Linear Programming Relaxations and a Heuristic for the Buffer Sharing Model - Discounted Case

We investigate a model for buffer management of multi-class traffic into a finite shared buffer. A hierarchy of increasingly stronger linear programming relaxations for this model is proposed. The number of hierarchies equals the number of job classes. Each relaxation in the hierarchy is constructed by projecting the original achievable performance region into a polytope with fewer variables and fewer constraints. Based on the first order LP relaxation, we propose a heuristic buffer management policy which can be obtained efficiently and is applicable to a wide range of reward functions including weighted sum of throughputs and weighted sum of buffer utilization. According to our simulations, the proposed heuristic performs close to optimum in all traffic conditions when the objective is to maximize the weighted sum of throughputs.