Mean Field and Refined Mean Field Approximations for Heterogeneous Systems

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as n interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers. asymptotically exact for composed homogeneous objects under mild conditions. In this paper, we what happens when are heterogeneous. This can represent servers with different speeds contents popularities. We define an interaction model that allows obtaining asymptotic convergence results heterogeneous object behavior, and show error mean order $O(1/n)$. More importantly, how adapt refined approximation, developed by Gast et al., reduced O(1/n^2). To illustrate applicability our result, present two examples. The first addresses list-based model, RANDOM(m), which extension RANDOM policy. second supermarket model. These examples proposed approximations computationally tractable very accurate. They also moderate system sizes (30) tends be more accurate than simulations any reasonable simulation time.