A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.

Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study the dynamic aspects of the coverage of a mobile sensor network that depend on the process of sensor movement. As time goes by, a position is more likely to be covered; targets that might never be detected in a stationary sensor network can now be detected by moving sensors. We characterize the area coverage at specific time instants and during time intervals, as well as the time it takes to detect a randomly located stationary target. Our results show that sensor mobility can be exploited to compensate for the lack of sensors and improve network coverage. For mobile targets, we take a game theoretic approach and derive optimal mobility strategies for sensors and targets from their own perspectives.

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies. 1

. The use of random fields, which allows one to take into account the spatial interaction among random variables in complex systems, becomes a frequent tool in numerous problems of statistical mechanics, spatial statistics, neural network modelling, and others. In particular, Markov random field based techniques can be of exceptional efficiency in some image processing problems, like segmentation or edge detection. In statistical image segmentation, that we address in this work, the model is generally defined by the probability distribution of the class field, which is assumed to be a Markov field, and the probability distributions of the observations field conditional to the class field. Under some hypotheses, the a posteriori distribution of the class field, i.e. conditional to the observations field, is still a Markov distribution and the latter property allows one to apply different bayesian methods of segmentation like Maximum a Posteriori (MAP) or Maximum of Posterior Mode (MPM). However, in such models the segmentation of textured images is difficult to perform and one has to resort to some model approximations. The originality of our contribution is to consider the markovianity of the couple (class field, observations field). We obtain a different model; in particular, the class field is not necessarily a Markov field. However, the posterior distribution of the class field is a Markov distribution, which makes possible bayesian MAP and MPM segmentations. Furthermore, the model proposed makes possible textured image segmentation with no approximations. Key words: hidden Markov fields, pairwise Markov fields, bayesian image segmentation, textured images. 1.

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processorsharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.

This paper deals with the statistical segmentation of multisensor images. In a Bayesian context, the interest of using hidden Markov random fields, which allows one to take contextual information into account, has been well known for about 20 years. In other situations, the Bayesian framework is insufficient and one must make use of the theory of evidence. The aim of our work is to propose evidential models that can take into account contextual information via Markovian fields. We define a general evidential Markovian model and show that it is usable in practice. Different simulation results presented show the interest of evidential Markovian field model-based segmentation algorithms. Furthermore, an original variant of generalized mixture estimation, making possible the unsupervised evidential fusion in a Markovian context, is described. It is applied to the unsupervised segmentation of real radar and SPOT images showing the relevance of the proposed models and corresponding segmentation methods in real situations.

Flow level behaviour of data networks depends on the allocation of link capacities between competing flows. It has been recently shown that there exist allocations with the property that the stationary distribution of the number of flows in progress on different routes depends only on the traffic loads on these routes and is insensitive to any detailed traffic characteristics. Balanced fairness refers to the most efficient of such allocations. In this paper we develop a general recursive algorithm for efficiently calculating the corresponding performance metrics like flow throughput. Several examples are worked out using this algorithm including the practically interesting case of tree networks. 1

While Erlang’s formula has helped engineers to dimension telephone networks for over eighty years, such a three-way “performance- demand- capacity ” relationship is still lacking for data networks. It may be argued that the enduring success of Erlang’s formula is essentially due to its simplicity: the call blocking rate does not depend on the distribution of call duration but on overall demand only. In this paper, we consider data networks and characterize those capacity allocations which have the same insensitivity property, in the sense that performance of data transfers does not depend on precise traffic characteristics such as the distribution of data volume but on overall demand only. We introduce the notion of “balanced fairness ” and prove some key properties satisfied by this insensitive allocation. It is shown notably that the performance of balanced fairness is always better than that obtained if flows are transmitted in a “store-and-forward ” fashion, allowing simple formula applying to the latter to be used as a conservative evaluation for network design and provisioning purposes. 1

Abstract. A model is described for generating hierarchically scaled spatial pattern as represented in a thematic raster map. The model involves a series of Markov transition matrices, one for each level in the scaling hierarchy. In full generality, the model allows the transition matrices to be different at each level, potentially making available a large number of parameters for landscape characterization. The model is self-similar when the transition matrices are all equal. A method is presented for fitting the model to data that take the form of a single-resolution thematic raster map. Explicit analytic solutions are obtained for the fitted parameters. The fitting method is based on a relationship between the hierarchical transitions in the model and spatial transitions at varying distance scales in the data map, a categorical analogy of the geostatistical variogram.

607] to obtain the sharp asymptotics of the steady state probability of a queueing network when one of the nodes gets large. We focus on a new phenomenon we call a bridge. The bridge cases occur when