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A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms
1.  Networks and Performance Engineering Research Group, Informatics Research Institute, University of Bradford, Bradford, BD7 1DP, United Kingdom, United Kingdom, United Kingdom 
References:
[1] 
I. F Akyildiz and C. C Huang, Exact analysis of multijob class networks of queues with blockingaftersevice,, in ''Proc. of the 2nd Inter. WS on Queueing Networks with Finite Capacity, (1992), 258. 
[2] 
J. S. Alanazi and D. D. Kouvatsos, On the experimentation with the unified ME algorithm for arbitrary open QNMsB,, Technical Report TR7NetPEnApril 11, (2011). 
[3] 
J. S. Alanazi and D. D. Kouvatsos, A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms,, in ''Proc. of the IEEE/IPSJ Workshop WS8: Future Internet Engineering of the SAINT 2011 International Symposium on Applications and the Internet, (2011), 292. doi: 10.1109/SAINT.2011.91. 
[4] 
T. Altiok and H. G. Perros, Approximate analysis of arbitrary configurations of queueing networks with blocking,, Ann. Oper. Res., 9 (1987), 481. doi: 10.1007/BF02054751. 
[5] 
S. A. Assi, D. D. Kouvatsos, I. M. Mkwawa and K. Smith, A unified ME decomposition algorithm of open queueing network modes with blocking,, in ''Tech. Proc. of HETNETs 08 International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks, (2008). 
[6] 
S. Balsamo, V. D. Nitto Persone and R. Onvural, "Analysis of Queueing Networks with Blocking,", Kluwer Academic publishers, (2001). 
[7] 
S. Balsamo, Queueing networks with blocking: snalysis, solution algorithms and properties,, in ''Network Performance Engineering, 5233 (2011), 233. doi: 10.1007/9783642027420. 
[8] 
F. Baskett, K. M. Chandy, R. R. Muntz and F. G. Palacios, Open, closed and mixed networks of queues with different classes of customers,, J. ACM, 22 (1975), 248. doi: 10.1145/321879.321887. 
[9] 
V. E. Benes, "Mathematical Theory of Connecting Networks and Telephone Traffic,", Academic Press, (1965). 
[10] 
J. Beran, "Statistics for LongMemory Processes,", Chapman and Hall, (1994). 
[11] 
R. M. Bryant, A. E. Krzesinski, M. S. Lakshmi and K. M. Chandy, The MVA priority approximation,, T.O.C.S., 2 (1984), 335. 
[12] 
C. G. Chakrabarti and D. E. Kajal, BoltzmannGibbs entropy: axiomatic characterisation and application,, Internat. J. Math. Math. Sci., 23 (2000), 243. doi: 10.1155/S0161171200000375. 
[13] 
K. M. Chandy, U. Herzog and L. Woo, Approximate analysis of general queuing networks,, IBM J. of Res. Dev., 19 (1975), 43. doi: 10.1147/rd.191.0043. 
[14] 
Y. L. Chen and C. Chen, Performance analysis of nonpreemptive HOL GE/G/1 queue with two priority classes of SIPT signaling system in carrier grade VoIP network,, J. Chin. Inst. Eng., 33 (2010), 191. doi: 10.1080/02533839.2010.9671610. 
[15] 
P. J. Courtois, U. Herzog and L. Woo, "Decomposability: Queueing and Computer System Applications,", Academic Press, (1977). 
[16] 
M. A ElAffendi and D. D Kouvatsos, A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium,, Acta info., 19 (1983), 339. 
[17] 
A. Ferdinand, A statistical mechanical approach to systems analysis,, IBM J. Res. Dev., 14 (1970), 539. doi: 10.1147/rd.145.0539. 
[18] 
C. H. Foh, B. Meini, B. Wydrowski and M. Zuerman, Modelling and performance evaluation of GPRS,, in ''Proc. Of IEEE VTC, (2001), 2108. 
[19] 
E. Gelenbe and G. Pujolle, The behaviour of a single queue in a general queueing network,, Acta info., 7 (1974), 123. 
[20] 
E. Gelenbe and I. Mitrani, "Analysis and Synthesis of Computer Systems,", Academic Press, (1980). 
[21] 
J. H. Havrda and F. Charvat, Quantification methods of classificatory processes: concept of structural entropy,, Kybernatica, 3 (1967), 30. 
