Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model

We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be explicitly and analytically discussed. The simplicity of the model, its intimate connection with the original Bass' modeling framework and the exact transient solutions offer a rather unique theoretical stylized framework to describe how innovation jointly develops in space and time.Comment: 20 pages, 4 figure

Cooperative dynamics of loyal customers in queueing networks

We consider queueing networks (QN's) with feedback loops roamed by "intelligent” agents, able to select their routing on the basis of their measured waiting times at the QN nodes. This is an idealized model to discuss the dynamics of customers who stay loyal to a service supplier, provided their service time remains below a critical threshold. For these QN's, we show that the traffic flows may exhibit collective patterns typically encountered in multi-agent systems. In simple network topologies, the emergent cooperative behaviors manifest themselves via stable macroscopic temporal oscillations, synchronization of the queue contents and stabilization by noise phenomena. For a wide range of control parameters, the underlying presence of the law of large numbers enables us to use deterministic evolution laws to analytically characterize the cooperative evolution of our multi-agent systems. In particular, we study the case where the servers are sporadically subject to failures altering their ordinary behavio

Imitation, proximity and growth - A collective swarm dynamics approach

This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is presented, based on range-dependent processes that describe how firms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. Using a particularly tractable approach, we are able to analyze how drastically different economic growth scenarios emerge from different imitation strategies. These emerging scenarios range from diffusive growth where the variance of productivity grows indefinitely, to balanced growth described by a traveling wave with fixed variance. The latter scenario is sustained only when imitation strength among firms exceeds a critical bifurcation threshold

Centralized Versus Decentralized Control - A Solvable Stylized Model in Transportation

To analyze the potential outcomes resulting from interaction between autonomous decision-making "smart parts" in logistics networks, we propose here an exactly solvable stylized model that is able to quantify how much the dynamics can be enhanced by (fully decentralized) agent-based mechanisms. Cost functions are introduced in order to compare the performances of centralized versus decentralized organization and we are enable to conclude that for time horizons shorter than a critical value, multi-agent interactions generate smaller costs that an optimal effective central controller

Multi-Agent Adaptive Mechanism Leading to Optimal Real-Time Load Sharing

We propose a new real-time load sharing policy (LSP), which optimally dispatches the incoming workload according to the current availability of the operators. Optimality means here that the global service permanently requires the engagement of a minimum number of operators while still respecting due dates. To cope with inherent randomness due to operator failures as well as non-stationary fluctuating incoming workload, any optimal LSP rule will necessarily rely on real-time updating mechanisms. Accordingly, a permanent monitoring of the traffic workload, of the queue contents and of other relevant dynamic state variables is often realized by a central workload dispatcher. In this contribution, we abandon such a "classical" approach and we propose a fully decentralized algorithm which fulfils the optimal load sharing process. The underlying decentralized decisions rely on a "smart tasks" paradigm in which each incoming task is endowed with an autonomous routing decision mechanism. Incoming jobs hence possess, in this paper, the status of autonomous agents endowed with "local intelligence". Stigmergic interactions between these agents cause the optimal LSP to emerge. We emphasize that beside a manifest strict relevance for applications, our class of models is analytically tractable, a rather uncommon feature when dealing with multi-agent dynamics and complex adaptive logistics systems

Weariness and Loyalty Loss in Recurrent Service Models

For recurrent service providers (fast-food, entertainment, medical care,...), retaining loyal customers is obviously a key issue. The customers' loyalty essentially depends on their service satisfaction defined via an ad-hoc utility function. Among several criteria, the utility function strongly depends on the past perceived waiting time. Moreover, the patience that customers consent to allow in waiting does often decrease as a function of the successive utilizations of the service (i.e. weariness). We propose here an idealized queueing model in which the customers' loyalty is determined only by the individual experience gained during the successive visits to a service (i.e. the waiting time and the number of services yet recieved). For regimes where the law of large numbers holds, a deterministic approach enables to analytically discuss the resulting multi-agent dynamics governing the customers' flows. One is able, in particular, to fully calculate, analytically, the characteristics of the emerging complex patterns (i.e. here structured temporal oscillations) which are observed to be strongly structurally stable