Optimal Buffer and Bandwidth Allocation using Effective Bandwidth

We consider a single node which multiplexes a large number of traffic sources. We restrict ourselves to consideration of aggregates of i.i.d. flows that can modelled using effective bandwidth results. We are concerned with the amount of buffer and bandwidth that should be allocated to this aggregate, under a maximum overflow probability constraint. Unlike previous approaches which assume that the total buffer allocated to the class is either constant or linearly proportional to the number of sources, we wish to determine the minimum cost allocation given a cost per unit of each resource. We first consider a class of on/off fluid flows. We find that the optimal bandwidth allocation above the mean rate and the optimal buffer allocation are both proportional to the square root of the number of sources. Correspondingly, we find that the excess cost incurred by a fixed buffer allocation or by linear buffer allocations is proportional to the square of the percentage difference between the assumed number of sources and the actual number of sources and to the square root of the number of sources. We next consider a class of general i.i.d. sources for which the aggregate effective bandwidth is a decreasing convex function of buffer and linearly proportional to the number of sources. We find that the optimal buffer allocation is strictly increasing with the number of sources. Correspondingly, we find that the excess cost incurred by a fixed buffer allocation is an increasing convex function of the difference between the assumed number of sources and the actual number of sources. Keywords— Resource allocation, cost minimization, dimensioning