Upgrading unicast nodes to multicast-capable nodes in all-optical networks

Computer Networks 55 (2011) 2005–2021

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Computer Networks journal homepage: www.elsevier.com/locate/comnet

Upgrading unicast nodes to multicast-capable nodes in all-optical networks Tony K.C. Chan a, Yiu-Wing Leung b,⇑, Gaoxi Xiao c a b c

Emperor Group, Emperor Group Centre, 288 Hennessy Road, Wanchai, Hong Kong Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

a r t i c l e

i n f o

Article history: Received 12 February 2010 Received in revised form 29 November 2010 Accepted 3 February 2011 Available online 23 February 2011 Keywords: All-optical Networks Unicast Multicast Node architecture

a b s t r a c t We consider the problem of upgrading unicast all-optical networks to support multicast communication. In upgrading, it is necessary to modify the existing nodes to support optical multicast switching. It is desirable to: (i) retain and use the existing node components while adding the necessary components so that the upgrading cost is small, and (ii) avoid major modification of the existing node architecture so that the upgrading overhead is small. We propose three designs to realize these two goals: (i) the pre-splitting design adds splitting modules before the existing optical switches where a splitting module can split incoming light beams into multiple ones, (ii) the post-splitting design adds splitting modules after the existing optical switches, and (iii) the pre/post-splitting design adds splitting modules before and after the existing optical switches. The pre-splitting design and post-splitting designs are simpler and involve lower upgrading overhead, while the pre/post-splitting design gives smaller blocking probability and achieves better cost-effectiveness by suitably selecting the number of splitting modules of each type. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction All-optical networks provide very high data rates for bandwidth-demanding applications. Some of these applications involve multicast communication (e.g., various multimedia entertainment services, content distribution, virtual private networks and distributed computing [1–3]). If an all-optical network supports multicast at the optical layer, it provides a light-tree [4] to each multicast session such that the source uses one optical transmitter to send data to multiple destinations through this lighttree (e.g., see Fig. 1(a)). Multicast at the optical layer has been an active research area in the literature (e.g., see [1–13] and the references therein). To realize light-trees, the network must have multicast-capable nodes [1] which can split an incoming light beam into multiple light beams and switch them to the desired outgoing fibers.

⇑ Corresponding author. E-mail addresses: [email protected] (T.K.C. Chan), ywleung@ comp.hkbu.edu.hk (Y.-W. Leung), [email protected] (G. Xiao). 1389-1286/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comnet.2011.02.010

Several elegant designs of multicast-capable nodes were proposed in the literature [4,14–16]:  Sahasrabuddhe and Mukherjee [4] proposed a multicast-capable node shown in Fig. 1(b). It uses a light splitter [17,18] to split an incoming light beam into m identical light beams (m is called the fanout of the splitter) and then uses an optical switch to switch these light beams to the desired outputs.  Hu and Zeng [14] proposed a multicast-capable node shown in Fig. 1(c). It uses a new switch design, called split-and-delivery (SaD) switches, to split an incoming light beam and switch the resulting light beams to the desired outputs.  Yang et al. [15] proposed an enhanced design of SaD switch shown in Fig. 1(d). It uses passive light combiners instead of 2  1 switches, so its cost is lower.  Ali and Deogun [16] proposed another design of SaD switch shown in Fig. 1(e). In this SaD switch, only the incoming light beam with splitting requirement will be directed to the light splitter for splitting and then switching (see Fig. 1(e)).

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Destination nodes

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Multicast-capable node SaD Wavelength switches Wavelength Incoming demultiplexers (NxN) multiplexers Outgoing fibers fibers 1 1 1 2

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Light Optical Incoming splitters gates channels

2x1 switches

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Light combiners Outgoing channels 1

SaD switch Incoming channels 1 2

2

2

N

N

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Outgoing Optical 2x1 gates switches channels 1 2

Optical switch (NxN+1)

N

Light splitter

(e) (d) Fig. 1. Existing designs of multicast-capable nodes. (a) Example of a light-tree and the functions of multicast-capable nodes. (b) 2  2 multicast-capable wavelength-routing switch [4]. (c) Multicast-capable node using SaD switches [14]. (d) Design of SaD switch with light combiners [15]. (e) Design of SaD switch with splitter sharing [16].

