Abstract
So-called Whittle networks have recently been shown to give tight approximations for the performance of non-locally balanced networks with blocking, including practical routing policies such as joining the shortest queue. In the present paper, we turn the attention to networks without blocking. To this end, we consider a set of “insensitive” dynamic load balancing schemes preserving the structure of Whittle networks in the case of infinite buffers and examine their efficiency. Using Hausdorff’s theorem, we prove that the optimal insensitive schemes are static in this case, i.e., routing decisions do not depend on the current state of the queues. On the other hand, simulations show that the performance of static policies is generally much worse than that of “non balanced” sensitive dynamic policies. This demonstrates that strict insensitivity and efficiency may be incompatible objectives for networks with dynamic load balancing in case of infinite buffers.
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References
T. Bonald, M. Jonckheere, and A. Proutière, Insensitive load balancing. In Proc of ACM Sigmetrics/Performance (2004) pp. 367–378.
T. Bonald, A. Proutière, L. Massoulié, and J. Virtamo, A queueing analysis of max-min fairness, proportional fairness, and balanced fairness. Accepted for publication in Queueing Systems, (2005).
T. Bonald and A. Proutière, Insensitivity in processor-sharing networks. Performance Evaluation 49 (2002) 193–209.
T. Bonald and A. Proutière, Insensitive bandwidth sharing in data networks. Queueing Systems 44(1) (2003) 69–100.
X. Chao, M. Miyazawa, R. Serfozo and H. Takada, Markov network processes with product form stationary distributions. Queueing Systems 28 (1998) 377–401.
G. Choquet, Le théorème de représentation intégrale dans les ensembles convexes compacts. Annales de l’institut Fourier 10 (1960) 333–344.
A. Ephremides, P. Varaiya, and J. Walrand, A simple dynamic routing problem. IEEE Transactions on Automatic Control 25 (1980) 690–693.
W. Feller, An Introduction to Probability Theory and its Applications, Volume II, (Wiley, 1971).
G.H. Hardy, Divergent Series (Oxford University Press, 1949).
F. Hausdorff, Summationsmethoden und Momentfolgen. Math. Zeit, (1921).
A. Hordijk and G. Koole, On the assignment of customers to parallel queues. Probability in the Engineering and Informational Sciences 6 (1992) 495–511.
F.P. Kelly, Reversibility and Stochastic Networks (Wiley, 1979).
J.C. Gupta, The moment problem for the standard k-dimensional simplex. The Indian Journal of Statistics, 61 (A, Pt. 2) (1999) 286–291.
T.H. Hildebrandt and I.J. Schoenberg, On linear functional operations and the moment problem in one or several dimensions. Annals of Mathematics (1933).
M. Jonckheere and J. Virtamo, Optimal insensitive routing and bandwidth sharing in simple data networks. In Proc. of ACM Sigmetrics (2005).
R. Phelps, Lectures on Choquet’s Theorem. Van Nostrand Mathematical studies, 7 (1966).
R. Serfozo, Introduction to Stochastic Networks (Springer, 1999).
D. Towsley, D. Panayotis Sparaggis and C. Cassandras, Optimal routing and buffer allocation for a class of finite capacity queueing systems. IEEE Transactions on Automatic Control 37(9) (1992) 1446–1451.
W. Whitt, Deciding which queue to join: some counterexamples. Operations Research 34(1) (1986) 226–244.
W. Winston, Optimality of the shortest line discipline. Journal of Applied Probability 14 (1977) 181–189.
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AMS Subject Classifications 60K25 · 68M20
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Jonckheere, M. Insensitive versus efficient dynamic load balancing in networks without blocking. Queueing Syst 54, 193–202 (2006). https://doi.org/10.1007/s11134-006-0066-3
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DOI: https://doi.org/10.1007/s11134-006-0066-3