[22] 
H. E. Hurst, Longterm storage capacity of reservoirs,, Transactions of the American Society of Civil Engineers, 116 (1951), 770. 
[23] 
E. T. Jaynes, Information theory and statistical mechanics,, Phys. Rev., 106 (1957), 620. doi: 10.1103/PhysRev.106.620. 
[24] 
E. T. Jaynes, Information theory and statistical mechanics II,, Phys. Rev., 108 (1957), 171. doi: 10.1103/PhysRev.108.171. 
[25] 
R. Johnson, Properties of crossentropy minimization,, IEEE Trans. Info. Theory, 27 (1981), 472. doi: 10.1109/TIT.1981.1056373. 
[26] 
J. N. Kapur, "Maximumentropy Models in Science and Engineering,", John Wiley, (1989). 
[27] 
J. N. Kapur and H. K. Kesavan, "Entropy Optimization Principles with Applications,", Academic Press, (1992). 
[28] 
F. P. Kelly, "Reversibility and Stochastic Networks,", Wiley, (1979). 
[29] 
D. D. Kouvatsos, Maximum entropy methods for general queueing networks,, in ''Modelling Techniques and Tools for Performance Analysis, (1985), 589. 
[30] 
D. D. Kouvatsos, Maximum entropy and the G/G/1/N queue,, Acta info., 23 (1986), 545. 
[31] 
D. D. Kouvatsos, A universal maximum entropy algorithm for the analysis of general closed networks,, in ''Computer Networks and Performance Evaluation, (1986), 113. 
[32] 
D. D. Kouvatsos, A maximum entropy analysis of the G/G/1 queue at equilibrium,, J. Opl. Res. Soc., 39 (1988), 183. 
[33] 
D. D. Kouvatsos and N. P. Xenios, MEM for arbitrary queueing networks with multiple general servers and repetitive service blocking,, Performance Evaluation, 10 (1989), 169. doi: 10.1016/01665316(89)900096. 
[34] 
D. D. Kouvatsos, P. H. Georgatsos and N. TabetAouel, A universal maximum entropy algorithm for general multiple class open networks with mixed service disciplines,, in ''Modelling Techniques and Tools for Computer Performance Evaluation, (1989), 397. doi: 10.1007/9781461305330_26. 
[35] 
D. D. Kouvatsos and N. M. TabetAouel, A maximum entropy priority approximation for a stable G/G/1 queue,, Acta info., 27 (1989), 247. 
[36] 
D. D. Kouvatsos and N. M. TabetAouel, Productform approximations for an extended class of general closed queueing networks,, in ''Performance '90', (1990), 301. 
[37] 
D. D. Kouvatsos and S. G. Denazis, Entropy maximised queueing networks with blocking and multiple job classes,, Performance Evaluation, 17 (1993), 189. doi: 10.1016/01665316(93)90041R. 
[38] 
D. D. Kouvatsos, Entropy maximisation and queueing network models,, Annals of Oper. Res., 48 (1994), 63. doi: 10.1007/BF02023095. 
[39] 
D. D. Kouvatsos and I. U. Awan, MEM for arbitrary closed queueing networks with RSblocking and multiple job classes,, Annals of Oper. Res., 79 (1998), 231. doi: 10.1023/A:1018922705462. 
[40] 
D. D. Kouvatsos and I. U. Awan, Entropy maximisation and open queueing networks with priorities and blocking,, Performance Evaluation, 51 (2003), 191. doi: 10.1016/S01665316(02)000925. 
[41] 
D. D. Kouvatsos, I. U. Awan, R. J. Fretwell and R. Dimakopoulos, G. A costeffective approximation for SRD traffic in arbitrary multibuffered networks,, Computer Networks, 34 (2000), 97. doi: 10.1016/S13891286(00)000992. 
[42] 
D. D. Kouvatsos, Y. Li and W. Xi, Performance modelling and analysis of a 4G handoff priority scheme for cellular networks,, in ''Performance Modelling and Analysis of Heterogeneous Networks, (2009), 215. 
