We consider a generalized Jackson network with reneging customers in heavy traffic. In particular, each customer joining a particular station may abandon the network if his service does not begin within a station-dependent, exponential amount of time. We establish that in heavy traffic this system can be approximated by a multi-dimensional regulated Ornstein-Uhlenbeck process.

We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random network models to accommodate data limitations or prove asymptotic results. Our main theorems show that on large random networks, centrality measures are close ...

It is known that a generalized open Jackson queueing network after appropriate scaling (in both time and space) converges almost surely to a uid network under the uniform topology. Under the same topology, we show that the distance between the scaled queue length process of the queueing network and the uid level process of the corresponding uid network converges to zero in probability at an exp...

If work in psychology has clearly brought to light the existence of “conceptual flexibility” in the categorisation of objects, which led to a re-questioning of the traditional conception of categorisation which considers rigid and discontinuous categories, it is not the case in linguistics and psycholinguistics. We propose, through a highlighting of the role of analogy in the categorisation of ...

In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for the closed Jackson network. Our algorithm is based on Markov chain Monte Carlo (MCMC) method. Thus, our scheme returns an approximate solution, of which the size of error satisfies a given error rate. To our knowledge, the algorithm is the first polynomial time MCMC algorithm for closed Jackson network...

We develop an index of segregation based on two premises: (1) a measure of segregation should disaggregate to the level of individuals, and (2) an individual is more segregated the more segregated are the agents with whom she interacts. We present an index which satisfies (1) and (2), and that is based on agents’ social interactions: the extent to which Blacks interact with Blacks, Whites with ...

This paper analyzes the formation of communication networks when players choose endogenously their investment on communication links. We consider two alternative de…nitions of network reliability; product reliability, where the decay of information depends on the product of the strength of communication links, and min reliability where the speed of connection is a¤ected by the weakest communica...

S ocial structure, especially in the form of social networks, affects economic outcomes for three main reasons. First, social networks affect the flow and the quality of information. Much information is subtle, nuanced and difficult to verify, so actors do not believe impersonal sources and instead rely on people they know. Second, social networks are an important source of reward and punishmen...

I survey the literature on network formation in situations where the possible gains from cooperation of coalitions of agents are modeled by a coalitional game. I discuss the models that appear in the literature and their predictions on the networks that will be formed according to various equilibrium concepts, as well as the eventual payoffs to the players in equilibrium networks. ∗Most of what...

We propose an allocation rule that takes into account the importance of players and their links and characterizes it for a fixed network. Unlike previous rules, our characterization does not require component additivity. Next, we extend it to flexible networks à la Jackson (2005). Finally, we provide a comparison with other fixed (network Myerson and Position value) and flexible network (player...