Multicast capacity of optical ring network with hotspot traffic: The bi-directional WDM packet ring

doi:10.1016/j.osn.2011.05.002

Optical Switching and Networking

Volume 9, Issue 1, January 2012, Pages 61-80

https://doi.org/10.1016/j.osn.2011.05.002 Get rights and content

Abstract

Packet-switching WDM ring networks with a hotspot transporting unicast, multicast, and broadcast traffic are important components of high-speed metropolitan area networks. For an arbitrary multicast fanout traffic model with uniform, hotspot destination, and hotspot source packet traffic, we analyze the maximum achievable long-run average packet throughput, which we refer to as multicast capacity, of bi-directional shortest path routed WDM rings. We identify three segments that can experience the maximum utilization, and thus, limit the multicast capacity. We characterize the segment utilization probabilities through bounds and approximations, which we verify through simulations. We discover that shortest path routing can lead to utilization probabilities above one half for moderate to large portions of hotspot source multi- and broadcast traffic, and consequently multicast capacities of less than two simultaneous packet transmissions. We outline a one-copy routing strategy that guarantees a multicast capacity of at least two simultaneous packet transmissions for arbitrary hotspot source traffic.

Highlights

► Three segments can have maximum utilization in a WDM optical packet ring with multicast traffic. ► Hotspot source multicast can lead to a capacity of less than two simultaneous packet transmissions. ► One-copy routing guarantees a capacity of at least two simultaneous packet transmissions.

Introduction

Optical packet-switched ring wavelength division multiplexing (WDM) networks have emerged as a promising solution to alleviate the capacity shortage in the metropolitan area, which is commonly referred to as metro gap. Packet-switched ring networks, such as the Resilient Packet Ring (RPR) [1], overcome many of the shortcomings of circuit-switched ring networks, such as low provisioning flexibility for packet data traffic [2]. In addition, the use of multiple wavelength channels in WDM ring networks, see e.g., [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], overcomes a key limitation of RPR, which was originally designed for a single wavelength channel in each ring direction. In optical packet-switched ring networks, the destination nodes typically remove (strip) the packets destined to them from the ring. This destination stripping allows the destination node as well as other nodes downstream to utilize the wavelength channel for their own transmissions. With this so-called spatial wavelength reuse, multiple simultaneous transmissions can take place on any given wavelength channel. Spatial wavelength reuse is maximized through shortest path routing, whereby the source node sends a packet in the ring direction that reaches the destination with the smallest hop distance, i.e., traversing the smallest number of intermediate network nodes.

Multicast traffic is widely expected to account for a large portion of the metro area traffic due to multi-party communication applications, such as tele-conferences [15], virtual private network interconnections, interactive distance learning, distributed games, and content distribution. These multi-party applications are expected to demand substantial bandwidths due to the trend to deliver the video component of multimedia content in the High-Definition Television (HDTV) format or in video formats with even higher resolutions, e.g., for digital cinema and tele-immersion applications. While there is at present scant quantitative information about the multicast traffic volume, there is ample anecdotal evidence of the emerging significance of this traffic type [16], [17]. As a result, multicasting has been identified as an important service in optical networks [18] and has begun to attract significant attention in optical networking research as outlined in Section 1.1.

Metropolitan area networks consist typically of edge rings that interconnect several access networks (e.g., Ethernet Passive Optical Networks [19], [20]) and connect to a metro core ring [2]. The metro core ring interconnects several metro edge rings and connects to the wide area network. The node connecting a metro edge ring to the metro core ring is typically a traffic destination hotspot on the metro edge ring as it collects traffic from the other metro edge ring nodes for forwarding to the metro core ring (and onwards to the wide area network). At the same time, the node interconnecting metro edge and core rings is typically a traffic source hotspot on the metro edge ring as it receives the traffic arriving from the wide area network and the metro core ring for distribution to the other metro edge ring nodes. Similarly, the node connecting the metro core ring to the wide area network collects traffic from the other metro core ring nodes for forwarding to the wide area network and is thus a destination traffic hotspot on the metro core ring. Also, this node interconnecting the wide area network and the metro core ring receives traffic from the wide area network for forwarding to the other metro core ring nodes and is therefore a source traffic hotspot on the metro core ring. Examining the capacity of optical packet-switched ring networks with a traffic hotspot is therefore very important.

