We study a network model in which each network link is associated with a set of delays and costs. These costs are a function of the delays and reflect the prices paid in return for delay guarantees. Such a cost structure can model a setting in which the service provider provides multiple service classes with a different price and delay guarantee for each class. We are given a source node s, a sink node t, and an end-to-end delay constraint D. Our aim is to choose an s-t path and determine a set of per link delay guarantees along this path so as to satisfy the constraint D while minimizing the total cost incurred. In the case where the s-t path is known, we aim to optimally partition the end-to-end delay constraint into link constraints along the path. We present approximation algorithms for both problems, since they are known to be NP-hard. Our algorithms guarantee to produce solutions that are within a factor 1 + " of the optimal, where " is a parameter of our choice. The running ti..
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