The above designs can cost-effectively construct new multicast-capable nodes from the beginning. In this paper, we consider a different and new problem in designing multicast-capable nodes: how to upgrade an existing unicast node to a multicast-capable node. This problem arises when a telecommunication company wants

to upgrade its existing unicast all-optical network to support multicast communication. After upgrading, the network can support both unicast and multicast services and there are two resulting advantages: (i) The telecommunication company can create new business opportunities because it can support or offer multicast services (e.g.,

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high-definition TV channels, online cinema, support for grid computing, etc.). (ii) Using one network for both unicast and multicast services, network resources/equipment can be shared for better cost-effectiveness. Although the existing designs of multicast-capable nodes [4,14–16] can cost-effectively construct new multicast-capable nodes from the beginning, they are not directly applicable to upgrading an existing unicast node to a multicast-capable node because they would involve significant cost and difficulty for the following reasons: 1. Some designs require special optical switches with embedded splitting capability [14,15] (see Fig. 1(c) and (d)). If these designs are adopted for upgrading, the existing optical switches in the unicast node cannot be reused. This is undesirable because optical switches are very expensive. 2. Some designs require optical switches of different dimensions [4,16] (see Fig. 1(b) and (e)). It may be costly and difficult to increase the dimension of the existing optical switches in the unicast node. For example, it is very difficult to increase the dimension of MEMS optical switches [19–22] because all mirrors of each mirror array are fabricated on a single substrate [20,21]; it involves significant overhead and difficulty to increase the dimension of multi-stage switches because it is necessary to rearrange the interconnections among the existing and the newly-added switch elements while the resulting insertion loss should be acceptably small; etc. In this paper, we investigate how to upgrade an existing unicast node to a multicast-capable node to realize two goals: (i) retain and use the existing node components while adding the necessary components so that the upgrading cost is small, and (ii) avoid major modification of the existing node architecture so that the upgrading overhead is small. It would be challenging to achieve very good performance while fulfilling these two goals because these goals would become design constraints (e.g., the constraint of reusing the existing node components) and reduce the design freedom. To solve this new problem, we propose three upgrading designs called pre-splitting, postsplitting and pre/post-splitting. Each of these designs add splitting modules to the existing node architecture, so that the existing components such as optical switches can be reused (i.e., small upgrading cost) and the existing node architecture is essentially kept (i.e., small upgrading overhead). We demonstrate that each design has its own features and merits. Our work is different from the existing ones in three major aspects: (i) Different problem: Our designs are used for upgrading existing nodes while the existing designs are used for constructing new nodes from the beginning. (ii) Different goals and different designs: Our designs realize two goals (namely, reusing the existing node components for low cost and avoiding major architectural modification for low overhead), while the existing designs do not consider these goals. As a result, our designs are significantly different from the existing ones. For example, most existing designs focus on designing the split-and-delivery

