In the past few years, there has been growing interest in wide area ``All Optical Networks'''' with {\em wavelength division multiplexing\/} (WDM), using {\em wavelength routing}. Due to the huge bandwidth inherent in optical fiber, and the use of WDM to match user and network bandwidths, the wavelength routing architecture is an attractive candidate for future backbone transport networks. A {\em virtual topology\/} over a WDM WAN consists of clear channels between nodes called {\em lightpaths}, with traffic carried from source to destination without electronic switching ``as far as possible'''', but some electronic switching may be performed. Virtual topology design aims at combining the best of optical switching and electronic routing abilities. Designing a virtual topology on a physical network consists of deciding the lightpaths to be set up in terms of their source and destination nodes and wavelength assignment. In this survey we first describe the context and motivations of the virtual topology design problem. We provide a complete formulation of the problem, describe and compare the formulations and theoretical results as well as algorithms, heuristics and some results in the current literature in the field. The reconfigurability issue, which is another attractive characteristic of optical networks, is also discussed and the literature surveyed. This survey is restricted to transport networks with wavelength routing. Similar virtual topology problems also arise in multihop broadcast local area optical networks, but this work does not directly apply to them and corresponding literature is not included in this survey. This survey also relates to the design of a static topology, not one in which individual lightpaths are set up and torn down in response to traffic demand.

A Survey of Virtual Topology Design Algorithms for Wavelength Routed Optical Networks

As the operation of our fiber-optic backbone networks migrates from interconnected SONET rings to arbitrary mesh topology, traffic grooming on wavelength-division multiplexing (WDM) mesh networks becomes an extremely important research problem. To address this problem, we propose a new generic graph model for traffic grooming in heterogeneous WDM mesh networks. The novelty of our model is that, by only manipulating the edges of the auxiliary graph created by our model and the weights of these edges, our model can achieve various objectives using different grooming policies, while taking into account various constraints such as transceivers, wavelengths, wavelength-conversion capabilities, and grooming capabilities. Based on the auxiliary graph, we develop an integrated traffic-grooming algorithm (IGABAG) and an integrated grooming procedure (INGPROC) which jointly solve several traffic-grooming subproblems by simply applying the shortest-path computation method. Different grooming policies can be represented by different weight-assignment functions, and the performance of these grooming policies are compared under both nonblocking scenario and blocking scenario. The IGABAG can be applied to both static and dynamic traffic grooming. In static grooming, the traffic-selection scheme is key to achieving good network performance. We propose several traffic-selection schemes based on this model and we evaluate their performance for different network topologies.

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A novel generic graph model for traffic grooming in heterogeneous WDM mesh networks

We present a new approach to the virtual-topology reconfiguration problem for a wavelength-division-multiplexing- based optical wide-area mesh network under dynamic traffic demand. By utilizing the measured Internet backbone traffic characteristics, we propose an adaptation mechanism to follow the changes in traffic without a priori knowledge of the future traffic pattern. Our work differs from most previous studies on this subject which redesign the virtual topology according to an expected (or known) traffic pattern, and then modify the connectivity to reach the target topology. The key idea of our approach is to adapt the underlying optical connectivity by measuring the actual traffic load on lightpaths continuously (periodically based on a measurement period) and reacting promptly to the load imbalances caused by fluctuations on the traffic, by either adding or deleting one or more lightpath at a time. When a load imbalance is encountered, it is corrected either by tearing down a lightpath that is lightly loaded or by setting up a new lightpath when congestion occurs. We introduce high and low watermark parameters on lightpath loads to detect any over- or underutilized lightpath, and to trigger an adaptation step. We formulate an optimization problem which determines whether or not to add or delete lightpaths at the end of a measurement period, one lightpath at a time, as well as which lightpath to add or delete. This optimization problem turns out to be a mixed-integer linear program. Simulation experiments employing the adaptation algorithm on realistic network scenarios reveal interesting effects of the various system parameters (high and low watermarks, length of the measurement period, etc.). Specifically, we find that this method adapts very well to the changes in the offered traffic.

Virtual-topology adaptation for WDM mesh networks under dynamic traffic

We present a new approach to the virtual-topology reconfiguration problem for wavelength-routed, optical wide-area networks under dynamic traffic demand. By utilizing the measured Internet backbone traffic characteristics, an adaptation mechanism is proposed to follow the changes in traffic without assuming that the future traffic pattern is known. In that sense, our work differs from previous studies which redesign the virtual-topology according to an expected (or known) traffic pattern, and then modify the connectivity to reach the target topology. The key idea of our approach is to adapt the underlying optical connectivity by measuring the actual traffic load on lightpaths continuously (periodically based on a measurement period) and reacting promptly to the imbalances caused by fluctuations in the traffic by adding or deleting one lightpath at a time. We aim to correct the encountered load imbalance directly, either by tearing down a lightpath that is lightly loaded or by setting up a new lightpath when congestion occurs. We introduce high and low watermark parameters on lightpath loads to detect any over/underutilized lightpath, and to trigger an adaptation step. The adaptation method is evaluated through simulations and the effect of system parameters (high and low watermarks, length of the measurement period) are investigated.

