Two tandem queues with general renewal input I: Diffusion approximation and integral representations

SIAM Journal on Applied Mathematics

Volumn 59, Issue 6, 1999, Pages 1917-1959

  Knessl, Charles ^a   Tier, Charles ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CLIENT SERVER COMPUTER SYSTEMS; CONGESTION CONTROL (COMMUNICATION); DATA COMMUNICATION SYSTEMS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; TELECOMMUNICATION TRAFFIC;

DIFFUSION APPROXIMATION; INTEGRAL REPRESENTATIONS; TANDEM QUEUES;

QUEUEING NETWORKS;

EID: 0033322320     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0003613999732846     Document Type: Article

References (19)

1. J. P. C. BLANC, The relaxation time of two queueing systems in seríes, Comm. Statist. Stochastic Models, 1 (1985). pp. 1-16.
2. C. KNESSL AND C. TIER, Asymptotic properties of first passage times for tandem Jackson networks I: Buildup of large queue lengths, Comm. Statist. Stochastic Models, 11 (1995). pp. 133-162.
3. J. M. HARRISON AND M. I. REIMAN, On the distribution of multidimensional reflected Brownian motion, SIAM J. Appl. Math., 41 (1981), pp. 345-361.
4. C. KNESSL AND X. TAN, Integral representations and asymptotics for infinite-and finite-capacity queues described by the unfinished work II, SIAM J. Appl. Math., 57 (1997), pp. 824-870.
5. A. GANESH AND V. ANANTHARAM, The stationary tail probability of an exponential server tandem fed by renewal arrivals, presented at IMA Workshop on Stochastic Networks, University of Minnesota, March 3, 1994.
6. G. J. FOSCHINI, Equilibria for diffusion models for pairs of communicating computers-symmetric case, IEEE Trans. Inform. Theory, 28 (1982). pp. 273-284.
7. F. BACCELLI AND G. FAYOLLE, Analysis of models reducible to a class of diffusion processes in the positive quarter plane, SIAM J. Appl. Math., 47 (1987), pp. 1367-1385.
8. J. A. MORRISON, Diffusion approximation for head-of-the-line processor sharing for two parallel queues, SIAM J. Appl. Math., 53 (1993), pp. 471-490.
9. C. KNESSL AND X. TAN, A fork-join queueing model: Diffusion approximation, integral representations and asymptotics, Queueing Systems Theory Appl., 22 (1996), pp. 287-322.
10. J. W. COHEN, The Single Server Queue, North-Holland, Amsterdam, 1982.
11. C. KNESSL, Refinements to heavy traffic limit theorems in queueing theory, J. Oper. Res., 38 (1990), pp. 826-837.
12. O. J. BOXMA, On a tandem queueing model with identical service times at both counters I, Adv. Appl. Prob., 11 (1979), pp. 616-643.
13. O. J. BOXMA, On a tandem queueing model with identical service times at both counters II, Adv. Appl. Prob., 11 (1979), pp. 644-659.
14. R. L. DOBRUSHIN AND E. A. PECHERSKY, Large deviations for tandem queueing systems, J. Appl. Math. Stochastic Anal., 7 (1994), pp. 301-330.
15. G. F. NEWELL, Approximate Behavior of Tandem Queues, Springer-Verlag, New York, 1979.
16. E. SKUDRZYK, The Foundations of Acoustics, Springer-Verlag, New York, 1971.
17. C. KNESSL AND C. TIER, Two tandem queues with general renewal input II: Asymptotic expansions for the diffusion model, SIAM J. Appl. Math., 59 (1999), pp. 1960-1997.
18. A. A. BOROVKOV, Asymptotic Methods in Queuing Theory, Wiley, New York, 1984.
19. F. I. KARPELEVICH AND A. Y. KREININ, Two-phase queueing systems GI/G/1 → G′/1/∞ under heavy traffic conditions, Theory Probab. Appl., 26 (1981), pp. 293-313.