We consider the fundamental problem of managing a bounded size queue buffer where traffic consists of packets of varying size, each packet requires several rounds of processing before it can be transmitted out, and the goal is to maximize the throughput, i.e., total size of successfully transmitted packets. Our work addresses the tension between two conflicting algorithmic approaches: favoring packets with fewer processing requirements as opposed to packets of larger size. We present a novel

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... el for studying such systems and study the performance of online algorithms that aim to maximize throughput.