[43] 
D. D. Kouvatsos and S. A. Assi, Generalised entropy maximisation and queues with bursty and/or heavy tails,, in ''Network Performance Engineering, 5233 (2011), 357. doi: 10.1007/9783642027420. 
[44] 
D. D. Kouvatsos and S. A. Assi, On the analysis of queues with heavy tails: a nonextensive maximum entropy formalism and a generalisation of the Zipfmandelbrot distribution,, in ''Special IFIP LNCS issue in Honour of Guenter Haring, (2011). 
[45] 
R. A. Marie, An approximate analytical method for general queueing networks,, IEEE Trans. Software Eng., 5 (1979), 530. doi: 10.1109/TSE.1979.234214. 
[46] 
B. B. Mandelbrot, "The Fractal Geometry of Nature,", W. H. Freeman, (1982). 
[47] 
R. O. Onvural and I. F. Akyildiz, "Queueing Networks with Finite Capacity,", Elsevier Science publishers, (1993). 
[48] 
R. O. Onvural, Survey of closed queueing networks with blocking,, ACM Comput. Surv., 22 (1990), 83. doi: 10.1145/78919.78920. 
[49] 
H. G. Perros and T. Altiok, "Queueing Networks with Blocking,", Elsevier Science publishers, (1989). 
[50] 
H. G. Perros, Approximate algorithms for open queueing networks with blocking,, in ''Stochastic Analysis of Computer and Communication Systems, (1990), 451. 
[51] 
H. G. Perros, "Queueing Networks with Blocking,", Oxford University Press, (1994). 
[52] 
E. Pinsky and Y. Yemini, A statistical mechanics of some interconnection networks,, in ''Performance '48', (1984), 147. 
[53] 
E. Pinsky and Y. Yemini, The canonical approximation in performance analysis,, in ''Computer Networking and Performance Evaluation, (1986), 125. 
[54] 
M. Reiser and H. Kobayashi, Accuracy of the diffusion approximation for some queuing systems,, IBM J. Res. Dev., 18 (1974), 110. doi: 10.1147/rd.182.0110. 
[55] 
K. C. Sevcik, A. I. Levy, S. Tripathi and J. L. Zahorjan, Improving approximations of aggregated queuing network subsystems,, in ''Computer Performance, (1977), 1. 
[56] 
C. E. Shannon and W. Weaver, A mathematical theory of communication,, Bell Syst. Tech. J., 27 (1948), 379. 
[57] 
J. Shore and R. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum crossentropy,, IEEE Trans. Info. Theory, 26 (1980), 26. doi: 10.1109/TIT.1980.1056144. 
[58] 
J. E. Shore, Information theoretic approximations for M/G/1 and G/G/1 queuing systems,, Acta info., 17 (1982), 43. 
[59] 
K. Smith and D. D. Kouvatsos, "Entropy Maximisation and QNM with Blocking after Service,", Research report RS0801, (2001), 08. 
[60] 
K. Smith and D.D. Kouvatsos, Entropy maximisation and QNM with blocking before service,, in ''Proc. of the 2nd Annual Postgraduate Symposium on Convergence of Telecommunications, (2001), 78. 
[61] 
Y. Takahashi and H. Miyahara, An approximation method for open restricted queueing networks,, Oper. Res., 28 (1980), 594. doi: 10.1287/opre.28.3.594. 
[62] 
C. Tsallis, Possible generalisation of boltzmanngibbs statistics,, Journal of Statistical Physics, 52 (1988), 479. doi: 10.1007/BF01016429. 
[63] 
M. Tribus, "Rational Descriptions, Decisions and Designs,", Pergamon, (1969). 
[64] 
B. R. Walstra, "Iterative Analysis of Networks of Queues,", Ph.D thesis, (1984). 
[65] 
D. Yao and J. A Buzacott, Modelling a class of state dependent routing in flexible manufacturing systems,, Annals of Oper. Res., 3 (1985), 153. doi: 10.1007/BF02024744. 
