Abstract
A universal analytic approximation is proposed for the performance analysis of a general queueing model of a shared buffer ATM switch architecture with bursty arrivals. The forms of the joint, aggregate and marginal state probabilities are characterised via entropy maximisation. As an application, a continuous-time maximum entropy (ME) solution is implemented at equilibrium by assuming that the arrival process to each port of the ATM switch is modelled by a Compound Poisson Process (CPP) with geometrically distributed batches. Consequently, efficientz-transform-type recursive expressions of low computational cost are derived. Validation tests against simulation show that the ME approximation is credible with a very good error-level. Moreover, performance bounds for the mean queue length and cell-loss probability at each output port are experimentally defined over those generated by Interrupted Poisson Processes (IPPs) having the same first two interarrival-time moments.
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References
F.A. Tobagi, Fast packet switch architectures for broadband integrated services networks, Proc. IEEE 78 (1990) 1133–1167.
M. Devault, J.-Y. Cochennec and M. Servel, The “Prelude” ATD experiment: Assessments and future prospects, IEEE J. Sel. Areas Comm. SAC-6(1988) 1528–1537.
P. Boyer, M.R. Lehnert and P.J. Kuehn, Queueing in an ATM basic switch element, Technical Report CNET-123-030-CD-CC, CNET, France (1988).
H. Kuwahara, N. Endo, M. Ogino and T. Kozaki, A shared buffer memory switch for an ATM exchange,Int. Conf. on Communications, Boston, MA (June 1989) pp. 441–448.
H. Lee, K. Kook, C.S. Rim, K. Jun and S.-K. Lim, A limited shared output buffer switch for ATM,4th Int. Conf. on Data Communication Systems and Their Performance, Barcelona (1990) pp. 163–179.
A.E. Eckberg and T.-C. Hou, Effects of output buffer sharing on buffer requirements in an ATDM packet switch,INFOCOM '88 (March 1988) pp. 459–466.
G.H. Petit and E.M. Desmet, Performance evaluation of shared buffer multiserver output queue switches used in ATM,7th ITC Specialist Seminar, New Jersey (1990) paper 7.1.
I. Iliadis, Performance of a packet switch with shared buffer and input queueing, in:Teletraffic and Datatraffic in a Period of Change, ITC-13, eds. A. Jensen and V.B. Iversen (North-Holland, 1991) pp. 911–916.
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 and S. Hong, Performance modelling of a shared buffer ATM switch architecture, in:Teletraffic and Datatraffic in a Period of Change, eds. A. Jensen and V.B. Iversen (North-Holland, 1991).
S. Hong, H.G. Perros and 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).
H.G. Perros, private communication (1992).
E.T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957) 620–630.
D.D. Kouvatsos, A maximum entropy analysis of theG/G/1 queue at equilibrium, J. Oper. Res. Soc. 39 (1989) 183–200.
D.D. Kouvatsos and N.P. Xenios, MEM for arbitrary queueing networks with multiple general servers and repetitive-service blocking, Perf. Eval. 10 (1989) 169–195.
H.G. Perros and R. Onvural, On the superposition of arrival processes for voice and data,4th Int. Conf. on Data Communication Systems and Their Performance, Barcelona (June 1990) pp. 341–357.
F. Kamoun and L. Kleinrock, Analysis of shared finite storage in a computer network node environment under general traffic conditions, IEEE Trans. Comm. COM-28 (1980).
A.C. Williams and R.A. Bhandiwad, A generating function approach to queueing network analysis of multiprogrammed computers, Networks 6 (1976) 1–22.
D.D. Kouvatsos, Maximum entropy and theG/G/1/N queue, Acta Inf. 23 (1986) 545–565.
C. Sauer, 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 getting arbitrary coefficient of variation by two stages,Trans. IEICE '70 (1987) 33–36.
M. Veran and D. Potier, QNAP-2: A portable environment for queueing network modelling, in:Modelling Techniques and Tools for Performance Analysis (North-Holland, 1985) pp. 25–63.
K.M. Chandy, U. Herzog and L. Woo, Approximate analysis of general queueing networks, IBM J. Res. Develop. 19 (1975).
F.P. Kelly,Reversibility and Stochastic Networks (Wiley, 1979).
D.D. Kouvatsos and N.M. Tabet-Aouel, GGeo-type approximations for general discrete-time queueing systems, IFIP Trans. C-15, Special issue on Modelling and Performance Evaluation of ATM Technology (1993) 469–483.
D.D. Kouvatsos, Entropy maximisation and queueing network models, Ann. Oper. Res. 48 (1994) 63–126.
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This work is sponsored by the Science and Engineering Research Council (SERC), UK, under grants GR/F 29271 and GR/H 18609.
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Kouvatsos, D.D., Denazis, S.G. A universal building block for the approximate analysis of a shared buffer ATM switch architecture. Ann Oper Res 49, 241–278 (1994). https://doi.org/10.1007/BF02031600
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DOI: https://doi.org/10.1007/BF02031600