Moment characterization of matrix exponential and Markovian arrival processes

Annals of Operations Research

Volumn 160, Issue 1, 2008, Pages 51-68

  Bodrog, Levente ^b   Horváth, András ^a   Telek, Miklós ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Inter arrival time distribution; Lag correlation; Markov arrival process; Matrix exponential distribution; Matrix exponential process; Moment matching; Phase type distribution

Indexed keywords

EID: 39249083230     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-007-0296-8     Document Type: Article

References (16)

1. Asmussen, S., & Bladt, M. (1996). Renewal theory and queueing algorithms for matrix-exponential distributions. In Proc. 1st int. conference on matrix-analytic methods in stochastic models (pp. 313-341).
2. Asmussen, S., & Bladt, M. (1999). Point processes with finite-dimensional conditional probabilities. Stochastic Processes and their Applications, 82, 127-142 (16), July.
3. Asmussen, S., & O'Cinneide, C. A. (1997). Matrix-exponential distributions-distributions with a rational Laplace transform. In S. Kotz & C. Read (Eds.), Encyclopedia of statistical sciences (pp. 435-440). New York: Wiley.
4. Bladt, M., & Neuts, M. (2003). Matrix-exponential distributions: calculus and interpretations via flows. Stochastic Models, 19(1), 113-124.
5. Bodrog, L., Heindl, A., Horvath, G., & Telek, M. (2007). A Markovian canonical form of second-order matrix-exponential processes. European Journal of Operational Research, in press.
6. Fackrell, M. (2005). Fitting with matrix-exponential distributions. Stochastic Models, 21, 377-400.
7. Gragg, W. B., & Linquist, A. (1983). On the partial realization problem. Linear Algebra and Applications, 50, 277-319.
8. He, Q.-M., & Zhang, H. (2007). On matrix-exponential distributions. Advances in Applied Probability, 39(1), 271-292.
9. Latouche, G., & Ramaswami, V. (1999). Introduction to matrix analytic methods in stochastic modeling. Philadelphia: SIAM.
10. Lipsky, L. (1992). Queueing theory: a linear algebraic approach. New York: MacMillan.
11. Mitchell, K., & van de Liefvoort, A. (2003). Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals. Performance Evaluation, 51, 137-152.
12. Mitchell, K., Sohraby, K., van de Liefvoort, A., & Place, J. (2000). Approximation models of wireless cellular networks using moment matching. In Proc. conf. on computer communications (IEEE Infocom) (pp. 189-197).
13. Neuts, M. (1979). A versatile Markovian point process. Journal of Applied Probability, 16, 764-779.
14. Neuts, M. (1981). Matrix-geometric solutions in stochastic models. Baltimore: John Hopkins University Press.
15. Telek, M., & Heindl, A. (2002). Matching moments for acyclic discrete and continuous phase-type distributions of second order. International Journal of Simulation Systems, Science & Technology, 3(3-4), 47-57. Special Issue on: Analytical & Stochastic Modelling Techniques.
16. van de Liefvoort, A. (1990). The moment problem for continuous distributions (Technical Report). University of Missouri, WP-CM-1990-02, Kansas City.