Global attraction of ODE-based mean field models with hyperexponential job sizes

Mean field modeling is a popular approach to assess the performance of large scale computer systems. The evolution of many mean field models is characterized by a set of ordinary differential equations that have a unique fixed point. In order to prove that this unique fixed point corresponds to the limit of the stationary measures of the finite systems, the unique fixed point must be a global attractor. While global attraction was established for various systems in case of exponential job sizes, it is often unclear whether these proof techniques can be generalized to non-exponential job sizes. In this paper we show how simple monotonicity arguments can be used to prove global attraction for a broad class of ordinary differential equations that capture the evolution of mean field models with hyperexponential job sizes. This class includes both existing as well as previously unstudied load balancing schemes and can be used for systems with either finite or infinite buffers. The main novelty of the approach exists in using a Coxian representation for the hyperexponential job sizes and a partial order that is stronger than the componentwise partial order used in the exponential case.Comment: This paper was accepted at ACM Sigmetrics 201

Free Energy Approximations for CSMA networks

In this paper we study how to estimate the back-off rates in an idealized CSMA network consisting of $n$ links to achieve a given throughput vector using free energy approximations. More specifically, we introduce the class of region-based free energy approximations with clique belief and present a closed form expression for the back-off rates based on the zero gradient points of the free energy approximation (in terms of the conflict graph, target throughput vector and counting numbers). Next we introduce the size $k_{max}$ clique free energy approximation as a special case and derive an explicit expression for the counting numbers, as well as a recursion to compute the back-off rates. We subsequently show that the size $k_{max}$ clique approximation coincides with a Kikuchi free energy approximation and prove that it is exact on chordal conflict graphs when $k_{max} = n$. As a by-product these results provide us with an explicit expression of a fixed point of the inverse generalized belief propagation algorithm for CSMA networks. Using numerical experiments we compare the accuracy of the novel approximation method with existing methods

Simultaneous EEG and functional MRI: A noninvasive tool in the presurgical evaluation of focal epilepsy

Verdaasdonk, R.M. [Promotor]Boon, P.A.J.M. [Promotor]Ossenblok, P.P.W. [Copromotor]Munck, J.C. de [Copromotor

The Necessity of Contingency or Contingent Necessity: Meillassoux, Hegel, and the Subject

This article addresses the relationship of contingency to necessity as developed by Quentin Meillassoux and G.W.F. Hegel. Meillassoux criticizes the restriction of possibility by modern philosophy to the conditions of the transcendental subject, which he calls ‘correlationism', and opposes to this correlationism, mathematics as an absolute form of thought. The arch-figure of a metaphysical version of correlationism for Meillassoux is Hegel. This article argues that, while Meillassoux is right to criticize a version of correlationism for restricting the range of contingency, he overlooks Hegel's unique contribution to this issue. Hegel provides us a version of necessity modeled on the mathematical proof which answers Meillassoux's concerns about correlationist versions of necessity but does not altogether jettison the concept of the subject. Instead, the subject in Hegel is a contingent interruption which emerges from the breaks in the kinds of necessity we posit about the world. Hegel offers us a way of tying these two concepts together in what I call ‘contingent necessity'

Cellular immune response in human melanoma : Insights for patient tailored therapy

Meijer, C.J.L.M. [Promotor]Oudejans, J.J. [Copromotor]Hooijberg, E. [Copromotor

Periodic review base-stock replenishment policy with endogenous lead times.

In this paper, we consider a two stage supply chain where the retailer's inventory is controlled by the periodic review, base-stock level (R,S) replenishment policy and the replenishment lead times are endogenously generated by the manufacturer's production system with finite capacity. We extend the work of Benjaafar and Kim (2004) who study the effect of demand variability in a continuously reviewed base-stock policy with single unit demands. In our analysis, we allow for demand in batches of variable size, which is a common setting in supply chains. A procedure is developed using matrix analytic methods to provide an exact calculation of the lead time distribution, which enables the computation of the distribution of lead time demand and consequently the safety stock in an exact way instead of using approximations. Treating the lead time as an endogenous stochastic variable has a substantial impact on safety stock. We numerically show that the exogenous lead time assumption may dramatically degrade customer service.Production/inventory systems; Base-stock replenishment policy; endogenous lead times; Safety stock; Phase-type distribution; Matrix-analytical methods;