________________________ 2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14, 2003
Chunxiao Chigan
Department of Electrical & Computer Engineering, Michigan Technological University,
EERC 121, 1400 Townsend Dr., Houghton, MI 49931
cchigan@mtu.edu
Ramesh Nagarajan and Gary Atkinson
Performance Analysis Department, Bell labs
101 Crawfords Corner Road, Holmdel, NJ 07733 atkinson@bell-labs.com
Abstract: A topology mapping scheme is presented in this short paper, which together with the
“shortest path” preprocessing, significantly simplifies the otherwise much more complicate mathematical modeling problem for our proposed joint multiplayer restoration mechanism.
1. Introduction
Recent advances in generalized multiprotocol label switching (GMPLS) opens up the possibility for coordinated actions across the two networking layers.
In this context, we proposed and evaluated a novel joint protection scheme for future packet-over-optical networks [1, 2]. There are two aspects that make the proposed joint restoration scheme novel and, furthermore, cost effective. 1) It captures the best tradeoff between the finer grooming granularity of the packet layer and the cheaper port cost of the optical layer; 2) It reuses network resources from both the primary paths and the paths existed for the link failure protection by the optical layer. Our study shows that the proposed joint restoration is much more cost-effective than the traditional pure packet layer restoration scheme, in all cases for realistic costs of the various components. For the details of this joint restoration scheme, please refer to [1, 2].
In this paper, we address one of the important mathematical modeling issues in this joint restoration approach: the topology mapping between the packet layer logical paths and the real physical paths of the packet routing/rerouting for this joint restoration scheme. Especially, we propose a topology mapping scheme, which together with the “shortest path” preprocessing, significantly simplifies the otherwise much more complicate mathematical modeling problem.
2. Motivation
Since the packet router ports are much more expensive (5 ~ 10 times) than the optical ports, to save the cost of the packet router ports, it makes sense to have the full OCh (optical channels) demands routed directly (via “express logical links”) at the optical layer between terminal nodes, thus avoiding unnecessary grooming at intervening packet router ports. The question now is, does this imply that, for the partial or complete packet layer rerouting within the full joint restoration scheme, the fractional traffic demands have to be aggregated at every intermediate router along their backup paths? The answer is NO. Since, although without grooming, it may cost more on link wavelengths for traffic recovery, but at the same time, the expensive router ports can be left out. Therefore, to let the joint multilayer restoration scheme capture the best tradeoff between these two factors (i.e., the finer grooming granularity and the cheaper optical port cost) for all packet traffic demands, the proposed model should allow the packet layer logical topology be flexible and not tightly coupled to the physical network topology.
This implies that the sub-OCh part of any demand does not have to be groomed at each node along the path in the packet layer, thus reducing unnecessary packet ports.
3. Topology Mapping Approach
The flexible packet logical topology mapping should be able to capture the best path choice for each endto-end traffic demand. However, to introduce the flexible packet topology mapping features into this design problem, the MIP (Mixed Integer
Programming) modeling of the proposed joint restoration problem is not a trivial task. Indeed, with the concern of the flexible mapping of the network logical topology and the physical topology, a node/site n in a network has to be described by both the packet router
Connect (OXC) n n
Router
OX and the Optical Crossat node n. Correspondingly, there are more variables, therefore, more complex mathematical formulations, to be added to capture the flexible packet layer topology mapping features.

________________________ 2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14, 2003
OXC6
R6
To simplify the mathematical modeling, we propose a novel approach, which mathematically formulates a modified full mesh version of the original network, as if the packet logical layer topology is equivalent to the physical layer topology, by introducing an additional preprocessing of the original network. It can be shown that this simplified modeling approach is capable of capturing the full flexibility of packet logical topology mapping.
R1
OXC1
20L
20L
OXC2
2L
R3
OXC3 modeling while keeps the optimality of the otherwise much more complicate problem. However, it is worthy to point out that, although this approach simplifies the mathematical modeling itself, since the full mesh network topology are more complex than the original network topology, the input matrix of the model is correspondingly bigger.
Reference:
[1] Chunxiao Chigan, Gary W. Atkinson, Ramesh
Nagarajan, “On Joint Restoration of Packet-over-
Optical Networks”, Proceedings of NFOEC 2002,
Dallas, Texas, September 2002.
[2] Chunxiao Chigan, “Network Resource Allocation and Provisioning Issues”, Ph.D. dissertation,
Aug., 2002, State University of New York at
Stony Brook.
[3] Integer and
Combinatorial Optimization , John Wiley & Sons,
New York, 1988
2L
R4
2L
R5
2L
OXC4
OXC5
Figure 1. The preprocessed full mesh logical topology implies flexible packet logical topology allowed
In fact, the preprocessing introduced here can be any kind of “shortest path” algorithm.
That is, by the preprocessing and finding out the “shortest path”
(i.e., the “minimum cost path” among all the possible optical layer alternatives) for every end-to-end packet router pair, the original packet-over-optical network is transformed into a full mesh network as shown in figure 1, in which the direct link between every endto-end packet router pair associates with the path of minimum link cost. With this full mesh network topology as the input network to be studied, even if the mathematical modeling of the joint restoration scheme is simplified by confining the packet layer logical topology equivalent to the physical layer network, the complete list of the all possible physical alternative paths can still be caught by the mathematical model, therefore, guarantee the best mapping of packet layer logical topology and the physical topology.
4. Conclusion
Our study [2] demonstrates that the topology mapping, by the introduction of the full mesh network via the “shortest path” preprocessing, significantly simplifies the MIP mathematical