@techreport{eprints1620,
       publisher = {IMT Institute for Advanced Studies Lucca},
           month = {June},
            type = {CSA Technical Report},
           title = {Applying Mean-field Approximation to Continuous Time Markov Chains},
          author = {Anna Kolesnichenko and Alireza Pourranjabar and Valerio Senni},
            year = {2013},
     institution = {IMT Institute for Advanced Studies Lucca},
        keywords = {Continuous Time Markov Chains; Mean-field Approximation;  Performance Analysis; Model Checking},
        abstract = {The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent
deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications
of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique,
moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and 
uid model checking analysis techniques. },
             url = {http://eprints.imtlucca.it/1620/}
}