A key problem in networks that support advance reservations is the routing and time scheduling of
connections with flexible starting time and known data transfer size. In this paper we present a multicost
routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the
data should start and end transmission at each link so as to minimize the reception time at the destination,
or optimize some other performance criterion. The utilization profiles of the network links, the link
propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm.
We initially present a scheme of non-polynomial complexity to compute a set of so-called non-dominated
candidate paths, from which the optimal path can be found. We then propose two mechanisms to
appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of
polynomial complexity. We examine the performance of the algorithms in the special case of an Optical
Burst Switched network. Our results indicate that the proposed polynomial time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network
propagation delays and link-state update policies have on performance.