closed form expressions for the first two moments of the effective flow, play the role of building blocks in the solution process. Typical numerical results are included to demonstrate the utility and computational efficiency of the ME procedure. Comments on current work, involving discrete time finite capacity queues with space priority and correlated traffic, are included.
Supported by the Engineering and Physical Sciences Research Council (EPSRC), UK, under grant GR/H/18609 and by iT the Post Office.
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References
F.A. Tobagi, “Fast packet switch architecture’s for broadband integrated services networks”, Proc. IEEE 78: pp. 1133–1167, January 1990.
M. Devault, J.-Y. Cochennec and M. Servel, “The Prelude ATD experiment: Assessments and future prospects”, IEEE J SAC 6 (9), pp. 1528–1537, December 1988.
H. Kuwaha, N. Endo, M. Ogino and T. Kozaki, “A Shared Buffer Memory Switch for an ATM Exchange”, Int. Conf. on Communications, pp.441–445, Boston, MA, June 1989
H. Lee, K. Kook, C.S. Rim, K. Jun and S-K. Lim, “A Limited Shared Output Buffer Switch for ATM”, Fourth In. Conf. on Data Communication Systems and their Performance, pp.163–179, Barcelona, 1990
A.E. Eckberg and T-C. Hou, “Effects of Output Buffer Sharing on Buffer Requirements in an ATDM Packet Switch”, INFOCOM ‘88, pp. 459–466, March 1988
G.H. Petit and E.M. Desmet, “Performance Evaluation of Shared Buffer Multiserver Output Queue Switches used in ATM”, 7th. ITC Specialist Seminar, paper 7.1, New Jersey, 1990
P.G. Harrison and A. de C. Pinto, `Blocking in Asynchronous Buffered Banyan Networks“, Proc. Int. Seminar, Kyoto, Japan, December 1991
H. Yamashita, H.G. Perros, S-W. Hong}, “Performance Modelling of a Shared Buffer ATM Switch Architecture”, ITC-13, Teletraffic and Datatraffic in a Period of Change, ed. Jensen and Iverson, North-Holland, pp. 993–999, 1991
S-W. Hong, H.G. Perms, H. Yamashita, “A Discrete-Time Queueing Model of the Shared Buffer ATM Switch with Bursty Arrivals”’, Research Report, Computer Science Dept., North Carolina State University, 1992
E.T. Jaynes, “Information Theory and Statistical Mechanics”, Phys. Rev. 106 (4), pp. 620–630, 1957
D.D. Kouvatsos, “Maximum Entropy Methods for General Queueing Networks”, in Modelling Techniques and Tools for Performance Analysis, ed. D. Potier, North-Holland, pp. 589–609, 1985
D.D. Kouvatsos, “Maximum Entropy and the G/G/1/N Queue”, Acta Informatica 23, pp. 545–565, 1986
D.D. Kouvatsos, “A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium”, J. Op. Res. Soc. 39 (2), pp. 183–200, 1989
D. D. Kouvatsos and N.P. Xenios, “MEM for Arbitrary Queueing Networks with Multiple General Servers and Repetitive Service Blocking”, Perf. Eval. 10, pp. 169–195, 1989
D.D. Kouvatsos and S.G. Denazis, “A Universal Building Block for the Approximate Analysis of a Shared Buffer ATM Switch Architecture”’, Annals of Operations Research 44, Special Issue on Performance Analysis of High Speed Networks, pp. 241–278, 1994
D. D. Kouvatsos, N. M. Tabel-Aouel and S.G. Denazis, “ME Based Approximations for General Discrete-Time Queueing Models”, Perf. Eval. 21, pp. 81–109, 1994
D.D. Kouvatsos, N. M. Tabel-Aouel and S.G. Denazis, “Approximate Analysis of Discrete-Time Queueing Networks with or without Blocking”, IFIP Transactions C-21, Special Issue on High Speed Networks and their Performance, North-Holland, pp. 399–434, 1994
D.D. Kouvatsos and N.M. Tabet-Aouel, “GGeo-type Approximations for General Discrete-Time Queuing Systems”, IFIP Transactions C-15, Special Issue on Modelling and Performance Evaluation of ATM Technology, North-Holland, pp. 469–483, 1993
A. Gravey, G. Hebuterne, —Simultaneity in Discrete Time Single Server Queues with Bernoulli Inputs“’, Performance Evaluation 14, pp. 123–131, 1992
D.D. Kouvatsos, “Cost-Effective Solutions for Queueing Models of ATM Networks”, in Tutorial Proceedings of 2nd IFIP Workshop on the Performance Modelling and Evaluation of ATM Networks, ed. D.D. Kouvatsos, University of Bradford, pp.8/1–8/40, 4–7th July, 1994.
E.T. Jaynes, “Information Theory and Statistical Mechanics II”, Phys. Rev. 108, pp. 171–190, 1957
J.E. Shore and R.W. Johnson, “Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy”, IEEE Trans. Inf. Theory IT-26, pp. 26–27, 1980
C. Saur, “Configuration of Computing Systems: An Approach Using Queueing Network Models”, Ph.D. Thesis, University of Texas, 1975
S. Nojo and H. Watanabe, “A New Stage Method of getting Arbitrary Coefficient of Variation by Two Stages”, Trans. IEICE 70, pp. 33–36, 1987
A.C. Williams and R.A. Bhandiwad, “A Generating Function Approach to Queueing Network Analysis of Multiprogrammed Computers”, Networks 6, pp. 1–22, January 1976
Afonso de Compos Pinto “Models of Finite-buffered Packet-switched Multistaged Interconnection Networks” PhD Thesis, University of London, Imperial College of Science, Technical and Medicine (Dept. of Computing), 1994
M. Veran and D. Potier, “QNAP-2: A Portable Environment for Queueing Network Modelling”, in Modelling Techniques and Tools for Performance Analysis, ed. D. Potier, North-Holland, pp. 25–63, 1985
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Kouvatsos, D.D., Wilkinson, J. (1995). A Product Form Approximation for Arbitrary Discrete Time Networks of Shared Buffer Queues. In: Kouvatsos, D.D. (eds) Performance Modelling and Evaluation of ATM Networks. ATM 1994. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34881-0_19
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