[66] 
, "Tsallis Statistics, Statistical Mechanics for Nonextensive Systems and LongRange Interactions,", Notebook, (2007). 
show all references
References:
[1] 
I. F Akyildiz and C. C Huang, Exact analysis of multijob class networks of queues with blockingaftersevice,, in ''Proc. of the 2nd Inter. WS on Queueing Networks with Finite Capacity, (1992), 258. 
[2] 
J. S. Alanazi and D. D. Kouvatsos, On the experimentation with the unified ME algorithm for arbitrary open QNMsB,, Technical Report TR7NetPEnApril 11, (2011). 
[3] 
J. S. Alanazi and D. D. Kouvatsos, A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms,, in ''Proc. of the IEEE/IPSJ Workshop WS8: Future Internet Engineering of the SAINT 2011 International Symposium on Applications and the Internet, (2011), 292. doi: 10.1109/SAINT.2011.91. 
[4] 
T. Altiok and H. G. Perros, Approximate analysis of arbitrary configurations of queueing networks with blocking,, Ann. Oper. Res., 9 (1987), 481. doi: 10.1007/BF02054751. 
[5] 
S. A. Assi, D. D. Kouvatsos, I. M. Mkwawa and K. Smith, A unified ME decomposition algorithm of open queueing network modes with blocking,, in ''Tech. Proc. of HETNETs 08 International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks, (2008). 
[6] 
S. Balsamo, V. D. Nitto Persone and R. Onvural, "Analysis of Queueing Networks with Blocking,", Kluwer Academic publishers, (2001). 
[7] 
S. Balsamo, Queueing networks with blocking: snalysis, solution algorithms and properties,, in ''Network Performance Engineering, 5233 (2011), 233. doi: 10.1007/9783642027420. 
[8] 
F. Baskett, K. M. Chandy, R. R. Muntz and F. G. Palacios, Open, closed and mixed networks of queues with different classes of customers,, J. ACM, 22 (1975), 248. doi: 10.1145/321879.321887. 
[9] 
V. E. Benes, "Mathematical Theory of Connecting Networks and Telephone Traffic,", Academic Press, (1965). 
[10] 
J. Beran, "Statistics for LongMemory Processes,", Chapman and Hall, (1994). 
[11] 
R. M. Bryant, A. E. Krzesinski, M. S. Lakshmi and K. M. Chandy, The MVA priority approximation,, T.O.C.S., 2 (1984), 335. 
[12] 
C. G. Chakrabarti and D. E. Kajal, BoltzmannGibbs entropy: axiomatic characterisation and application,, Internat. J. Math. Math. Sci., 23 (2000), 243. doi: 10.1155/S0161171200000375. 
[13] 
K. M. Chandy, U. Herzog and L. Woo, Approximate analysis of general queuing networks,, IBM J. of Res. Dev., 19 (1975), 43. doi: 10.1147/rd.191.0043. 
[14] 
Y. L. Chen and C. Chen, Performance analysis of nonpreemptive HOL GE/G/1 queue with two priority classes of SIPT signaling system in carrier grade VoIP network,, J. Chin. Inst. Eng., 33 (2010), 191. doi: 10.1080/02533839.2010.9671610. 
[15] 
P. J. Courtois, U. Herzog and L. Woo, "Decomposability: Queueing and Computer System Applications,", Academic Press, (1977). 
[16] 
M. A ElAffendi and D. D Kouvatsos, A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium,, Acta info., 19 (1983), 339. 
[17] 
A. Ferdinand, A statistical mechanical approach to systems analysis,, IBM J. Res. Dev., 14 (1970), 539. doi: 10.1147/rd.145.0539. 
[18] 
C. H. Foh, B. Meini, B. Wydrowski and M. Zuerman, Modelling and performance evaluation of GPRS,, in ''Proc. Of IEEE VTC, (2001), 2108. 
[19] 
E. Gelenbe and G. Pujolle, The behaviour of a single queue in a general queueing network,, Acta info., 7 (1974), 123. 
[20] 
E. Gelenbe and I. Mitrani, "Analysis and Synthesis of Computer Systems,", Academic Press, (1980). 
[21] 
J. H. Havrda and F. Charvat, Quantification methods of classificatory processes: concept of structural entropy,, Kybernatica, 3 (1967), 30. 
