Overflow Management with Self-eliminations

Abstract

We study admission control with packet redundancy, where large data items, called superpackets, exceed some Maximum Transmission Unit (MTU) and therefore are broken into several smaller packets. It is assumed that each superpacket is comprised of k packets, and that a superpacket is considered useful if at least $(1-\beta )k$ of its packets arrive at the receiving end, for some redundancy parameter $\beta \in [0,1)$. Our goal is to maximize the total profit of useful superpackets, under an overloaded network, where we are forced to drop packets.

Our starting point is an algorithm, called priority, which is based on assigning a random priority to each superpacket. This algorithm was shown to perform well when $\beta = 0$, with and without a buffer. However, the performance of priority deteriorates with the increase of $\beta$, since it delivers too many packets for high priority superpackets. To tackle this issue, we propose an online algorithm which introduces randomized self-elimination of packets, called pse. When there is no buffer, we show that the competitive ratio of pse is better than the competitive ratio of priority, for the case where $(1-\beta )^3 \cdot \rho _{\max } \ge 1$, where $\rho _{\max }$ is the maximal burst size-router capacity ratio. For real-world values ($\rho _{\max } \le 1.5$), pse outperforms priority for $\beta \ge 0.14$. We also present simulation results, with a buffer, that demonstrate the behavior of pse in comparison with priority and tail-drop. It is shown that pse performs much better than priority when $\beta$ is large. In fact, it is shown that pse behaves at least as good as both algorithms.