In this paper we examine the multicast capacity (maximum achievable long-run average multicast packet throughput) of bi-directional WDM optical ring networks with a single hotspot for a general fanout traffic model comprising unicast, multicast, and broadcast traffic. We consider an arbitrary traffic mix composed of uniform traffic, hotspot destination traffic (from regular nodes to the hotspot), and hotspot source traffic (from the hotspot to regular nodes). We study the widely considered node architecture that allows nodes to transmit on all wavelength channels, but to receive only on one channel. We initially examine shortest path routing by deriving bounds and approximations for the ring segment utilization probabilities due to uniform, hotspot destination, and hotspot source packet traffic. We prove that there are three ring segments (in a given ring direction) that govern the maximum segment utilization probability. For the clockwise direction in a network with nodes $1, 2, \dots, N$ and wavelengths $1, 2, \dots, Λ$ (with $N / Λ \geq 1$ ), whereby node 1 receives on wavelength 1, node 2 on wavelength 2, …, node $Λ$ on wavelength $Λ$ , node $Λ + 1$ on wavelength 1, and so on, and with node $N$ denoting the index of the hotspot node, the three critical segments are identified as

(i)
the segment connecting the hotspot, node $N$ , to node 1 on wavelength 1,
(ii)
the segment connecting node $Λ - 1$ to node $Λ$ on wavelength $Λ$ , and
(iii)
the segment connecting node $N - 1$ to node $N$ on wavelength $Λ$ .

The utilization on these three segments limits the maximum achievable multicast packet throughput. We observe from the derived utilization probability expressions that the utilizations of the first two identified segments exceed 1/2 (and approach 1) for large fractions of hotspot source multi- and broadcast traffic, whereas the utilization of the third identified segment is always less than or equal to 1/2. Thus, shortest path routing achieves a long run average multicast throughput of less than two simultaneous packet transmissions (and approaching one simultaneous packet transmission) for large portions of hotspot source multi- and broadcast traffic.

We specify one-copy routing which sends only one packet copy for hotspot source traffic, while uniform and hotspot destination packet traffic is still served using shortest path routing. One-copy routing ensures a capacity of at least two simultaneous packet transmissions for arbitrary hotspot source traffic, and at least approximately two simultaneous packet transmissions for arbitrary overall traffic. We verify the accuracy of our bounds and approximations for the segment utilization probabilities, which are exact in the limit $N / Λ \to \infty$ , through comparisons with utilization probabilities obtained from discrete event simulations. We also quantify the gains in maximum achievable multicast throughput achieved by the one-copy routing strategy over shortest path routing through simulations.

This paper is structured as follows. In the following subsection, we review related work. In Section 2, we introduce the detailed network and traffic models and formally define the multicast capacity. In Section 3, we establish fundamental properties of the ring segment utilization in WDM packet rings with shortest path routing. In Section 4, we derive bounds and approximations for the ring segment utilization due to uniform, hotspot destination, and hotspot source packet traffic on the wavelengths that the hotspot is not receiving on, i.e., wavelengths $1, 2, \dots, Λ - 1$ in the model outlined above. In Section 5, we derive similar utilization probability bounds and approximations for wavelength $Λ$ that the hotspot receives on. In Section 6, we prove that the three specific segments identified above govern the maximum segment utilization and multicast capacity in the network, and discuss implications for packet routing. In Section 7, we present numerical results obtained with the derived utilization bounds and approximations and compare with verifying simulations. We conclude in Section 8.