[22] 
H. E. Hurst, Longterm storage capacity of reservoirs,, Transactions of the American Society of Civil Engineers, 116 (1951), 770. 
[23] 
E. T. Jaynes, Information theory and statistical mechanics,, Phys. Rev., 106 (1957), 620. doi: 10.1103/PhysRev.106.620. 
[24] 
E. T. Jaynes, Information theory and statistical mechanics II,, Phys. Rev., 108 (1957), 171. doi: 10.1103/PhysRev.108.171. 
[25] 
R. Johnson, Properties of crossentropy minimization,, IEEE Trans. Info. Theory, 27 (1981), 472. doi: 10.1109/TIT.1981.1056373. 
[26] 
J. N. Kapur, "Maximumentropy Models in Science and Engineering,", John Wiley, (1989). 
[27] 
J. N. Kapur and H. K. Kesavan, "Entropy Optimization Principles with Applications,", Academic Press, (1992). 
[28] 
F. P. Kelly, "Reversibility and Stochastic Networks,", Wiley, (1979). 
[29] 
D. D. Kouvatsos, Maximum entropy methods for general queueing networks,, in ''Modelling Techniques and Tools for Performance Analysis, (1985), 589. 
[30] 
D. D. Kouvatsos, Maximum entropy and the G/G/1/N queue,, Acta info., 23 (1986), 545. 
[31] 
D. D. Kouvatsos, A universal maximum entropy algorithm for the analysis of general closed networks,, in ''Computer Networks and Performance Evaluation, (1986), 113. 
[32] 
D. D. Kouvatsos, A maximum entropy analysis of the G/G/1 queue at equilibrium,, J. Opl. Res. Soc., 39 (1988), 183. 
[33] 
D. D. Kouvatsos and N. P. Xenios, MEM for arbitrary queueing networks with multiple general servers and repetitive service blocking,, Performance Evaluation, 10 (1989), 169. doi: 10.1016/01665316(89)900096. 
[34] 
D. D. Kouvatsos, P. H. Georgatsos and N. TabetAouel, A universal maximum entropy algorithm for general multiple class open networks with mixed service disciplines,, in ''Modelling Techniques and Tools for Computer Performance Evaluation, (1989), 397. doi: 10.1007/9781461305330_26. 
[35] 
D. D. Kouvatsos and N. M. TabetAouel, A maximum entropy priority approximation for a stable G/G/1 queue,, Acta info., 27 (1989), 247. 
[36] 
D. D. Kouvatsos and N. M. TabetAouel, Productform approximations for an extended class of general closed queueing networks,, in ''Performance '90', (1990), 301. 
[37] 
D. D. Kouvatsos and S. G. Denazis, Entropy maximised queueing networks with blocking and multiple job classes,, Performance Evaluation, 17 (1993), 189. doi: 10.1016/01665316(93)90041R. 
[38] 
D. D. Kouvatsos, Entropy maximisation and queueing network models,, Annals of Oper. Res., 48 (1994), 63. doi: 10.1007/BF02023095. 
[39] 
D. D. Kouvatsos and I. U. Awan, MEM for arbitrary closed queueing networks with RSblocking and multiple job classes,, Annals of Oper. Res., 79 (1998), 231. doi: 10.1023/A:1018922705462. 
[40] 
D. D. Kouvatsos and I. U. Awan, Entropy maximisation and open queueing networks with priorities and blocking,, Performance Evaluation, 51 (2003), 191. doi: 10.1016/S01665316(02)000925. 
[41] 
D. D. Kouvatsos, I. U. Awan, R. J. Fretwell and R. Dimakopoulos, G. A costeffective approximation for SRD traffic in arbitrary multibuffered networks,, Computer Networks, 34 (2000), 97. doi: 10.1016/S13891286(00)000992. 
[42] 
D. D. Kouvatsos, Y. Li and W. Xi, Performance modelling and analysis of a 4G handoff priority scheme for cellular networks,, in ''Performance Modelling and Analysis of Heterogeneous Networks, (2009), 215. 
