Periodic load balancing

Queueing Systems

Volumn 30, Issue 1-2, 1998, Pages 203-250

  Hjálmtýsson, Gísli ^a   Whitt, Ward ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

Heavy traffic diffusion approximations; Load balancing; Periodic load balancing; Reflected Brownian motion; Resource sharing; Transient behavior

Indexed keywords

BROWNIAN MOVEMENT; NORMAL DISTRIBUTION; RESOURCE ALLOCATION;

DIFFUSION APPROXIMATIONS; PERIODIC LOAD; REFLECTED BROWNIAN MOTION; RESOURCE SHARING; TRANSIENT BEHAVIOR;

QUEUEING THEORY;

EID: 0040577328     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019165004692     Document Type: Article

References (53)

1. J. Abate and W. Whitt, Transient behavior of regulated Brownian motion, I and II, Adv. in Appl. Probab. 19 (1987) 560-631.
2. J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Adv. in Appl. Probab. 20 (1988) 145-178.
3. J. Abate and W. Whitt, Calculating time-dependent performance measures for the M/M/1 queue, IEEE Trans. Commun. 37 (1989) 1102-1104.
4. J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10 (1992) 5-88.
5. J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA J. Comput. 7 (1995) 36-43.
6. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
7. F. Baccelli and P. Brémaud, Elements of Queueing Theory (Springer, New York, 1994).
8. A. Barak, G. Shai and R.G. Wheeler, The MOSIX Distributed Operating System: Load Balancing for UNIX (Springer, Berlin, 1993).
9. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
10. A.A. Borovkov, Stochastic Processes in Queueing Theory (Springer, New York, 1976).
11. G.L. Choudhury, D.M. Lucantoni and W. Whitt, Multidimensional transform inversion with applications to the transient M/G/1 queue, Ann. Appl. Probab. 4 (1994) 719-740.
12. E. Çinlar, Superpositions of point processes, in: Stochastic Point Processes: Statistical Analysis, Theory and Applications, ed. P.A.W. Lewis (Wiley, New York, 1972) pp. 549-606.
13. J.L. Davis, W.A. Massey and W. Whitt, Sensitivity to the service-time distribution in the nonstationary Erlang loss model, Managm. Sci. 41 (1995) 1107-1116.
14. D.L. Eager, E.D. Lazowska and J. Zahorjan, Adaptive load balancing in homogeneous distributed systems, IEEE Trans. Software Engrg. 12 (1986) 662-675.
15. S.N. Ethier and T.G. Kurtz, Characterization and Approximation of Markov Processes (Wiley, New York, 1986).
16. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, New York, 1968).
17. K.W. Fendick, V.R. Saksena and W. Whitt, Dependence in packet queues, IEEE Trans. Commun. 37 (1989) 1173-1183.
18. G.J. Foschini, Unobtrusive communication of status in a packet network in heavy traffic, AT&T Tech. J. 64 (1985) 463-479.
19. G.J. Foschini and J. Salz, A basic dynamic routing problem and diffusion, IEEE Trans. Commun. 26 (1978) 320-327.
20. B. Hajek, Performance of global load balancing by local adjustment, IEEE Trans. Inform. Theory 36 (1990) 1398-1414.
21. M. Harchol-Balter and A.B. Downey, Exploiting process lifetime distributions for dynamic load balancing, in: Proc. SIGMETRlCS '96 (1996).
22. G. Hjálmtýsson, Lightweight call setup - supporting connection and connectionless services, in: Teletraffic Contributions for the Information Age, Proc. of the 15th Internat. Teletraffic Congress, eds. V. Ramaswami and P.E. Wirth (Elsevier, Amsterdam, 1997) pp. 35-45.
23. G. Hjálmtýsson and K.K. Ramakrishnan, UNITE - An architecture for lightweight signalling in ATM networks, in: IEEE Infocom '98 (1998) pp. 832-840.
