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References 1, 5 introduce a transport protocol that o ers partially ordered service for multimedia applications. This paper investigates how m uch the selection of a linear extension a ects system performance in a partially ordered service. We rst show h o w t o identify better linear extensions of a partial order, and then determine the performance gains by using such linear extensions at the time of transmission. To quantify linear extensions of a partial order, we propose a new metric pBuf -metric that is derived from bu ering probabilities. Since pBuf -metric is complex to calculate, a simpli ed version called -metric is also investigated. An OPNET simulation shows that for certain partial orders, a linear extension optimized according to these metrics provides some delay, and signi cant bu er utilization improvements over a non-optimal linear extension. Thus, prudent transmission order selection in a partially ordered service does improve system performance. Results also show that, in general, -metric is as e ective a s pBuf -metric in identifying better linear extensions of a partial order.