[43] 
D. D. Kouvatsos and S. A. Assi, Generalised entropy maximisation and queues with bursty and/or heavy tails,, in ''Network Performance Engineering, 5233 (2011), 357. doi: 10.1007/9783642027420. 
[44] 
D. D. Kouvatsos and S. A. Assi, On the analysis of queues with heavy tails: a nonextensive maximum entropy formalism and a generalisation of the Zipfmandelbrot distribution,, in ''Special IFIP LNCS issue in Honour of Guenter Haring, (2011). 
[45] 
R. A. Marie, An approximate analytical method for general queueing networks,, IEEE Trans. Software Eng., 5 (1979), 530. doi: 10.1109/TSE.1979.234214. 
[46] 
B. B. Mandelbrot, "The Fractal Geometry of Nature,", W. H. Freeman, (1982). 
[47] 
R. O. Onvural and I. F. Akyildiz, "Queueing Networks with Finite Capacity,", Elsevier Science publishers, (1993). 
[48] 
R. O. Onvural, Survey of closed queueing networks with blocking,, ACM Comput. Surv., 22 (1990), 83. doi: 10.1145/78919.78920. 
[49] 
H. G. Perros and T. Altiok, "Queueing Networks with Blocking,", Elsevier Science publishers, (1989). 
[50] 
H. G. Perros, Approximate algorithms for open queueing networks with blocking,, in ''Stochastic Analysis of Computer and Communication Systems, (1990), 451. 
[51] 
H. G. Perros, "Queueing Networks with Blocking,", Oxford University Press, (1994). 
[52] 
E. Pinsky and Y. Yemini, A statistical mechanics of some interconnection networks,, in ''Performance '48', (1984), 147. 
[53] 
E. Pinsky and Y. Yemini, The canonical approximation in performance analysis,, in ''Computer Networking and Performance Evaluation, (1986), 125. 
[54] 
M. Reiser and H. Kobayashi, Accuracy of the diffusion approximation for some queuing systems,, IBM J. Res. Dev., 18 (1974), 110. doi: 10.1147/rd.182.0110. 
[55] 
K. C. Sevcik, A. I. Levy, S. Tripathi and J. L. Zahorjan, Improving approximations of aggregated queuing network subsystems,, in ''Computer Performance, (1977), 1. 
[56] 
C. E. Shannon and W. Weaver, A mathematical theory of communication,, Bell Syst. Tech. J., 27 (1948), 379. 
[57] 
J. Shore and R. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum crossentropy,, IEEE Trans. Info. Theory, 26 (1980), 26. doi: 10.1109/TIT.1980.1056144. 
[58] 
J. E. Shore, Information theoretic approximations for M/G/1 and G/G/1 queuing systems,, Acta info., 17 (1982), 43. 
[59] 
K. Smith and D. D. Kouvatsos, "Entropy Maximisation and QNM with Blocking after Service,", Research report RS0801, (2001), 08. 
[60] 
K. Smith and D.D. Kouvatsos, Entropy maximisation and QNM with blocking before service,, in ''Proc. of the 2nd Annual Postgraduate Symposium on Convergence of Telecommunications, (2001), 78. 
[61] 
Y. Takahashi and H. Miyahara, An approximation method for open restricted queueing networks,, Oper. Res., 28 (1980), 594. doi: 10.1287/opre.28.3.594. 
[62] 
C. Tsallis, Possible generalisation of boltzmanngibbs statistics,, Journal of Statistical Physics, 52 (1988), 479. doi: 10.1007/BF01016429. 
[63] 
M. Tribus, "Rational Descriptions, Decisions and Designs,", Pergamon, (1969). 
[64] 
B. R. Walstra, "Iterative Analysis of Networks of Queues,", Ph.D thesis, (1984). 
[65] 
D. Yao and J. A Buzacott, Modelling a class of state dependent routing in flexible manufacturing systems,, Annals of Oper. Res., 3 (1985), 153. doi: 10.1007/BF02024744. 
[66] 
, "Tsallis Statistics, Statistical Mechanics for Nonextensive Systems and LongRange Interactions,", Notebook, (2007). 
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