There has been increasing research interest in recent years for the wide range of aspects of multicast in general mesh circuit-switched WDM networks, including lightpath design, see for instance [21], traffic grooming, see e.g., [22], routing and wavelength assignment, see e.g., [23], [24], and connection carrying capacity [25]. Similarly, multicasting in packet-switched single-hop star WDM networks has been intensely investigated; see for instance [26], [27], [28]. In contrast to these studies, we focus on packet-switched WDM ring networks in this paper.

Multicasting in circuit-switched WDM rings, which are fundamentally different from the packet-switched networks considered in this paper, has been extensively examined in the literature. The scheduling of connections and cost-effective design of bi-directional WDM rings was addressed, for instance in [29]. Cost-effective traffic grooming approaches in WDM rings have been studied for instance in [30], [31]. The routing and wavelength assignment in reconfigurable bi-directional WDM rings with wavelength converters was examined in [32]. The wavelength assignment for multicasting in circuit-switched WDM ring networks has been studied in [33], [34], [35], [36]. For unicast traffic, the throughputs achieved by different circuit-switched and packet-switched optical ring network architectures are compared in [37].

Optical packet-switched WDM ring networks have been experimentally demonstrated; see for instance [38], [39], [12], [40], and studied for unicast traffic, see for instance [3], [4], [5], [7], [8], [9], [10], [11], [12], [14]. Multicasting in packet-switched WDM ring networks has received increasing interest in recent years [41], [10]. The photonics level issues involved in multicasting over ring WDM networks are explored in [42], while a node architecture suitable for multicasting is studied in [43]. The general network architecture and MAC protocol issues arising from multicasting in packet-switched WDM ring networks are addressed in [38], [44]. The fairness issues arising when transmitting a mix of unicast and multicast traffic in a ring WDM network are examined in [45]. The multicast capacity of packet-switched WDM ring networks has been examined for uniform packet traffic in [46], [47], [48], [49], [50], [51]. In contrast, we consider non-uniform traffic with a hotspot node, as it commonly arises in metro edge rings [52].

Studies of non-uniform traffic in optical networks have generally focused on issues arising in circuit-switched optical networks; see for instance [53], [54], [31], [55], [56]. A comparison of circuit-switching to optical burst switching network technologies, including a brief comparison for non-uniform traffic, was conducted in [57]. The throughput characteristics of a mesh network interconnecting routers on an optical ring through fiber shortcuts for non-uniform unicast traffic were examined in [58]. The study [59] considered the throughput characteristics of a ring network with uniform unicast traffic, where the nodes may adjust their send probabilities in a non-uniform manner. The multicast capacity of a single wavelength packet-switched ring with non-uniform traffic was examined in [60]. In contrast to these works, we consider non-uniform traffic with an arbitrary fanout, which accommodates a wide range of unicast, multicast, and broadcast traffic mixes, in a WDM ring network.

Section snippets

System model and notations

Let $N$ denote the number of network nodes, which we index sequentially by $i, i = 1, \dots, N$ , in the clockwise direction and let $M ≔ {1, \dots, N}$ denote the set of network nodes. For convenience, we label the nodes modulo $N$ , e.g., node $N$ is also denoted by 0 or $- N$ . While tunable transmitters are mature and cost-effective, tunable receivers suitable for packet-switching have remained difficult and expensive to built [61]. We consider therefore the family of node structures where each node can transmit on any

General properties of segment utilization

First, we prove a general recursion formula for shortest path routing.