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switches as shown in Fig. 1(c)–(e), but our design cannot adopt this approach because we reuse the existing optical switches. (iii) Different applicability: The proposed designs are applicable to both single-fiber and multi-fiber networks. In contrast, the existing designs were not designed for multi-fiber networks (e.g., their splitting loss in multifiber networks would be large as we will demonstrate in Section 3.4). The rest of this paper is organized as follows. In Section 2, we describe three upgrading designs for single-fiber networks. In Section 3, we generalize these designs to multifiber networks. In Section 4, we conduct a cost analysis and show that upgrading using our designs is more costeffective than replacement (i.e., replacing the existing unicast optical switches by new multicast-capable optical switches). In Section 5, we present simulation results to evaluate the effectiveness of the proposed designs. In Section 6, we conclude our study. 2. Upgrading designs for single-fiber networks In this section, we propose three designs to upgrade a unicast node to a multicast-capable node in single-fiber networks. These nodes are used for lightpath switching. Nevertheless, the proposed designs are also applicable to packet switching if the nodes include the necessary components and control functions (such as buffer and conflict resolution function). We define two terms: (i) a light splitter has a fanout of m if it can split a light beam into m light beams. (ii) A multicast session has a fanout of m if its light beam is to be split into m light beams within the node. 2.1. Pre-splitting design In pre-splitting design, we add pre-splitting modules before the existing optical switches of the node, where a presplitting module can split each incoming light beam into multiple light beams. Fig. 2(a) shows an N  N pre-splitting module. Each incoming channel is connected to a light splitter with fanout m, where m is a design choice and is practically small (e.g., m = 2 or 3). For light splitter i, its m outputs are respectively connected to m optical gates and then to light combiners [(i + x  2) modN] + 1 for x = 1, 2, . . . , m. The presplitting module is modified from the SaD switch shown in Fig. 1(d), where the main difference is that the module provides only the splitting function without the switching function. Because of this major difference, the pre-splitting module can use light splitters with small fanout m to: (i) reduce the number/cost of optical gates, (ii) reduce the cost of amplification as the number of split light beams is smaller, and (iii) avoid the problems in non-ideal amplification of weak light beams [1,23] as the split light beams have relatively stronger power. A pre-splitting module is operated as follows. If an incoming light beam is to be split into n light beams (n 6 m) within the module, it is first split into m light beams by a light splitter. Then these m light beams reach m respective optical gates. By controlling the on–off states

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(a) Existing node architecture Upgraded node architecture Optical Pre-splittingOptical Wavelength switches Wavelength Wavelength modules switches Wavelength Incoming demultiplexers (NxN) Incoming demultiplexers (NxN) (NxN) multiplexers Outgoing multiplexers Outgo fibers fibers fibers fiber 1 Pre 1 1 1 1 1 Upgrading 2

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(b) Fig. 2. Pre-splitting design for single-fiber networks. (a) N  N pre-splitting module. (b) Upgrading an existing unicast node to a multicast-capable node.

of these optical gates, n of these m beams can pass through the optical gates to reach n respective light combiners and then n outputs of the module. The module properly controls its optical gates such that at most one light beam goes to each light combiner at a time. The pre-splitting module provides the splitting function but does not provide the switching function (it splits each light beam into m light beams where m is very small in practice (e.g., m = 2), so it does not realize all possible input-to-output connections for switching). The switching function is provided by reusing the existing optical switches. In this manner, the pre-splitting modules (i.e., the components required for upgrading) have low complexity, low cost and low splitting loss. Fig. 2(b) shows the process of upgrading a unicast node to a multicast-capable node. If an incoming light beam is to be multicast to n outputs, it is split into n light beams by a pre-splitting module, and then these n light beams are switched to the n desired outputs by an optical switch. In this manner, the upgraded node can support multicast switching. The pre-splitting design retains and uses the existing node components while adding the pre-splitting modules (see Fig. 2(b)), so that the upgrading cost is small. Moreover, it essentially keeps the original node architecture (see Fig. 2(b)), so that the upgrading overhead is small.

2.2. Post-splitting design In post-splitting design, we add post-splitting modules after the existing optical switches of the node, where a post-splitting module can split certain incoming light beams into many outgoing light beams. Fig. 3(a) shows an N  N post-splitting module. It has s splitting-capable ports which can split and deliver incoming light beams to at most all output ports. s is a design choice and is practically small for better cost-effectiveness. Each splitting-capable port is connected to a light splitter with fanout N, then to N optical gates and then to N light combiners. The post-splitting module is modified from the SaD switch shown in Fig. 1(e), where the main modification is to use multiple light splitters in order to support multiple multicast sessions. A post-splitting module is operated as follows. If an incoming light beam is to be split and delivered to n specific outputs, it enters the post-splitting module through a splitting-capable port. It is split into N light beams by a light splitter to reach N respective optical gates. By controlling the on–off states of the optical gates, n of these N light beams pass through the optical gates to reach n light combiners and then the n desired outputs. The module properly controls its optical gates such that at most one light beam goes to each light combiner at a time.

