Heavy traffic analysis of a Markov-modulated queue with finite capacity and general service times

SIAM Journal on Applied Mathematics

Volumn 58, Issue 1, 1998, Pages 257-323

  Knessl, Charles ^a   Tier, Charles ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Asymptotics; Heavy traffic; Queueing theory

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; FUNCTIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

HEAVY TRAFFIC ANALYSIS;

QUEUEING THEORY;

EID: 0032003341     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613995293853     Document Type: Article

References (13)

1. D. ANICK, D. MITRA, AND M. M. SONDHI, Stochastic theory of a data-handling system with multiple sources, Bell System Tech. J., 61 (1982), pp. 1871-1894.
2. A. WEISS, A new technique for analyzing large traffic systems, Adv. Appl. Probab., 18 (1986), pp. 506-532.
3. J. A. MORRISON, Asymptotic analysls of a data-handling system with many sources, SIAM J. Appl. Math., 49 (1989), pp. 617-637.
4. C. KNESSL AND J. A. MORRISON, Heavy-traffic analysis of a data-handling system with many sources, SIAM J. Appl. Math., 51 (1991), pp. 187-213.
5. P. S. HAGAN, C. R. DOERING, AND C. D. LEVERMORE, Mean exit times driven by weakly colored noise, SIAM J. Appl. Math., 49 (1989), pp. 1480-1513.
6. A. SIMONIAN AND J. VIRTAMO, Transient and stationary distributions for fluid queues and input processes with a density, SIAM J. Appl. Math., 51 (1991), pp. 1732-1739.
7. H. J. KUSHNER AND L. F. MARTINS, Heavy traffic analysis of a data transmission system with many independent sources, SIAM J. Appl. Math., 53 (1993), pp. 1095-1122.
8. C. M. BENDER AND S. A. ORSZAG, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
9. J. KEVORKIAN AND J. D. COLE, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981.
10. I. S. GRADSHTEYN AND I. M. RYZHIK, Table of Integrals, Series and Products, 4th ed., Academic Press, Boston, 1980.
11. M. ABRAMOWITZ AND I. A. STEGUN, Handbook of Mathematical Functions, 9th ed., Dover, New York, 1972.
12. J. W. COHEN, The Single Server Queue, North-Holland, Amsterdam, 1982.
13. E. T. WHITTAKER AND G. N. WATSON, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, Cambridge, UK, 1927.