American Institute of Mathematical Sciences

Advanced
2011, 1(4): 781-816. doi: 10.3934/naco.2011.1.781

A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms

Demetres D. Kouvatsos 1, , Jumma S. Alanazi 1, and  Kevin Smith 1,

1. 

Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom, United Kingdom, United Kingdom

Received  June 2011 Revised  September 2011 Published  November 2011

A generic maximum entropy (ME) product-form approximation is proposed for arbitrary single class open first-come-first-served (FCFS) queueing network models with blocking (QNMs-B), subject to bursty GE-type interarrival and service times and the mixed blocking mechanisms (BMs) of Blocking-After-Service (BAS), Blocking-Before-Service (BBS) and Repetitive-Service (RS) Blocking with Random (RS-RD) and Fixed (RS-FD) destinations. A new GE-type analytic framework is devised, based on the ME analysis of a virtual multiple class GE/GE/1/N+U queueing system with finite capacity, $N (N>1)$ augmented by $U (U\geq1)$ auxiliary-waiting lines, to determine the first two moments of BAS- and BBS-dependent effective service times towards a node-by-node decomposition of the entire network. In this context, a unified ME algorithm is devised for the approximate analysis of arbitrary open FCFS QNMs-B with a mixture of the BMs of BAS, BBS, RS-RD and RS-FD. Typical numerical tests are carried out to assess the credibility of the unified ME algorithm against discrete event simulation and also establish GE-type experimental performance bounds. A critique on the feasibility of ME formalism for QNMs-B and suggested extensions are included.
Keywords: Blocking with Random (RS-RD) and Fixed (RS-FD) destinations, first-come-first-served (FCFS), maximum entropy (ME) principle, generalized exponential (GE) distribution., Blocking-After-Service (BAS), Queueing network models with blocking (QNMs-B), Repetitive-Service (RS), Blocking-Before-Service (BBS).
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781
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show all references

References:
[1]

in ''Proc. of the 2nd Inter. WS on Queueing Networks with Finite Capacity" (eds. R. O Onvural and I. F Akyildiz), Res. Tringle Park, (1992), 258-271. Google Scholar

[2]

Technical Report TR7-NetPEn-April 11, University of Bradford, 2011. Google Scholar

[3]

in ''Proc. of the IEEE/IPSJ Workshop WS-8: Future Internet Engineering of the SAINT 2011 International Symposium on Applications and the Internet", Munich, (2011), 292-296. doi: 10.1109/SAINT.2011.91.  Google Scholar

[4]

Ann. Oper. Res., 9 (1987), 481-509. doi: 10.1007/BF02054751.  Google Scholar

[5]

in ''Tech. Proc. of HET-NETs 08 International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks", Blekinge Institute of Technology, (2008), A19.1-A19.10. Google Scholar

[6]

Kluwer Academic publishers, Dordrecht, 2001.  Google Scholar

[7]

in ''Network Performance Engineering, A Handbook on Convergent Multi-Service Networks and Next Generation Internet, Lecture Notes in Computer Science" (ed. D.D. Kouvatsos), 5233 (2011), 233-257. doi: 10.1007/978-3-642-02742-0.  Google Scholar

[8]

J. ACM, 22 (1975), 248-260. doi: 10.1145/321879.321887.  Google Scholar

[9]

Academic Press, New York, 1965.  Google Scholar

[10]

Chapman and Hall, Boca Raton, 1994.  Google Scholar

[11]

T.O.C.S., 2 (1984), 335-359. Google Scholar

[12]

Internat. J. Math. Math. Sci., 23 (2000), 243-251. doi: 10.1155/S0161171200000375.  Google Scholar

[13]

IBM J. of Res. Dev., 19 (1975), 43-49. doi: 10.1147/rd.191.0043.  Google Scholar

[14]

J. Chin. Inst. Eng., 33 (2010), 191-206. doi: 10.1080/02533839.2010.9671610.  Google Scholar

[15]

Academic Press, New York, 1977. Google Scholar

[16]

Acta info., 19 (1983), 339-355.  Google Scholar

[17]

IBM J. Res. Dev., 14 (1970), 539-547. doi: 10.1147/rd.145.0539.  Google Scholar

[18]

in ''Proc. Of IEEE VTC", (2001), 2108-2112. Google Scholar

[19]

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[20]

Academic Press, London, 1980.  Google Scholar

[21]

Kybernatica, 3 (1967), 30-35. Google Scholar

[22]