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NxN post-splitting module Incoming channels 1

Light Optical splitters gates

Light combiners

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Upgraded node architecture Pre-splitting Optical Post-splitting modules switches modules Wavelength Wavelength Incoming demultiplexers (NxN) (NxN) (NxN) multiplexers Outgoing fibers fibers Post 1 Pre 1 1

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Fig. 4. Pre/post-splitting design for single-fiber networks. It adds presplitting and post-splitting modules to upgrade an existing unicast node to a multicast-capable node.

…

N Splitting-capable ports

N …

2.3. Pre/post-splitting design

(a) Upgraded node architecture Optical Post-splitting Wavelength switches modules Wavelength Incoming demultiplexers (NxN) (NxN) multiplexers Outgoing fibers fibers 1 1 Post 1 2

2

Post

2

N

W

Post

N

(b) Fig. 3. Post-splitting design for single-fiber networks. (a) N  N postsplitting module with s splitting-capable ports. (b) Upgraded multicastcapable node.

Fig. 3(b) shows the upgraded node in which a postsplitting module is added after each optical switch. If an incoming light beam to the node is to be multicast to n outputs, it is switched by an optical switch to an available splitting-capable port of the post-splitting module. This module splits it into n light beams and delivers them to the n desired outputs. In this manner, the upgraded node can support multicast switching. The post-splitting design retains and uses the existing node components while adding the post-splitting modules (see Fig. 3(b)), so that the upgrading cost is small. Moreover, it essentially keeps the original node architecture (see Fig. 3(b)), so that the upgrading overhead is small.

In pre/post-splitting design, we add pre-splitting modules before the existing optical switches and post-splitting modules after these optical switches. Fig. 4 shows the upgraded node. This design integrates the strengths of both types of splitting modules. The pre-splitting modules can costeffectively handle many multicast sessions with small fanout while the post-splitting modules can cost-effectively handle a few multicast sessions with large fanout. Using the pre/post-splitting design, the node uses the presplitting modules to handle the multicast sessions with small fanout and the post-splitting modules to handle the multicast sessions with large fanout. In this manner, the node can effectively handle all traffic patterns. The pre/post-splitting design retains and uses the existing node components while adding the pre-splitting and post-splitting modules (see Fig. 4), so that the upgrading cost is small. Moreover, it essentially keeps the original node architecture (see Fig. 4), so that the upgrading overhead is small. 2.4. Discussion and comparison Each of the proposed designs has its own features and merits: (1) Pre-splitting design: This design can effectively handle many multicast sessions with small fanout. It is because the pre-splitting module can costeffectively split each incoming beam into a small number of beams. This design is simpler and hence involves smaller upgrading overhead than the pre/ post-splitting design.

Table 1 Necessary components required when an existing unicast node has an unused switch port and it is upgraded using the proposed design (post-splitting design) and the existing design (shown in Fig. 1(e)). Design

Necessary components per wavelength Active components

Post-splitting design

 N optical gates

Existing design in Fig. 1(e)

 N optical gates  N 2  1 optical switches

Passive components  1  N light splitter  N–1 2  1 light combiners  1  N light splitter

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(2) Post-splitting design: This design can effectively handle a few multicast sessions with large fanout. It is because the post-splitting module can costeffectively split a few light beams into many ones. This design is simpler and hence involves smaller upgrading overhead than the pre/post-splitting design. (3) Pre/post-splitting design: This design can effectively handle multicast sessions with small and large fanout because it uses both pre-splitting and post-splitting modules. It gives smaller blocking probability and achieves better cost-effectiveness by suitably selecting the number of splitting modules of each type (see the simulation results in Section 5).

