Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable

Scaling limits for infinite-server systems in a random environment

This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$ time units, yielding an i.i.d. sequence of arrival rates $\Lambda_1,\Lambda_2, \ldots$. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., $\Delta$ is small relative to $\Lambda$) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues

Bulk and Transhorizon Measurements in AdS/CFT

We discuss the construction of bulk operators in asymptotically AdS spacetimes, including the interiors of AdS black holes. We use this to address the question "If Schrodinger's cat were behind the horizon of an AdS black hole, could we determine its state by a measurement in the dual CFT?"Comment: 32 pages, 5 figures. v2: Author added, appendix on spacelike Green's function added, discussion of non-dependence on boundary Hamiltonian expande

De arbeidsdeelname van oudere werknemers

Heuvel, L.H. [Promotor]van den Lutjens, E. [Promotor

Bringing Europe to the Western Balkans: The Europeanisation of Croatia and Serbia Compared. College of Europe EU Policy Paper 6/2020.

This paper uses Europeanisation theory to explain why, through the enlargement policy of the European Union (EU), Croatia converged more successfully with the EU’s acquis than Serbia. It assesses two policy areas (compliance with the International Criminal Tribunal of the Former Yugoslavia and the Third Energy Package), considering three theoretical models (external incentives model, social learning model and lesson-drawing model) on three analytical levels (domestic, EU, and regional level). On all analytical levels, the dynamics of Serbia’s and Croatia’s Europeanisation processes best accord with the external incentives model: domestic elites weigh and act upon the costs and benefits of the EU’s demanded reforms. These are affected by third state interference and the EU’s enlargement strategies. The domestic level further provides evidence for the social learning model: the EU’s conduct affects the candidate states’ Europeanisation through discursive inclusion and exclusion. The paper finds no evidence for the lesson-drawing model: enlargement policy remains an EU-driven process. Croatia converged easier than Serbia to the EU acquis as it faced less political constraints domestically, is less prone to regional power interference, and was subjected to a more consistent enlargement strategy by the EU

Neighbourhood Europeanisation: extending a hand to Southern partners or securing internal security interests?

This thesis aims to shed new light on the usage of Europeanisation as a framework within which to evaluate the consequences of neighbourhood Europeanisation. This is done by looking at the diffusion of European values towards the EU’s Southern ENP Partners in the period of 2007 up and until 2013. A comparative case study is drawn, assessing the normative or structural nature of the Union’s narrative brought out by examining the reflections of the rapporteurs of the European Commission pertaining to the diffusion of the centrality of peace, democracy, and rule of law onto the Union’s Southern ENP Partner States through the European Neighbourhood Policy. Discussion of the two case studies of Morocco and Egypt presented show reflection of a normative approach by the EU, but also indicate that normative diffusion can only be effective if the necessary instruments are sufficiently developed.https://www.ester.ee/record=b5357128*es