Transactions of the American Society of Civil Engineers, 116 (1951), 770-808. Google Scholar

[23]

Phys. Rev., 106 (1957), 620-630. doi: 10.1103/PhysRev.106.620.  Google Scholar

[24]

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[25]

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[26]

John Wiley, New York, 1989.  Google Scholar

[27]

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[28]

Wiley, New York, 1979.  Google Scholar

[29]

in ''Modelling Techniques and Tools for Performance Analysis" (ed. D. Potier), North-Holland, (1985), 589-609. Google Scholar

[30]

Acta info., 23 (1986), 545-565.  Google Scholar

[31]

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[32]

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[34]

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[35]

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[36]

in ''Performance '90' " (eds. P. J. B. King et al.), North-Holland, (1990), 301-315.  Google Scholar

[37]

Performance Evaluation, 17 (1993), 189-205. doi: 10.1016/0166-5316(93)90041-R.  Google Scholar

[38]

Annals of Oper. Res., 48 (1994), 63-126. doi: 10.1007/BF02023095.  Google Scholar

[39]

Annals of Oper. Res., 79 (1998), 231-269. doi: 10.1023/A:1018922705462.  Google Scholar

[40]

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[41]

Computer Networks, 34 (2000), 97-113. doi: 10.1016/S1389-1286(00)00099-2.  Google Scholar

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in ''Network Performance Engineering, A Handbook on Convergent Multi-Service Networks and Next Generation Internet, Lecture Notes in Computer Science," 5233 (2011), 357-392. doi: 10.1007/978-3-642-02742-0.  Google Scholar

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in ''Special IFIP LNCS issue in Honour of Guenter Haring," University of Vienna, 2011, to appear. Google Scholar

[45]

IEEE Trans. Software Eng., 5 (1979), 530-538. doi: 10.1109/TSE.1979.234214.  Google Scholar

[46]

W. H. Freeman, New York, 1982. Google Scholar

[47]

Elsevier Science publishers, Amsterdam, 1993. Google Scholar

[48]

ACM Comput. Surv., 22 (1990), 83-121. doi: 10.1145/78919.78920.  Google Scholar

[49]

Elsevier Science publishers, Amsterdam, 1989. Google Scholar

[50]

in ''Stochastic Analysis of Computer and Communication Systems" (ed. H. Takagi), North-Holland, (1990), 451-494. Google Scholar

[51]

Oxford University Press, New York, 1994. Google Scholar

[52]

in ''Performance '48' " (ed. E. Gelenbe), North-Holand, (1984), 147-158.  Google Scholar

[53]

in ''Computer Networking and Performance Evaluation" (eds. T. Hasegawa et al.), North-Holand, (1986), 125-137. Google Scholar

[54]

IBM J. Res. Dev., 18 (1974), 110-124. doi: 10.1147/rd.182.0110.  Google Scholar

[55]

in ''Computer Performance" (eds. K. M. Chandy and M. Reiser), North-Holland, (1977), 1-22. Google Scholar

[56]

Bell Syst. Tech. J., 27 (1948), 379-423, 623-656.  Google Scholar

[57]

IEEE Trans. Info. Theory, 26 (1980), 26-37. doi: 10.1109/TIT.1980.1056144.  Google Scholar

[58]

Acta info., 17 (1982), 43-61.  Google Scholar

[59]

Research report RS-08-01, University of Bradford, 2001. Google Scholar

[60]

in ''Proc. of the 2nd Annual Postgraduate Symposium on Convergence of Telecommunications, Networking and Broadcasting PG Net 2001" (eds. M. Merabti and R. Pereira), Liverpool John Moores University Publishers, (2001), 78-83. Google Scholar

[61]

Oper. Res., 28 (1980), 594-602. doi: 10.1287/opre.28.3.594.  Google Scholar

[62]

Journal of Statistical Physics, 52 (1988), 479-487. doi: 10.1007/BF01016429.  Google Scholar

[63]

Pergamon, New York, 1969. Google Scholar

[64]

Ph.D thesis, Toronto University, Canada, 1984. Google Scholar

[65]

Annals of Oper. Res., 3 (1985), 153-167. doi: 10.1007/BF02024744.  Google Scholar

[66]

Notebook, Center for the Study of Complex Systems, University of Michigan, 2007. Available from: http://www.cscs.umich.edu/crshalizi/notabene/tsallis.html. Google Scholar

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