Speed scaling under QoS constraints with finite buffer

A single server with variable speed and a finite buffer is considered under a maximum packet drop probability constraint. The cost of processing by the server is a convex function of the speed of the server. If a packet arrives when the buffer is full, it is dropped instantaneously. Given the finite server buffer, the objective is to find the optimal dynamic server speed to minimize the overall cost subject to the maximum packet drop probability constraint. Finding the exact optimal solution is known to be hard, and hence algorithms with provable approximation bounds are considered. We show that if the buffer size is large enough, the proposed algorithm achieves the optimal performance. For arbitrary buffer sizes, constant approximation guarantees are derived for a large class of packet arrival distributions such as Bernoulli, Exponential, Poisson etc.