The optimal buffer allocation problem

Pathwise probabilistic arguments are used to justify a simple rule of thumb by which buffer allocation can be carried out. The model for the underlying network is the skeleton of an open Jackson network. The problem of how to distribute in the best possible way a fixed number N of available buffer spaces among the nodes of the network is considered. The goal is to optimize some performance criterion associated with the time to buffer overflow, such as its mean or the probability that it exceeds some value. It is argued that for any such performance criterion the assignment should be done roughly in inverse proportion to the logarithms of the effective service rates at the nodes. Effective service means the ratio of the service rate to the stationary arrival rate at the node in the network with inifinite buffers