We consider data losses in a single node of a packet-switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both mode
ls {have} a built-in critical behavior with {a sharp} transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.
We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. {em By construction}, the model has critical behavior with a sharp t
ransition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics.
