Toward Understanding of Metastability in Cellular Networks: Emergence and Implications for Performance

We investigate the metastable behavior in a model of a cellular network with multiple service classes. While the Markov model provides an accurate "microscopic" model of the network behavior, the dimension of this model grows exponentially with the number of cells precluding solution of the corresponding Kolmogorov equations. Dimension of the mean-field approximation model grows only linearly with the number of cells making this approximation computationally tractable. Through numerical analysis we show that the equilibrium manifold of the mean-field model develops "folds" under increasing network load which give rise to multiple stable equilibria. These multiple equilibria can be interpreted as describing network\´s metastable states. By comparing simulation data with numerical computations we show that mean-field approximation can be used to predict equilibrium states of a realistic network. We construct a sample phase diagram showing distribution of metastable regions in the user load plane, derive a formula for the likelihood of successful service completion for metastable states and discuss performance characteristics of the network.