Proposition 3.1

Let $λ \in {1, \dots, Λ}$ be a fixed wavelength. For all nodes $n \in {0, \dots, N - 1}$ , $P (\overset{↷}{{(n + 1)}_{λ}}) = P ({\overset{↷}{n}}_{λ}) + P (S = n) - P (G_{λ} = n) .$

Proof

There are two complementary events leading to $\overset{↷}{{(n + 1)}_{λ}}$ : (A) the packet traverses (on wavelength $λ$ ) both the clockwise segment ${\overset{↷}{u}}_{n + 1}$ and the preceding clockwise segment ${\overset{↷}{u}}_{n}$ , i.e., the sender is a node $S \neq n$ , and (B) node $n$ is the sender ( $S = n$ ) and transmits the packet in the clockwise direction, so that it traverses segment ${\overset{↷}{u}}_{n + 1}$

Uniform traffic

In the setting of uniform traffic, one has for all $n \in {- Λ + λ + 1, \dots, λ}$ and $k \in {0, \dots, η - 1}$ , for reasons of symmetry: $P_{α} ({\overset{↷}{n}}_{λ}) = P_{α} (\overset{↷}{{(n + k Λ)}_{λ}}) .$ For $n \in {- Λ + λ + 1, \dots, λ}$ , the difference between critical and non-critical edges, corresponding to Corollary 3.2, can be estimated by $0 \leq P_{α} (S \in {n, \dots, λ - 1}, G_{λ} \neq S) \leq P_{α} (S \in {n, \dots, λ - 1}) = \frac{λ - n}{N} .$

With shortest path routing, on average $N - E_{α} ({| CLG |}_{λ})$ segments are traversed on $λ$ to serve a uniform traffic packet. Equivalently, we obtain the expected number of traversed segments by summing the

Bounds on segment utilization for $λ = Λ$

For uniform traffic this case, of course, does not differ from the case $λ \neq Λ$ .

Evaluation of largest segment utilization and selection of routing strategy

With (4.25) and a detailed consideration of wavelength $λ = Λ$ , we prove in Appendix C the main theoretical result:

Theorem 6.1

The maximum segment utilization probability is $max_{n \in {1, \dots, N}} max_{λ \in {1, \dots, Λ}} P ({\overset{↷}{n}}_{λ}) = max {P ({\overset{↷}{1}}_{1}), P ({\overset{↷}{Λ}}_{Λ}), P ({\overset{↷}{N}}_{Λ})} .$

It thus remains to compute the three probabilities on the right-hand side. We have no exact result in the most general setting (it would be possible to give recursive formulas, but these would be prohibitively complex). However, we have given upper and lower bounds and approximations

Numerical and simulation results

In this section we present numerical results obtained from the derived bounds and approximations of the utilization probabilities as well as verifying simulations. We initially simulate individual, stochastically independent packets generated according to the traffic model of Section 2 and routed according to the shortest path routing policy using a simulator written in the C programming language. We determine estimates of the utilization probabilities of the three segments ${\overset{↷}{1}}_{1}$ , ${\overset{↷}{Λ}}_{Λ}$ , and ${\overset{↷}{N}}_{Λ}$

Conclusion

We have analytically characterized the segment utilization probabilities in a bi-directional WDM packet ring network with a single hotspot. We have considered arbitrary mixes of unicast, multicast, and broadcast traffic in combination with an arbitrary mix of uniform, hotspot destination, and hotspot source traffic. For shortest path routing, we found that there are three segments that can attain the maximum utilization, which in turn limits the maximum achievable long-run average multicast

Acknowledgments

We are grateful to Martin Herzog, formerly of EMT, INRS, and Ravi Seshachala of Arizona State University for assistance with the numerical and simulation evaluations.

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Design of micro-optics array to realize two dimensional perfect shuffle transform
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Citation Excerpt :
With the development of the optical digital computer, optical interconnection techniques have become one of the most important fields, attracting more and more researchers because of its potential to implement massively parallel architectures [1–3].
Two-dimensional (2D) perfect shuffle transform (PST) plays an important role in optical communication and optical information processing due to very high space-bandwidth product (SBWP) and spatial degrees of freedom. The planar-array of micro-blazed grating has been proposed to realize 2D PST based on its interesting properties such as high diffraction efficiency, small size, high degree of integration, and easy to fabricate. 2D PST could be realized in free space through controling the etching direction and the period of micro-blazed grating, which results in signal beams can reach the desired spatial position. Unlike the conventional method depending on the operation of dividing, magnification, interlacing, and superimposing, this approach, which mainly relies on the diffractive properties of signal beams and the distribution of light intensity, presents a single diffractive element to perform 2D PST. Thus, this approach has the advantages of high energy efficiency, high feasibility, compact in structure, and easy to integrate. The theoretical analyses and the experimental results show that it should be helpful in optical interconnection network, especially, in PS omega network.

