Approximate expected delay costs for call and contact centre models under light traffic regimes

This paper studies the form of certain expected delay costs as a function of the arrival rate for customers who pass through a service facility that allows for reneging and retrials. We show that, under certain light traffic conditions, these costs are continuously increasing and convex functions of the arrival rate (within a finite interval). This result is first explored for the processor sharing system, in which a penalty cost is incurred for reneging from the service facility for good without ever receiving service, and then we consider a system with a more general structure governing the output processes and costs incurred per unit time, but without the penalty cost. A suggested application for these results, in which game theoretic considerations are utilized for gauging customer behaviour within a decentralized context, is briefly discussed

Modeling trend progression through an extension of the Polya Urn Process

Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the network. The context of the trend is not included in our model. We show that every state of the RG model maps to a state of the Polya process. We find that the limit of the component size distribution of the RG model shows power-law behaviour. These results are also supported by simulations.Comment: 11 pages, 2 figures, NetSci-X Conference, Wroclaw, Poland, 11-13 January 2016. arXiv admin note: text overlap with arXiv:1502.0016

Optimal weighing schemes

We study the problem of determining the masses of a set of weights, given one standard weight, based on comparing two disjoint subsets of those weights with approximately equal mass. The question is how to choose a weighing scheme, i.e., different pairs of subsets, such that the masses can be determined as accurately as possible within a given number of measurements. In this paper we discuss a new way of using the so-called STS method of comparing two approximately equal masses, and we will give optimal weighing schemes which turn out to outperform schemes that are currently used by national metrology institutes

Modelling of trends in Twitter using retweet graph dynamics

In this paper we model user behaviour in Twitter to capture the emergence of trending topics. For this purpose, we first extensively analyse tweet datasets of several different events. In particular, for these datasets, we construct and investigate the retweet graphs. We find that the retweet graph for a trending topic has a relatively dense largest connected component (LCC). Next, based on the insights obtained from the analyses of the datasets, we design a mathematical model that describes the evolution of a retweet graph by three main parameters. We then quantify, analytically and by simulation, the influence of the model parameters on the basic characteristics of the retweet graph, such as the density of edges and the size and density of the LCC. Finally, we put the model in practice, estimate its parameters and compare the resulting behavior of the model to our datasets.Comment: 16 pages, 5 figures, presented at WAW 201

Dynamic routing policies for multi-skill call centers

We consider the problem of routing calls dynamically in a multiskill call center. Calls from different skill classes are offered to the call center according to a Poisson process. The agents in the center are grouped according to their heterogeneous skill sets that determine the classes of calls they can serve. Each agent group serves calls with independent exponentially distributed service times. We consider two scenarios. The first scenario deals with a call center with no buffers in the system, so that every arriving call either has to be routed immediately or has to be blocked and is lost. The objective in the system is to minimize the average number of blocked calls. The second scenario deals with call centers consisting of only agents that have one skill and fully cross-trained agents, where calls are pooled in common queues. The objective in this system is to minimize the average number of calls in the system. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on one-step policy improvement using the relative value functions of simpler queuing systems. Numerical experiments demonstrate the good performance of the routing policies. Finally, we discuss how the algorithm can be used to handle more general cases with the techniques described in this article. © 2009 Cambridge University Press

Parameter dependent convergence bounds and complexity measure for a class of conceptual hydrological models

We provide analytical bounds on convergence rates for a class of hydrologic models and consequently derive a complexity measure based on the Vapnik–Chervonenkis (VC) generalization theory. The class of hydrologic models is a spatially explicit interconnected set of linear reservoirs with the aim of representing globally nonlinear hydrologic behavior by locally linear models. Here, by convergence rate, we mean convergence of the empirical risk to the expected risk. The derived measure of complexity measures a model’s propensity to overfit data. We explore how data finiteness can affect model selection for this class of hydrologic model and provide theoretical results on how model performance on a finite sample converges to its expected performance as data size approaches infinity. These bounds can then be used for model selection, as the bounds provide a tradeoff between model complexity and model performance on finite data. The convergence bounds for the considered hydrologic models depend on the magnitude of their parameters, which are the recession parameters of constituting linear reservoirs. Further, the complexity of hydrologic models not only varies with the magnitude of their parameters but also depends on the network structure of the models (in terms of the spatial heterogeneity of parameters and the nature of hydrologic connectivity)