On the furthest-distance-first principle for data scattering with set-up

Message size, packetization, the set-up time, queueing delays, and the order of dispatching packets interact with one another in complicated ways. The paper studies how such interaction affects the performance of the data scattering operation. First, we show that the maximum buffer size needed is at most that of the largest packet. A counter-example demonstrates that the well-known furthest-distance-first (FDF) principle no longer guarantees optimal performance on trees when both the set-up time and packetization are allowed; however, it still works for linear arrays. The packetization problem with set-up time is shown to be reduced to a convex programming problem, which can be solved in polynomial time. Furthermore, we prove that a special class of data scattering problems is also reducible to the same optimization problem. In the absence of set-up time, the FDF principle can produce optimal schedules for trees. Finally, we show that, for any network, the FDF principle can be applied to any breadth-first spanning tree to obtain the optimal schedule in the absence of the set-up time