In this letter, we consider the problem of maximizing the number of lightpaths that may be established in a wavelength routed optical network (WRON), given a connection matrix, i.e., a static set of demands, and the number of wavelengths the fiber supports. The problem of establishing all the connections of the connection matrix using the fewest number of wavelengths has been investigated in Banerjee and Mukherjee (1996) and Baroni et al. (1998). We call the former problem max-RWA (problem of maximizing the number of lightpaths) and the latter problem min-RWA (minimizing the number of wavelengths). In this letter, we only consider WRONs with no wavelength conversion capabilities. We formulate the max-RWA problem when no wavelength conversion is allowed as an integer linear programme (ILP) which may be solved to obtain an optimum solution. We hope to solve the ILP exactly for small size networks (few nodes). For moderately large networks (tens of nodes) we develop algorithms based on solutions obtained by solving the LP-relaxation of the ILP formulation. Results obtained for networks such as NSFNET and EONNET are presented.

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Algorithms for routing and wavelength assignment based on solutions of LP-relaxations

We consider the problem of constructing logical topologies over a wavelength-routed optical network with no wavelength changers. We present a general linear formulation which considers routing traffic demands, and routing and assigning wavelengths to lightpaths, as a combined optimization problem. The formulation also takes into account the maximum number of hops a lightpath is permitted to take, multiple logical links in the logical topology, multiple physical links in the physical topology, and symmetry/asymmetry restrictions in designing logical topologies. The objective is to minimize congestion. We show by examples how equality and inequality logical degree constraints have a bearing on congestion. We prove that, under certain conditions, having equality degree constraints with multiple edges allowed in the design of logical topologies does not affect congestion. This helps in reducing the dimensionality of the search space and hence speeds up the search for an optimal solution of the linear formulation. We solve the linear formulation for small examples and show the tradeoff between congestion, number of wavelengths available and the maximum number of hops a lightpath is allowed to take. For large networks, we solve the linear formulation by relaxing the integer constraints. We develop topology design algorithms for large networks based on rounding the solutions obtained by solving the relaxed problem. Since the whole problem is linearizable, the solution obtained by relaxation of the integer constraints yields a lower bound on congestion. This is useful in comparing the efficiency of our heuristic algorithms. Following Bienstock and Gunluk (1995), we introduce a cutting plane which helps in obtaining better lower bounds on congestion and also enables us to reduce the previously obtained upper bounds on congestion.

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Design of logical topologies: a linear formulation for wavelength-routed optical networks with no wavelength changers

In this paper we present a exact linear formulation (mixed integer linear program) for designing a logical topology with no wavelength changers. Since the objective of our linear formulation is minimizing the maximum offered load on any link, which is called congestion, the resulting logical topology reflects the traffic intensities between the nodes. Our linear formulation yields a logical topology and routing and wavelength assignment for the logical links. Previously (see IEEE Journal on Selected Areas in Communications, vol.40, no.1, p.840-51, 1996) the problem of logical topology design is considered but the number of wavelengths the fiber can support is not a constraint. In this paper we take into consideration the number of wavelengths the fiber supports, the hop length of a logical link, and show the trade-offs involved in minimizing congestion. Since the whole problem is linearizable the solution obtained by relaxation of the integer constraints yields a lower bound on the congestion. This can be used to compare the efficiency of heuristic algorithms. We solve the problem exactly for a small size network and for large size networks we develop some heuristic algorithms to obtain a feasible solution using the solution obtained by relaxing the integer constraints. We introduce a cutting plane which enables us to reduce the previously obtained upper bounds on congestion. Numerical results for a six node wide area network and the National Science Foundation Network (NSFNET) are presented for various cases.

/pdf/design-of-logical-topologies-a-linear-formulation-for-1tcgwm5f8m.pdf

R.M. Krishnaswamy

Papers

Design of logical topologies: a linear formulation for wavelength-routed optical networks with no wavelength changers

Algorithms for routing and wavelength assignment based on solutions of LP-relaxations

Design of logical topologies: A linear formulation for wavelength routed optical networks with no wavelength changers