Elsevier

Computer Networks

Volume 54, Issue 5, 8 April 2010, Pages 716-725
Computer Networks

ILP formulations for non-simple p-cycle and p-trail design in WDM mesh networks

https://doi.org/10.1016/j.comnet.2009.09.019Get rights and content

Abstract

Conventional simple p-cycle (Preconfigured Protection Cycle) concept allows fast and capacity-efficient span protection in WDM mesh networks. Unlike simple p-cycle, non-simple p-cycle can traverse a node or span multiple times. The recently proposed p-trail (Pre-Cross-Connected Trail) concept further removes the cycle constraint by allowing arbitrary protection trails, leading to the most flexible and general design. Although non-simple p-cycles and p-trails are expected to be more capacity-efficient than simple p-cycles, it is still unclear how much capacity gain they can achieve compared with simple p-cycles. In this paper, we first point out some unique features of non-simple p-cycles and p-trails which are not fully explored in previous studies. This motivates us to formulate a new suite of ILPs (Integer Linear Programs) for optimal design of non-simple p-cycles and p-trails, based on which the achievable capacity gain over simple p-cycles can be investigated. Different from all the previous studies, the proposed ILPs are free of candidate cycle/trail enumeration, and can truly achieve an optimal design of non-simple p-cycles and p-trails. Our numerical results show that the capacity gain can be significant in some small-size networks with lightly-loaded traffic, but is generally trivial as the network size and the traffic load increase.

Introduction

WDM (Wavelength Division Multiplexing) technology allows hundreds of wavelengths to be multiplexed onto a single fiber for parallel transmission. To minimize service downtime and data loss upon a span/link failure (such as a fiber-cut), the most crucial issue is to achieve immediate optical recovery using a fast protection scheme. As pointed out in [1], the key for achieving fast protection is the pre-cross-connection of the backup path/wavelengths. Protection schemes can be further classified into span-based and path/segment-based schemes. Span-based protection tends to be faster in optical recovery, because failure detection and traffic switching are carried out locally by the two end nodes of the failed span and thus the signaling overhead is minimized. In this paper, we focus on span-based protection with pre-cross-connected backup wavelengths.

The classical p-cycle (Preconfigured Protection Cycle) concept [2] allows fast span protection with high capacity efficiency. Generally, a p-cycle refers to a simple p-cycle which traverses a node or span at most once. It is a ring-like loop-back pre-cross-connection using one backup wavelength (i.e., one unit of spare capacity) on each span it traverses. If a span is traversed by a p-cycle, it is called an on-cycle span of this p-cycle; otherwise it is a straddling span if its both end nodes are traversed by the p-cycle. Assume a single span failure at a time. The pre-cross-connected spare capacity reserved along a p-cycle can be shared to protect all its on-cycle and straddling spans. This leads to very high capacity efficiency. Meanwhile, only the two end nodes of the failed span need to carry out real time switching, and this leads to fast optical recovery. For a given network, an optimal set of simple p-cycles for 100% span protection can be found in two steps [2], [3]. The first step enumerates all the distinct simple cycles in the network to form a candidate set. The second step adopts an ILP (Integer Linear Program) to find an optimal set of p-cycles from the candidate set, so as to minimize the required spare or total capacity. The p-cycle concept is also extended to non-simple p-cycles [3], [4], where a non-simple p-cycle can traverse some nodes or spans multiple times (see Fig. 1a). So far, the same two-step approach based on non-simple cycle enumeration is the only way for non-simple p-cycle design. However, enumerating all non-simple cycles in a network is generally a formidable task.

Besides simple and non-simple p-cycles, the p-trail concept (Pre-Cross-Connected Trail or PXT [1]) is also introduced for fast protection. Let vi-1 and vi be the two end nodes of a span ei. A trail can be denoted by an alternating sequence (v0,e1,v1,e2,v2,,vn-1,en,vn) of nodes vi and spans ei, as shown in Fig. 1b. If a span is traversed by a trail, it is called an on-trail span; otherwise it is a straddling span if its two end nodes are traversed by the trail. As defined in [1], a trail can traverse a node multiple times but a span at most once. To facilitate our analysis on p-trails, in this paper we extend the concept by allowing a p-trail to traverse a span once per direction. If v0vn, the trail is called an open trail; otherwise it is a closed trail, which is indeed a simple or non-simple cycle. A p-trail is implemented by pre-cross-connecting the backup wavelengths along the trail. Similar to p-cycles, p-trails can achieve fast optical recovery due to the pre-cross-connection nature. Since simple p-cycles can be regarded as a special case of non-simple p-cycles and both simple and non-simple p-cycles are special cases of p-trails, theoretically a non-simple p-cycle solution will never has poorer capacity efficiency than its simple p-cycle counterpart, and a p-trail solution will give the best capacity efficiency.

