Delay-Constrained Shortest Paths: Approximation Algorithms and Second-Order Cone Models

Abstract

Routing real-time traffic with maximum packet delay in contemporary telecommunication networks requires not only choosing a path, but also reserving transmission capacity along its arcs, as the delay is a nonlinear function of both components. The problem is known to be solvable in polynomial time under quite restrictive assumptions, i.e., Equal Rate Allocations (all arcs are reserved the same capacity) and identical reservation costs, whereas the general problem is N P-hard. We first extend the approaches to the ERA version to a pseudopolynomial Dynamic Programming one for integer arc costs, and a FPTAS for the case of general arc costs. We then show that the general problem can be formulated as a mixed-integer Second-Order Cone (SOCP) program, and therefore solved with off-the-shelf technology. We compare two formulations: one based on standard big-M constraints, and one where Perspective Reformulation techniques are used to tighten the continuous relaxation. Extensive computational experi-

Delay-constrained routing problems: Accurate scheduling models and admission control

“…In all the previous developments in the literature [22,23,21,7,8], a "pessimistic" view has been taken where one assumes that…”

“…However, allocating the same rate at each link may be too constraining [21,6], i.e., results in much larger reserved rates (and, therefore, lower overall network performance) than would be possible if non-uniform rate allocation was allowed. Recently, [7] presented exact, approximate and heuristic approaches to that latter problem, showing that-despite N P-hardness-optimal solutions can be found in split-second times for realistic-sized networks. Furthermore, it has been shown in [8], by means of extensive simulations on real-world networks with realistic data, that joint path computation and non-uniform rate allocation leads to remarkable performance gains in terms of flow blocking probability, significantly outperforming simpler routing approaches (e.g.…”

“…Furthermore, all previous works-comprised [7,8]-have resorted to simplifying the latency formulae by assuming that the guaranteed rate of a flow is equal to its reserved rate. The reserved rate in fact lower bounds the guaranteed rate, and the two are only equal if all the links of the path are used up to capacity; in less loaded scenarios, the two may differ greatly.…”

“…In Section 3 we recall the MI-SOCP model proposed in [7] and used in [8] only for the case of SRP schedulers and under the bound assumption; we then improve it, and extend it to several other well-known schedulers. To do so, we need to introduce explicit admission control constraints that ensure that the existing flows still meet their deadline without changing their path and reserved rates; these constraints were implicit for SRP (under the bound assumption), but are not so (whether or not that assumption is maintained) for all other schedulers.…”

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AbstractIt has been recently shown [7] that the problem of routing a new packet flow in a computer network subject to a constraint on the worst-case end-to-end delay of its packets can be formulated as a Mixed-Integer Second-Order Cone Program (MI-SOCP), and solved with general-purpose tools on instances of realistic size in time compatible with real-time use. However, that result was obtained for only one of the classes of schedulers in use in today's networks, namely Strictly Rate-Proportional ones.

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