Higher order approximations for the single server queue with splitting, merging and feedback

European Journal of Operational Research

Volumn 124, Issue 3, 2000, Pages 447-467

  Girish, Muckai K ^a   Hu, Jian Qiang ^b  

^a SBC Technology Resources   (United States)

^b BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CLIENT SERVER COMPUTER SYSTEMS; FEEDBACK; MARKOV PROCESSES; MERGING; PERFORMANCE; QUEUEING NETWORKS;

HIGHER ORDER APPROXIMATION; MARKOV RENEWAL PROCESS; PERFORMANCE EVALUATION;

SYSTEMS ANALYSIS;

EID: 0033745768     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(99)00174-5     Document Type: Article

References (32)

1. Albin S.L. Approximating a point process by a renewal process, II: Superposition arrival processes to queues. Operations Research. 32:1984;1133-1162.
2. Baker, G.A., 1975. Essentials of Padé Approximants. Academic Press, New York.
3. Baskett F., Chandy K.M., Muntz R.R., Palacios F.G. Open, closed, and mixed networks of queues with different classes of customers. Journal of the Association for Computer Machinery. 22(2):1975;248-260.
4. Bitran G.R., Dasu S. Approximating nonrenewal processes by Markov chains: Use of Super-Erlang (SE) chains. Operations Research. 41(5):1993;903-923.
5. i/Ph/1 queue Operations Research. 42(1):1994;158-174.
6. Buzacott J.A., Yao D.D. On queueing network models of flexible manufacturing systems. Questa. 1:1986;5-27.
7. Chen, H., Hu, J.Q., Girish, M.K., 1997. Markov-modulated queueing networks: Diffusion limits and their applications, submitted for publication.
8. Cherry, W.P., 1972. The Superposition of Two Independent Markov Renewal Processes, Ph.D. Dissertation and Technical Report No. 72-10, Department of Industrial Engineering and Operations Research, University of Michigan, Ann Arbor, MI.
9. Girish, M.K., 1996. Higher Order Approximations for General Open Queueing Networks, Ph.D. Dissertation, Department of Manufacturing Engineering, Boston University, Boston, MA.
10. Girish M.K., Hu J.Q. Higher order approximations for tandem queueing networks. Questa. 22:1996;249-276.
11. Girish, M.K., Hu, J.Q., 1996b. The departure process of the MAP/G/1 queue, submitted for publication.
12. Girish, M.K., Hu, J.Q., 1997a Modeling correlated arrival processes in ATM multiplexers, Invited paper. In: Proceedings of the 9th INFORMS Applied Probability Conference, Boston, MA.
13. Girish M.K., Hu J.Q. An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation. Questa. 26:1997;269-284.
14. Gong W.B., Hu J.Q. The MacLaurin series for the GI/G/1 queue. Journal of Applied Probability. 29:1992;176-184.
15. Gordon W.J., Newell G.F. Closed queueing systems with exponential servers. Operations Research. 15(2):1967;254-265.
16. Harrison J.M., Nguyen V. The QNET method for two-moment analysis of open queueing networks. Questa. 6:1990;1-32.
17. Hu J.Q. The departure process of the GI/G/1 queue and its MacLaurin series. Operations Research. 44:1996;810-815.
18. Jackson J.R. Jobshop-like queueing systems. Management Science. 10(1):1963;131-142.
19. Johnson M.A., Taaffe M.R. Matching moments to phase distributions: Mixtures of Erlang distributions of common order. Stochastic Models. 5(4):1989;711-743.
20. Johnson M.A., Taaffe M.R. An investigation of phase-distribution moment matching algorithms for use in queueing models. Questa. 8:1991;129-148.
21. Johnson M.A., Taaffe M.R. A graphical investigation of error bounds for moment-based queueing approximations. Questa. 8:1991;295-312.
22. Johnson M.A. Selecting parameters of phase distributions: Combining nonlinear programming, heuristics, and Erlang distributions. ORSA Journal on Computing. 5(1):1993;69-83.
23. Kleinrock, L., 1975a. Queueing Systems, Wiley, New York.
24. Kleinrock, L., 1975b. Queueing Systems, 2, Wiley, New York.
25. Kuehn P.J. Approximate analysis of general queueing networks by decomposition. IEEE Transactions on Communications. 27:1979;113-126.
26. Petrushev, P.P., Popov, V.A., 1987. Rational Approximation of Real Functions, Cambridge University Press, Cambridge.
27. Schmickler L. MEDA: Mixed Erlang distributions as phase-type representations of empirical distribution functions. Stochastic Models. 8(1):1992;131-155.
28. Suri, R., Sanders, J.L., Kamath, M., 1993. Performance Evaluation of Production Networks, Handbooks in OR & MS, vol. 4. Elsevier, Amsterdam, pp. 199-286.
29. Whitt W. The queueing network analyzer. Bell System Technical Journal. 62(9):1983;2779-2815.
30. Whitt W. Performance of the queueing network analyzer. The Bell System Technical Journal. 62(9):1983;2817-2843.
31. Whitt W. Approximating a point process by a renewal process I: Two basic methods. Operations Research. 50:1982;125-147.
32. Zhu Y., Li H. The MacLaurin expansion for a G/G/1 queue with Markov-modulated arrivals and services. Questa. 14:1993;125-134.