In a network where weighted fair-queueing schedulers are used at each link, a flow is guaranteed an end-to-end worst-case delays which depends on the rate reserved for it at each link it traverses. Therefore, it is possible to compute resource-constrained paths that meet target delay constraints, and optimize some key performance metrics (e.g., minimize the overall reserved rate, maximize the remaining capacity at bottleneck links, etc.). Despite the large amount of literature that has appeared on weighted fair-queueing schedulers since the mid '90s, this has so far been done only for a single type of scheduler, probably because the complexity of solving the problem in general appeared forbidding. In this paper, we formulate and solve the optimal path computation and resource allocation problem for a broad category of weighted fair-queueing schedulers, from those emulating a Generalized Processor Sharing fluid server to variants of Deficit Round Robin. We classify schedulers according to their latency expressions, and show that a significant divide exists between those where routing a new flow affects the performance of existing flows, and those for which this do not happen. For the former, explicit admission control constraints are required to ensure that existing flows still meet their deadline afterwards. However, despite this major difference and the differences among categories of schedulers, the problem can always be formulated as a Mixed-Integer Second-Order Cone problem (MI-SOCP), and be solved at optimality in split-second times even in fairly large networks