Although it is obvious that non-simple p-cycles and p-trails can achieve better capacity efficiency than simple p-cycles, it is still unclear how much capacity gain they can achieve. This is due to two reasons. First, we notice that previous studies have ignored some distinct features of non-simple p-cycles and p-trails. Unlike a simple p-cycle (which can protect one unit of working capacity on each on-cycle span and two units on each straddling span), a non-simple p-cycle or p-trail may protect more than two units of working capacity on a particular on-cycle/on-trail or straddling span. Besides, the same set of on-cycle/on-trail spans can be pre-cross-connected in different patterns to generate different non-simple p-cycles/p-trails with different protection capabilities. Without observing those distinct features, a non-simple p-cycle or p-trail solution cannot be properly obtained. Second, designing an optimal non-simple p-cycle or p-trail solution is very complex. With the conventional two-step approach based on candidate cycle enumeration, even simple p-cycle design is very complex, because the total number of candidate cycles in a network increases exponentially with the network size. If non-simple cycles are considered, the size of the candidate set will be dramatically boosted. This is because multiple simple cycles can be geometrically combined in a combinatorial manner to form different non-simple cycles. Besides, multiple non-simple p-cycles can be generated from the same set of on-cycle spans depending on the pre-cross-connection patterns. Obviously, if a similar trail enumeration approach is adopted for p-trail design, the total number of candidate trails in a network will be far more than that of non-simple cycles. A large candidate set leads to a huge number of ILP variables which significantly slows down the optimization process. Although the size of the candidate set can be reduced by using only a subset of all the candidates in the design [3], [4], [5], [6], [7], the solution quality may be impaired accordingly [8]. Recently, some ILPs without candidate cycle enumeration were formulated for simple p-cycle design [8], [9], [10], but they cannot be directly extended to non-simple p-cycle or p-trail design.

It is clear that both non-simple p-cycles and p-trails have not been sufficiently studied so far, and finding the corresponding optimal solutions is still a difficult task. Motivated by the above observations, our work contributes to the related studies in the following three aspects: (1) the paper identifies those distinct features of non-simple p-cycles and p-trails, such that their potential benefits can be fully explored; (2) by taking those distinct features into account, a set of optimal ILP models is formulated for non-simple p-cycle and p-trail design. We claim that our ILPs are the first efforts on optimally solving the problem without candidate cycle/trail enumeration; and (3) based on the ILPs formulated, the paper investigates the capacity gain of non-simple p-cycles and p-trails over the conventional simple p-cycles. To the best of our knowledge, the paper is the first study that initiates an optimal performance comparison among simple p-cycles, non-simple p-cycles and p-trails. We conclude that the capacity gain can be significant in small-size and lightly-loaded networks but is generally trivial as network size and traffic load increase. This makes it clear that the capacity gain due to non-simple p-cycles and p-trails is generally trivial in most practical designs.

The rest of the paper is organized as follows. Section 2 highlights the distinct features of non-simple p-cycles and p-trails. Section 3 formulates the ILPs without candidate cycle/trail enumeration. Numerical results are presented in Section 4, and we conclude the paper in Section 5.

Section snippets

Distinct features of non-simple p-cycles and p-trails

In an undirected network, a simple p-cycle can protect one unit of traffic on each on-cycle span and two units on each straddling span [2]. Fig. 2a shows an example of simple p-cycle protection. For the p-cycle 0–4–1–3–2–0, if on-cycle span (2, 3) fails, it provides one backup path 2–0–4–1–3; if straddling span (0, 1) fails, it provides two backup paths 0–4–1 and 0–2–3–1 and thus two units of traffic on (0, 1) can be protected.

In Fig. 2, the number next to each span indicates the amount of traffic

ILPs for non-simple p-cycle and p-trail design

Without loss of generality, we consider an undirected network. Two scenarios are taken into account for comparison: a non-simple p-cycle/p-trail can traverse a span at most once per direction, or at most once in either direction. To facilitate our ILP formulations on both scenarios, we map each span (u, v) onto two directed vectors (u, v) and (v, u). If a vector is traversed by a p-cycle/p-trail, it is defined as an on-cycle/on-trail vector, and the corresponding span is an on-cycle/on-trail span.

