Optimal buffer sharing

We address the problem of designing optimal buffer management policies in shared memory switches when packets already accepted in the switch can be dropped (pushed-out). Our goal is to maximize the overall throughput, or equivalently to minimize the overall loss probability in the system. For a system with two output ports, we prove that the optimal policy is of push-out with threshold type (POT). The same result holds if the optimality criterion is the weighted sum of the port loss probabilities. For this system, we also give an approximate method for the calculation of the optimal threshold, which we conjecture to be asymptotically correct. For the N-ported system, the optimal policy is not known in general, but we show that for a symmetric system (equal traffic on all ports) it consists of always accepting arrivals when the buffer is not full, and dropping one from the longest queue to accommodate the new arrival when the buffer is full. Numerical results are provided which reveal an interesting and somewhat unexpected phenomenon. While the overall improvement in loss probability of the optimal POT policy over the optimal coordinate-convex policy is not very significant, the loss probability of an individual output port remains approximately constant as the load on the other port varies and the optimal POT policy is applied, a property not shared by the optimal coordinate-convex policy