24. D.L. Iglehart and W. Whitt, Multiple channel queues in heavy traffic, I and II, Adv. in Appl. Probab. 2 (1970) 150-177 and 355-369.
25. O. Kella and W. Whitt, Diffusion approximations for queues with server vacations, Adv. in Appl. Probab. 22 (1990) 706-729.
26. J. Köllerström, Heavy traffic theory for queues with several servers, I, J. Appl. Probab. 11 (1974) 544-552.
27. C.N. Laws, Resource pooling in queueing networks with dynamic routing, Adv. in Appl. Probab. 24 (1992) 699-726.
28. W.E. Leland and T.J. Ott, Load balancing heuristics and process behavior, Sigmetrics 86(14) (1986) 54-69.
29. A. Mandelbaum and M.I. Reiman, On pooling in queueing networks, Managm. Sci., to appear.
30. W.A. Massey and W. Whitt, Peak congestion in multi-server service systems with slowly varying arrival rates, Queueing Systems 25 (1997) 157-172.
31. S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability (Springer, New York, 1993).
32. M.I. Reiman, Some diffusion approximate with state space collapse, in: Modelling and Performance Evaluation Methodology, eds. F. Baccelli and G. Fayolle (Springer, Berlin, 1984) pp. 209-240.
33. M.H. Rothkopf and P. Rech, Perspectives on queues: Combining queues is not always beneficial, Oper. Res. 35 (1987) 906-909.
34. p/(1 - p), Ann. Inst. Statist. Math. 29 (1977) 67-75.
35. R.F. Serfozo, Partitions of point processes: multivariate Poisson approximations, Stochastic Process. Appl. 20 (1985) 281-294.
36. D.R. Smith and W. Whitt, Resource sharing for efficiency in traffic systems, Bell System Tech. J. 60 (1981) 39-55.
37. D. Stoyan, Comparison Methods for Queues and Other Stochastic Models (Wiley, New York, 1983).
38. M.R. Taaffe and K.L. Ong, Approximating Ph(t)/M(t)/S/C queueing systems, Ann. Oper. Res. 8 (1987) 103-116.
39. L. Takács, Introduction to the Theory of Queues (Oxford Univ. Press, New York, 1962).
40. E. van Doorn, Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (Springer, New York, 1981).
41. R.W. Weber, On the optimal assignment of customers to parallel servers, J. Appl. Probab. 15 (1978) 406-413.
42. W. Whitt, Weak convergence theorems for priority queues: Preemptive-resume discipline, J. Appl. Probab. 8 (1971) 74-94.
43. W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res. 5 (1980) 67-85.
44. W. Whitt, Comparing counting processes and queues, Adv. in Appl. Probab. 13 (1981) 207-220.
45. W. Whitt, Deciding which queue to join: Some counterexamples, Oper. Res. 34 (1986) 55-62.
46. W. Whitt, Planning queueing simulations, Managm. Sci. 35 (1989) 1341-1366.
47. W. Whitt, Understanding the efficiency of multi-server service systems, Managm. Sci. 38 (1992) 708-723.
48. W. Whitt, Approximations for the GI/G/m queue, Production Oper. Managm. 2 (1993) 114-160.
49. M.H. Willebeck-LeMair and A.P. Reeves, Strategies for dynamic load balancing on highly parallel computers, IEEE Trans. Parallel Distrib. Systems 9 (1993) 979-993.
50. W. Winston, Optimality of the shortest line discipline, J. Appl. Probab. 14 (1977) 181-189.
51. R.W. Wolff, An upper bound for multi-channel queues, J. Appl. Probab. 14 (1977) 884-888.
52. H. Zhang, G. Hsu and R. Wang, Heavy traffic limit theorems for a sequence of shortest queueing systems, Queueing Systems 21 (1995) 217-238.
53. S. Zhou, A trace-driven simulation study of dynamic load balancing, IEEE Trans. Software Engrg. 14 (1988) 1327-1341.