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+/spl epsiv/ of the optimal, where /spl epsiv/ is a parameter of our choice. The run times are polynomial in the input size and 1//spl epsiv/. We also provide a number of heuristics for the second problem and present simulation results. Previous work on related problems either focused on optimal solutions for special cost functions or on heuristics that have no performance guarantees. In contrast, we present provably good approximation algorithms and heuristics which apply to general cost functions.
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