A decomposition of the universal embedding space for the near polygon {{\mathbb H}_n}

Let ${{\mathbb H}_n, n \geq 1}$ , be the near 2n-gon defined on the 1-factors of the complete graph on 2n?+?2 vertices, and let e denote the absolutely universal embedding of ${{\mathbb H}_n}$ into PG(W), where W is a ${\frac{1}{n+2} \left(\begin{array}{c}2n+2 \\ n+1\end{array}\right)}$ -dimensional vector space over the field ${{\mathbb F}_2}$ with two elements. For every point z of ${{\mathbb H}_n}$ and every ${i \in {\mathbb N}}$ , let Δ _i (z) denote the set of points of ${{\mathbb H}_n}$ at distance i from z. We show that for every pair {x, y} of mutually opposite points of ${{\mathbb H}_n, W}$ can be written as a direct sum ${W_0 \oplus W_1 \oplus \cdots \oplus W_n}$ such that the following four properties hold for every ${i \in \{0,\ldots,n \}}$ : (1) ${\langle e(\Delta_i(x) \cap \Delta_{n-i}(y)) \rangle = {\rm PG}(W_i)}$ ; (2) ${\left\langle e \left( \bigcup_{j \leq i} \Delta_j(x) \right) \right\rangle = {\rm PG}(W_0 \oplus W_1 \oplus \cdots \oplus W_i)}$ ; (3) ${\left\langle e \left( \bigcup_{j \leq i} \Delta_j(y) \right) \right\rangle = {\rm PG}(W_{n-i}\oplus W_{n-i+1} \oplus \cdots \oplus W_n)}$ ; (4) ${\dim(W_i) = |\Delta_i(x) \cap \Delta_{n-i}(y)| = \left(\begin{array}{c}n \\ i\end{array}\right)^2 - \left(\begin{array}{c}n \\ i-1\end{array}\right) \cdot \left(\begin{array}{c}n \\ i+1\end{array}\right)}$ .     

A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline

This paper considers a simple discrete-time queueing model with two types (classes) of customers (types 1 and 2) each having their own dedicated server (servers A and B resp.). New customers enter the system according to a general independent arrival process, i.e., the total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. Service times are deterministically equal to 1 slot each. The system uses a “global FCFS” service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. As a consequence of the “global FCFS” rule, customers of one type may be blocked by customers of the other type, in that they may be unable to reach their dedicated server even at times when this server is idle, i.e., the system is basically non-workconserving. One major aim of the paper is to estimate the negative impact of this phenomenon on the queueing performance of the system, in terms of the achievable throughput, the system occupancy, the idle probability of each server and the delay. As it is clear that customers of different types hinder each other more as they tend to arrive in the system more clustered according to class, the degree of “class clustering” in the arrival process is explicitly modeled in the paper and its very direct impact on the performance measures is revealed. The motivation of our work are systems where this kind of blocking is encountered, such as input-queueing network switches or road splits.     

Modeling churn using customer lifetime value

The definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution is to redefine the notion of customer loyalty by considering it from a customer-centric viewpoint instead of a product-centric one. We hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer’s activity. Hence, a churner is defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease is used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classifiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures for prediction need to be revised and a more profit oriented focus may be desirable.     

Characterizations of the Suzuki tower near polygons

In recent work, we constructed a new near octagon \(\mathcal {G}\) from certain involutions of the finite simple group \(G_2(4)\) and showed a correspondence between the Suzuki tower of finite simple groups, \(L_3(2)< U_3(3)< J_2< G_2(4) < Suz\), and the tower of near polygons, \(\mathrm {H}(2,1) \subset \mathrm {H}(2)^D \subset \mathsf {HJ} \subset \mathcal {G}\). Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall–Janko near octagon \(\mathsf {HJ}\) is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, \(\mathrm {H}(2)^D\). We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for \(\mathrm {H}(2)^D\).     

Regular partitions of dual polar spaces

We describe several classes of regular partitions of dual polar spaces and determine their associated parameters and eigenvalues. We also give some general methods for computing the eigenvalues of regular partitions of dual polar spaces.     

The completion of the classification of the regular near octagons with thick quads

Brouwer and Wilbrink [3] showed the nonexistence of regular near octagons whose parameters s, t₂, t₃ and t satisfy s ≥ 2, t₂ ≥ 2 and t₃ ≠ t₂(t₂+1). Later an arithmetical error was discovered in the proof. Because of this error, the existence problem was still open for the near octagons corresponding with certain values of s, t₂ and t₃. In the present paper, we will also show the nonexistence of these remaining regular near octagons. MSC2000 05B25, 05E30, 51E12 Postdoctoral Fellow of the Research Foundation - Flanders     

A preemptive repeat priority queue with resampling: Performance analysis

In this paper, we analyze a discrete-time preemptive repeat priority queue with resampling. High-priority packets have preemptive repeat priority, and interrupted low-priority packets are subjected to independent retransmission attempts. Both classes contain packets with generally distributed transmission times. We show that the use of generating functions is beneficial for analyzing the system contents and packet delay of both classes. The influence of the priority scheduling on the performance measures is illustrated by some numerical examples. This work has been supported by the Interuniversity Attraction Poles Programme–Belgian Science Policy.     

Supplier quality improvement: The value of information under uncertainty

We consider supplier development decisions for prime manufacturers with extensive supply bases producing complex, highly engineered products. We propose a novel modelling approach to support supply chain managers decide the optimal level of investment to improve quality performance under uncertainty. We develop a Poisson–Gamma model within a Bayesian framework, representing both the epistemic and aleatory uncertainties in non-conformance rates. Estimates are obtained to value a supplier quality improvement activity and assess if it is worth gaining more information to reduce epistemic uncertainty. The theoretical properties of our model provide new insights about the relationship between the degree of epistemic uncertainty, the effectiveness of development programmes, and the levels of investment. We find that the optimal level of investment does not have a monotonic relationship with the rate of effectiveness. If investment is deferred until epistemic uncertainty is removed then the expected optimal investment monotonically decreases as prior variance increases but only if the prior mean is above a critical threshold. We develop methods to facilitate practical application of the model to industrial decisions by a) enabling use of the model with typical data available to major companies and b) developing computationally efficient approximations that can be implemented easily. Application to a real industry context illustrates the use of the model to support practical planning decisions to learn more about supplier quality and to invest in improving supplier capability.