Loss asymptotics in large buffers fed by heterogeneous long-tailed sources (Q2713163)

A queueing model in which sessions of type \(i \in \{1,\ldots,N\}\) with Poisson flows with rate \(\lambda_i\) arriving into the system is studied. Each type of session remains active for a random time \(\tau_i\), and while active, a session transmits at a rate \(r_i\). Under the assumption of average load \(\rho = \sum_{i=1}^N r_i \lambda_i E[\tau_i] < C\), where \(C\) is a server capacity, it is shown that both the tail distribution of the stationary content and the loss asymptotic in finite buffers of size \(z\) behave approximately as \(z^{-\kappa J_0}\). This result generalizes a known result for the homogeneous case. In addition, long-tailed sessions are considered.