Stochastic complement analysis of multi-server threshold queues with hysteresis

Performance Evaluation

Volumn 35, Issue 1, 1999, Pages 19-48

  Lui, John C S ^a   Golubchik, Leana ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b University of Maryland ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GREEN'S FUNCTION; HYSTERESIS; MARKOV PROCESSES; PROBABILITY; PROBLEM SOLVING; VECTORS;

MULTISERVER THRESHOLD QUEUEING SYSTEM; STOCHASTIC COMPLEMENT ANALYSIS;

QUEUEING THEORY;

EID: 0032638956     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(98)00043-1     Document Type: Article

References (21)

1. P.J. Courtois, Decomposability: Queueing and Computer System Applications, ACM Monograph Series, Academic Press, New York, 1977.
2. P.J. Courtois, P. Semal, Computable bounds for conditional steady-state probabilities in large Markov chains and queueing models, IEEE JSAC 4(6) (1986).
3. L. Golubchik, J.C.S. Lui, Bounding of performance measures for a threshold-based queueing system with hysteresis, ACM SIGMETRICS '97 Conference, vol. 25, 1, June 1997, pp. 147-157.
4. Grassman W.K. Transient solutions in Markovian queueing systems. Comput. Oper. Res. 4:1977;47-53.
5. S.C. Graves, J. Keilson. The compensation method applied to a one-product production/inventory problem, J. Math. Oper. Res. 6 (1981) 246-262.
6. O.C. Ibe, An approximate analysis of a multi-server queueing system with a fixed order of access, IBM Research Report, RC9346, 1982.
7. Ibe O.C., Maruyama K. An approximation method for a class of queueing systems. Performance Evaluation. 5:1985;15-27.
8. Ibe O.C., Keilson J. Multi-server threshold queues with hysteresis. Performance Evaluation. 21:1995;185-212.
9. J. Keilson, Green's Function Methods in Probability Theory, Charles Griffin, London, 1965.
10. J. Keilson, Markov Chain Models: Rarity and Exponentiality, Springer, New York, 1979.
11. F.P. Kelly, Reversibility and Stochastic Networks, Wiley, New York, 1979.
12. L. Kleinrock, Queueing Systems, vol. I, Wiley Interscience, New York, 1975.
13. Larsen R.L., Agrawala A.K. Control of a heterogeneous two-server exponential queueing system. IEEE Trans. Software Eng. 9:1983;526-552.
14. Lin W., Kumar P.R. Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Automatic Control. 29:1984;696-703.
15. Little J.D.C. A proof of the queueing formula. L=λW Oper. Res. 9:1967;383-387.
16. J.C.S. Lui, R.R. Muntz, Bounding methodology for computing steady state availability of repairable computer systems, J. ACM (1994) 676-707.
17. Lui J.C.S., Muntz R.R., Towsley D. Bounding the mean response time of the minimum expected delay routing policy: An algorithmic approach. IEEE Trans. Comput. 44(5):1995;1371-1382.
18. Meyer C.D. Stochastic complementation, uncoupling Markov chains and the theory of nearly reducible systems. SIAM Rev. 31(2):1989;240-272.
19. Morrison J.A. Two-server queue with one server idle below a threshold. Queueing Systems. 7:1990;325-336.
20. Nelson R., Towsley D. Approximating the mean time in system in a multiple-server queue that uses threshold scheduling. J. Oper. Res. 35:1987;419-427.
21. W.J. Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton Press, Princeton, NJ, 1994.