^☆: Supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.

¹: Present address: The Robert Koch Institute, Berlin, Germany.

²: Present address: Universite Paris Descartes, France.

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Multicast capacity of optical ring network with hotspot traffic: The bi-directional WDM packet ring☆

Abstract

Highlights

Introduction

Section snippets

System model and notations

General properties of segment utilization

Uniform traffic

Bounds on segment utilization for λ=Λ

Evaluation of largest segment utilization and selection of routing strategy

Numerical and simulation results

Conclusion

Acknowledgments

Optical Fiber Telecommunications

Optical Fiber Technology

Optical Switching and Networking

Computer Communications

Computer Communications

Computer Communications

IEEE 802.17 resilient packet ring tutorial

IEEE Communications Magazine

Novel MAC protocol with idle detection for all-optical WDM ring networks

OSA Journal of Optical Networking

On providing metro ethernet services over transparent WDM optical rings

IEEE Network

MAC protocols and fairness control in WDM multirings with tunable transmitters and fixed receivers

IEEE Journal of Lightwave Technology

Modeling slotted WDM rings with discrete-time Markovian models

Computer Networks

Efficient QoS support in a slotted multihop WDM metro ring

IEEE Journal on Selected Areas in Communications

Metropolitan area packet-switched WDM networks: a survey on ring systems

IEEE Communications Surveys and Tutorials

Photonic packet WDM ring networks architecture and performance

IEEE Communications Magazine

Demonstration and system analysis of the HORNET

IEEE/OSA Journal of Lightwave Technology

Metro WDM networks: performancee comparison of slotted ring and AWG star networks

IEEE Journal on Selected Areas in Communications

A novel optical-header processing and access control system for a packet-switched WDM metro ring network

IEEE/OSA Journal of Lightwave Technology

Architectural design and bandwidth demand analysis for multiparty videoconferencing on SONET/ATM rings

IEEE Journal on Selected Areas in Communications

Wide-area IP multicast traffic characterization

IEEE Network

Monitoring IP multicast in the internet: recent advances and ongoing challenges

IEEE Communications Magazine

Optical layer multicast: rationale, building blocks, and challenges

IEEE Network

Just-in-time scheduling for multichannel EPONs

IEEE/OSA Journal of Lightwave Technology

Optimal multicasting of multiple light-trees of different bandwidth granularities in a WDM mesh network with sparse splitting capabilities

IEEE/ACM Transactions on Networking

Design and provisioning of WDM networks with multicast traffic grooming

IEEE Journal on Selected Areas in Communications

A new multicast wavelength assignment algorithm in wavelength-routed WDM networks

IEEE Journal on Selected Areas in Communications

Comprehensive performancee modeling and analysis of multicasting in optical networks

IEEE Journal on Selected Areas in Communications

Multicast connection capacity of WDM switching networks with limited wavelength conversion

IEEE/ACM Transactions on Networking

A survey of multicasting protocols for broadcast-and-select single-hop networks

IEEE Network

A hybrid multicast scheduling algorithm for single-hop WDM networks

IEEE/OSA Journal of Lightwave Technology

A reservation-based multicast protocol for WDM optical star networks

IEEE Journal on Selected Areas in Communications

On scheduling all-to-all personalized connections and cost-effective designs in WDM rings

IEEE/ACM Transactions on Networking

Cost-effective traffic grooming in WDM rings

IEEE/ACM Transactions on Networking

Bounds on segment utilization for $λ = Λ$