Numerical results and discussion

We use hop-count as the span cost metric for all the examples (i.e., cuv=1 for each span (u, v)). The ILPs are implemented using ILOG CPLEX 11.0 on a server with 3 GHz Intel Xeon CPU 5160. To carry out accurate comparison among simple, non-simple p-cycles and p-trails, all the ILP problems are solved to generate optimal solutions.

We first consider the network in Fig. 9, where a number next to each span indicates the amount of traffic units on that span (same for other examples). Though we use

Conclusion

The paper investigated non-simple p-cycles and p-trails by identifying their distinct features which have never been explored in previous studies. We formulated a set of optimal ILP models for non-simple p-cycle and p-trail design. Our ILP models are characterized by removing candidate cycle/trail enumeration and taking all the identified features of non-simple p-cycles and p-trails into account, where a true optimal design can be achieved. Numerical results showed that in some small-size and

Bin Wu received the B.Eng. degree from Zhe Jiang University, Hangzhou, China, in 1993, M.Eng. degree from University of Electronic Science and Technology of China, Chengdu, China, in 1996, and Ph.D. degree from the University of Hong Kong, Hong Kong, in 2007. During 1997–2001, he served as the department manager of TI-Huawei DSP co-lab in Huawei Tech. Co. Ltd., Shenzhen, China. Currently, he is a postdoctoral research fellow at the University of Waterloo, Waterloo, Canada.

References (11)

  • T.Y. Chow et al.

    Fast optical layer mesh protection using pre-cross-connected trails

    IEEE/ACM Transactions on Networking

    (2004)
  • W.D. Grover et al.

    Cycle-oriented distributed preconfiguration: ring-like speed with mesh-like capacity for self-planning network restoration

    IEEE ICC ’98

    (1998)
  • D.A. Schupke et al.

    Optimal configuration of p-cycles in WDM network

    IEEE ICC ’02

    (2002)
  • C.G. Gruber

    Resilient networks with non-simple p-cycles

    IEEE ICT ’03

    (2003)
  • W.D. Grover, J. Doucette, Advances in optical network design with p-cycles: joint optimization and pre-selection of...
There are more references available in the full text version of this article.

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Bin Wu received the B.Eng. degree from Zhe Jiang University, Hangzhou, China, in 1993, M.Eng. degree from University of Electronic Science and Technology of China, Chengdu, China, in 1996, and Ph.D. degree from the University of Hong Kong, Hong Kong, in 2007. During 1997–2001, he served as the department manager of TI-Huawei DSP co-lab in Huawei Tech. Co. Ltd., Shenzhen, China. Currently, he is a postdoctoral research fellow at the University of Waterloo, Waterloo, Canada.

Kwan L. Yeung was born in 1969. He received his B.Eng. and Ph.D. degrees in Information Engineering from The Chinese University of Hong Kong in 1992 and 1995, respectively. He joined the Department of Electrical and Electronic Engineering, The University of Hong Kong in July 2000, where he is currently an Associate Professor, and the Information Engineering Program Co-Director. Before that, he has spent 5 years in the Department of Electronic Engineering, City University of Hong Kong as an Assistant Professor. During the summer of 1993, he served with the Performance Analysis Department, AT&T Bell Laboratories (now Bell Labs, Lucent Technologies), Holmdel, USA, as a Member of Technical Staff. His research interests include next-generation Internet, packet switch/router design, all-optical networks and wireless data networks. He has obtained two patents and published over 120 papers in international journals and conferences since 1993.

Pin-Han Ho received his B.Sc. and M.Sc. degrees from the Electrical and Computer Engineering, Department of National Taiwan University in 1993 and 1995, respectively. He started his Ph.D. studies in 2000 at Queen’s University, Kingston, Ontario, Canada, focusing on optical communications systems, survivable networking, and QoS routing problems. He finished his Ph.D. in 2002, and joined the Electrical and Computer Engineering Department at the University of Waterloo as an Assistant Professor in the same year. He is the author/co-author of more than 100 refereed technical papers and book chapters, and the co-author of a book on optical networking and survivability. He is the recipient of the Distinguished Research Excellence Award in the ECE Department at the University of Waterloo, the Early Researcher Award in 2005, the Best Paper Award at SPECTS ’02 and the ICC ’05 Optical Networking Symposium, and the Outstanding Paper Award in HPSR ’02.

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