Coxian representations of generalized erlang distributions

Acta Mathematicae Applicatae Sinica

Volumn 25, Issue 3, 2009, Pages 489-502

  He, Qi Ming ^a   Zhang, Han Qin ^b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Coxian distribution; Matrix analytic methods; Phase type distribution

Indexed keywords

EID: 66749181849     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s10255-008-8827-x     Document Type: Article

References (21)

1. Asmussen, S. Ruin Probabilities. World Scientific Publishing, Singapore, 2000
2. Asmussen, S. Applied Probability and Queues, 2nd Edition. Springer-Verlag, New York, 2003
3. Asmussen, S., Bladt, M. Renewal theory and queueing algorithms for matrix-exponential distributions, Proceedings of the First International Conference on Matrix Analytic Methods in Stochastic Models, Editors: A.S. Alfa and S. Chakravarthy, Marcel Dekker, New York, 1996
4. C. Commault S. Mocanu 2003 Phase-type distributions and representations: some results and open problems for system theory International Journal of Control 76 566 580
5. D.R. Cox 1955 On the use of complex probabilities in the theory of stochastic processes Proc. Camb. Phil. Soc. 51 313 319
6. D.R. Cox 1955 The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables Proc. Camb. Phil. Soc. 51 433 441
7. A. Cumani 1982 On the canonical representation of Markov processes modeling failure time distributions Microelectronics and Reliability 22 3 583 602 (Pubitemid 13439479)
8. M. Dehon G. Latouche 1982 A geometric interpretation of the relations between the exponential and the generalized Erlang distributions Adv. Appl. Prob. 14 885 897
9. S. Haddad P. Moreaux G. Chiola 1998 Cox and phase-type distributions in stochastic Petri nets - efficient derivation of solutions RAIRO Recherche Operationnelle - Operations Research 32 3 289 323
10. Q.M. He H.Q. Zhang 2006 Spectral polynomial algorithms for computing bi-diagonal representations for phase-type distributions and matrix-exponential distributions Stochastic Models 22 289 317
11. Q.M. He H.Q. Zhang 2007 On matrix-exponential distributions Adv. Appl. Prob. 39 271 292
12. Q.M. He H.Q. Zhang 2008 An Algorithm for Computing Minimal Coxian Representations INFORMS Journal of Computing 20 2 179 190
13. Latouche, G., Ramaswami, V. Introduction to matrix analytic methods in stochastic modelling. ASA & SIAM, Philadelphia, USA, 1999
14. Lipsky, L. Queueing theory: A linear algebraic approach. McMillan and Company, New York, 1992
15. Neuts, M.F. Matrix-geometric solutions in stochastic models - an algorithmic approach. The Johns Hopkins University Press, Baltimore, 1981
16. C.A. O'Cinneide 1989 On non-uniqueness of representations of phase-type distributions Stochastic Models 5 2 247 259
17. C.A. O'Cinneide 1990 Characterization of phase-type distributions Stochastic Models 6 1 1 57
18. C.A. O'Cinneide 1991 Phase-type distributions and invariant polytope Adv. Appl. Prob. 23 515 535
19. C.A. O'Cinneide 1993 Triangular order of triangular phase-type distributions Stochastic Models 9 4 507 529
20. C.A. O'Cinneide 1999 Phase-type distributions: open problems and a few properties Stochastic Models 5 4 731 757
21. Y. Sasaki H. Imai M. Tsunoyama 2004 Ikuo Ishii Approximation of probability distribution functions by Coxian distribution to evaluate multimedia systems Systems and Computers in Japan 35 2 16 24