Path selection in user-controlled circuit-switched optical networks

Abstract

User-controlled circuit-switched optical networks are gaining popularity in an effort to fulfill the insatiable data transport needs of the online community. In this paper we consider the resource allocation challenges that arise in such networks, in particular problems related to construction of end-to-end lightpaths for carrying large multimedia streams. Specifically, we discuss variations of the least cost and widest path problems that address two unique aspects of the user-controlled environment. First, since network resources are exposed for user-control using a service-oriented software control plane, each lightpath is subject to an expiry time. Second, because Wavelength Division Multiplexing (WDM) and resource partitioning introduces multiple redundant paths, classic least cost path computations tend to yield multiple optimal solutions, and so it is useful to break ties among these in a judicious manner. We present polynomial-time path selection techniques that address these issues using efficient data structures. We also show the benefit of breaking ties in shortest path computations in a manner that reduces harmful fragmentation of capacity.

Introduction

Novel data-intensive network applications are pushing the limits of the hardware and software foundations of the Internet. Rising to the challenge, recent research has focused on optical network architectures and advanced transport protocols. One specific paradigm, motivated by cutting edge e-science but relevant to ordinary Internet users and service providers, is to virtualize optical circuits and expose them for user control through a service-oriented software platform [1]. Such a platform allows users to establish optical circuits, subsequently referred to as lightpaths, across multiple management domains, on demand. Because such circuits are provisioned over an optical medium and are dedicated, they offer superior capacity and reliability, and permit the safe use of customized high-performance transport protocols. Lightpaths are also straight-forward to access thanks to link layer encapsulation protocols, which make a lightpath appear as a single 1 Gb/s or 10 Gb/s Ethernet link for IP routing.

Routing computations in user-controlled optical networks pose some unique challenges. To begin with, such networks comprise a diverse pool of resources advertised for lease by a global community of users. In particular, the advertisement of a lightpath is subject to an expiry time, up to which the lightpath can be leased by another user. The latter user can then partition the acquired lightpath, if needed, and advertise unwanted partitions for lease. Thus, end-to-end path computations must be constrained to take into account the time for which a lightpath is desired versus the time for which resources are available. Furthermore, we face the problem of resource fragmentation: as lightpaths are traded and partitioned, it is possible that capacity for a lightpath is available during some contiguous interval of time, but cannot be leased because it is logically represented by a set of distinct resource advertisements. Fragmentation of capacity is a well-known phenomenon in SONET/SDH networks, but its analog in the time domain is unique to the user-controlled environment. Time fragmentation occurs, for example, when two lightpaths with the same endpoints are advertised for lease, say one Monday to Tuesday and the other Wednesday to Friday, but it is not possible to combine them to create a single lightpath available nonstop Monday to Friday.

The second challenge in path computation is the complexity of the logical network topology. This is a consequence of the way signals are multiplexed in optical networks, namely through wavelength division (WDM) and time division (TDM) multiplexing. Under the combination of WDM and TDM, which is typical in current networks, a single physical optical fiber may be represented by hundreds or even thousands of distinct logical lightpaths during path computation. Aside from the obvious implication on the cost of path computations, we face the problem that the naive path optimization strategy based on hop count may yield many optimal paths that differ in other practical ways. For example, one of the many shortest paths may be the best choice for reducing resource fragmentation.

Path computation plays a role not only in the forwarding of IP traffic in layer 3 of the OSI model, but also in the establishment of circuits. The fundamental graph-theoretic approach to intra-domain routing is to compute the least cost path between two vertices in a graph $G$ with vertex set $V$ and edge set $E$, based on some cost function $W:E\to {\mathbb{R}}^{+}$. The most popular cost metric is hop count, which is the number of routing or switching devices traversed in a particular network layer on the path to the destination after leaving the source. Centralized computations using information from link state routing algorithms can be performed using Dijkstra’s algorithm, which assumes non-negative link costs and runs in $\mathcal{O}(\left|E\right|+\left|V\right|log\left|V\right|)$ time given an efficient Fibonacci heap data structure [2]. Distributed distance vector computations are based on a form of the Bellman–Ford algorithm. In order to break ties among least cost paths, techniques have been proposed that consider additional criteria either through modifications to the path computation algorithm, or by applying successive least cost computations with different cost functions [3], [4].

The widest path problem is concerned with finding a path with the largest bottleneck capacity. This is a natural problem to consider in our case since one of the intended uses of user-controlled optical networks is to establish dedicated lightpaths for individual data transfers, with the natural goal of reducing transfer time. The solution can be obtained using a slightly modified version of Dijkstra’s or the Bellman–Ford algorithm, where the + operator is replaced with the max operator, and the cost metric is taken to be the inverse of capacity. The time complexity of the computation is the same as in the least-cost problem (since the additional cost is merely $\mathcal{O}\left(\left|E\right|\right)$).

Natural variations of the least cost and widest path problems consider multiple weight functions and user-specific constraints [5], [6]. The link-constrained least cost path problem selects a path with least cost under one weight function but only considers edges that satisfy a constraint expressed with respect to a second weight function. For example, the user may wish to find the shortest path consisting of links whose capacity meets or exceeds some required value. This problem can be solved easily by applying any least cost path algorithm on a modified input graph that contains only those edges that satisfy the link constraints. The cost-constrained widest path problem selects the path that is widest with respect to one weight function but whose total cost under a second weight function does not exceed a given threshold. For example, the user may wish to find the path with greatest end-to-end capacity that is no longer than some fixed number of hops. The problem can be solved in polynomial time by applying $\mathcal{O}\left(\left|E\right|\right)$ ordinary least cost path computations, namely one for each possible value of the weight function by which link width is measured.

In this paper, we examine path computation problems associated with establishment of an end-to-end lightpath in a user-controlled optical network. Our specific contributions are as follows:

• We formulate the novel problem of finding an end-to-end lightpath that minimizes the time needed to transfer a fixed volume of data, such as a multi-media file. We propose centralized and distributed solutions to this problem, which achieve efficiency through the use of sophisticated data structures.

• We propose strategies for breaking ties among optimal solutions in a least cost path computation, and present computational techniques based on sophisticated weight functions that can be used with standard least cost path algorithms. Our approach is general, in that it permits breaking ties according to a hierarchy of optimization criteria, not necessarily starting with hop count. We also show, through simulation, the effectiveness of breaking ties in shortest path computations in a manner that reduces harmful fragmentation of capacity.

The remainder of the paper is organized as follows. We begin by reviewing relevant technologies in Section 2. Next, in Section 3, we describe our network model. Path selection problems and solution techniques are then covered. In Section 4, we address the minimum transfer time problem. Then, in Section 5, we consider breaking ties in shortest path computations. Section 6 concludes the paper.