On the counting process for a class of Markovian arrival processes with an application to a queueing system

Queueing Systems

Volumn 49, Issue 2, 2005, Pages 93-122

  Kawanishi, Ken'Ichi ^a  

^a GUNMA UNIVERSITY   (Japan)

Author keywords

Automatic call distribution; Baker Hausdorff lemma; Counting process; Explicit solution; Lie algebra; Markovian arrival process

Indexed keywords

AUTOMATION; MARKOV PROCESSES; NUMERICAL METHODS; QUEUEING NETWORKS; QUEUEING THEORY;

AUTOMATIC CALL DISTRIBUTION; COUNTING PROCESS; EXPLICIT SOLUTIONS; HAUSDORFF; LIE ALGEBRA; MARKOVIAN ARRIVAL PROCESS;

MATRIX ALGEBRA;

EID: 17444382323     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-005-6478-7     Document Type: Article

References (30)

1. R. Bellman, Introduction to Matrix Analysis (SIAM Society for Industrial & Applied Mathematics, Philadelphia, 1997).
2. A. Brandt and M. Brandt, On the M(n)/M(n)/s queue with impatient calls, Performance Evaluation 35 (1999) 1-18.
3. A. Brandt and M. Brandt, Asymptotic results and a Markovian approximation for the M(n)/M(n)/s + GI system, Queueing Systems 41 (2002) 73-94.
4. E. Celledoni and A. Iserles, Methods for the approximation of the matrix exponential in a Lie-algebraic setting, IMA Journal of Numerical Analysis 21 (2001) 463-488.
5. B.T. Doshi, Queueing system with vacations - A survey, Queueing Systems 1 (1986) 29-66.
6. B.T. Doshi, Single server queues with vacations, in: Stochastic Analysis of Computer Communication Systems, ed. H. Takagi (Elsevier, Amsterdam, 1990) pp. 217-265.
7. M.A. Feinberg, Performance characteristics of automated call distribution systems, in: Proceedings of the IEEE Conference on Global Telecommunications (GLOBECOM), San Diego, California, 1990, pp. 402A.4.
8. M.A. Feinberg, Analytical model of automated call distribution system, in: Proc. 13th International Teletraffic Congress - 1991 Workshops on Queueing, Performance and Control in ATM, Copenhagen, 1991, Vol. 15, pp. 193-197.
9. W. Fischer and K.S. Meier-Hellstern, The Markov-modulated Poisson process (MMPP) cookbook, Performance Evaluation 18 (1993) 149-171.
10. M.J. Fischer, D.A. Garbin and A. Gharakhanian, Performance modeling of distributed automatic call distribution systems, Telecommunications Systems 9 (1998) 133-152.
11. N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects, Manufacturing and Service Operations Management 5 (2003) 79-141.
12. D. Gross and C.M. Harris, Fundamentals of Queueing Theory (John Wiley & Sons, New York, 1998).
13. H. Heffes and D.M. Lucantoni, A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance, IEEE Journal on Selected Areas in Communications SAC-4 (1986) 856-868.
14. J.E. Humphreys, Introduction to Lie Algebra and Representation Theory (Springer Verlag, 1972).
15. I. Ide, Superposition of interrupted Poisson processes and its application to packetized voice multiplexers, in: Proceedings of the 12th International Teletraffic Congress, Torino, 1988, pp. 3.1 B.2.1.
16. A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett and A. Zanna, Lie-group methods, Acta Numerica 9 (2000) 215-365.
17. W.M. Jolley and R.J. Harris, Analysis of post-call activity in queueing systems, in: Proceedings of the 9th International Teletraffic Congress, Torremolinos, 1979, pp. 1-9.
18. G. Koole and A. Mandelbaum, Queueing models of call centers: An introduction, Annals of Operations Research 113 (2002) 41-59.
19. G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling (SIAM Society for Industrial & Applied Mathematics, Philadelphia, 1999).
20. D.M. Lucantoni, K.S. Meier-Hellstern and M.F. Neuts, A single-server queue with server vacations and a class of nonrenewal arrival processes, Advances in Applied Probability 22 (1990) 676-705.
21. I. Mitrani and R. Chakka, Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method, Performance Evaluation 23 (1995) 241-260.
22. C. Moler and C.V. Loan, Nineteen dubious ways to compute the exponential of a matrix, SIAM Review 20 (1978) 801-836.
23. M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications (Marcel Dekker, New York, 1989).
24. M.F. Neuts and J.-M. Li, An algorithm for the P(n, t) matrices of a continuous BMAP, in: Matrix-Analytic Methods in Stochastic Models, eds. S.R. Chakravarthy and A.S. Alfa (Marcel Dekker, New York, 1997) pp. 7-19.
25. P. Nowikow and K. Wajda, Agent scheduling for ACD switches, in: Proc. ITC Seminar, Cracow, 1991, Vol. 3, pp. 114-120.
26. M. Perry and A. Nilsson, Performance modelling of automatic call distributors: Assignable grade of service staffing, in: International Switching Symposium, Yokohama, 1992, Vol. 2, p. C8.3.
27. R.B. Sidje and W.J. Stewart, A survey of methods for computing large sparse matrix exponentials arising in Markov chains, Computational Statistics and Data Analysis 29 (1999) 345-368.
28. H. Takagi, Queueing Analysis: Foundation of Performance Evaluation, Vacation and Priority Systems (North Holland, Amsterdam, 1991) Part 1.
29. H.C. Tijms, Stochastic Models: An Algorithmic Approach (John Wiley & Sons, England, 1994).
30. A. Zanna and H.Z. Munthe-Kaas, Generalized polar decompositions for the approximation of the matrix exponential, SIAM Journal on Matrix Analysis and Applications 23 (2002) 840-862.