3. Upgrading designs for multi-fiber networks When a backbone network supports many users, its traffic volume is large and hence each link may need multiple fibers in order to provide sufficient wavelength channels (e.g., see Fig. 5). The resulting network, called multi-fiber networks [13,28–35], can provide large enough bandwidth to fulfill the ever-increasing bandwidth demand [24–26] (e.g., it is envisioned that the bandwidth demand will grow exponentially in the coming 20 years [27]). In fact, multi-fiber networks have been an active research area in the literature (e.g., see [13,28–35] and the references therein). These networks have a salient property that they have larger flexibility in channel assignment. To illustrate this property, we consider the multi-fiber network and its node architecture in Fig. 5. If we want to establish a lightpath from incoming link 1 to outgoing link 2, we can select any one of the incoming fibers 1, 2, 3 and 4 and any one of the outgoing fibers 5, 6, 7 and 8. This flexibility is available in multifiber networks but it is not available in single-fiber networks.

In Section 4, we will carry out a cost analysis, showing that upgrading is more cost-effective than replacement (i.e., replacing the existing unicast optical switches by new multicast-capable optical switches). We consider an interesting special case here. Suppose an existing unicast node has an unused switch port and it is upgraded using the existing design shown in Fig. 1(e). In this case, the existing optical switch can be reused. Nevertheless, our designs are still preferable for two reasons: (1) Our design has lower cost because it requires fewer active components to provide the same number of ports for supporting multicast, as shown in Table 1 (We remind that active components are more costly than passive components ). (2) Our design has larger design flexibility. Specifically, when the original node has an unused switch port and it is upgraded using the existing design in Fig. 1(e), the resulting node has only one port for supporting multicast. On the other hand, if the node is upgraded using the post-splitting design, the resulting node has s ports for supporting multicast where s is a design choice, 1 6 s 6 N, and a larger s gives better multicast performance at a higher cost.

Wavelength demultiplexers

One group of wavelength channels at λ 1

Fiber 1 Fiber 2

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Fig. 5. An example of a multi-fiber network. (a) A multi-fiber network with four nodes, four links and eight fibers per link. (b) Node architecture for this multi-fiber network.

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In this section, we consider all-optical multi-fiber networks and upgrade their unicast nodes to multicast-capable nodes. For this purpose, we generalize the upgrading designs proposed in Section 2 and exploit the flexibility inherent in multi-fiber networks for better cost-effectiveness as follows: (i) when it is necessary to use a particular link to establish a light-tree, we can flexibly select any available fiber in this link for this light-tree; and (ii) in a light tree, only one light beam is sent across each of its links and hence an incoming light beam to a node is only multicast to fibers of distinct outgoing links. In this manner, the resulting upgrading designs would be significantly

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different from the previous designs for single-fiber networks and their details are explained in the following subsections. Let the node have L incoming/outgoing links with F fibers per link. 3.1. Pre-splitting design In pre-splitting design, we add pre-splitting modules before the existing optical switches of the node. For convenience of explanation, we consider the channels at the same wavelength in the node. The channels coming from (or going to) the same link form one group. Fig. 6 illustrates

Fig. 7. Pre-splitting design for multi-fiber networks. (a) LF  LF super pre-splitting module with p pieces of L  L pre-splitting modules. (b) Upgrading an existing unicast node to a multicast-capable node.

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subsystem for providing multicast support to channels at the same wavelength is called super pre-splitting module. To upgrade a unicast node to a multicast-capable node, we add a super pre-splitting module before each existing optical switch. Fig. 7(b) shows the upgrading process. A node can be incrementally upgraded to handle more multicast sessions by adding more pre-splitting modules within each super pre-splitting module. We call this upgrading process incremental upgrade. The pre-splitting design essentially keeps the original node architecture and components (see Fig. 7(b)), so that the upgrading cost and overhead are small. Furthermore,

how channels are grouped. Since we can flexibly select any available channel in each group (i.e., any available fiber in each link) to establish a light-tree, we provide multicast support to p of the F channels of each group, where p is a design choice and a larger p provides multicast support to more multicast sessions at a larger cost. When a multicast session needs multicast support in this node, we select one of these p channels for this session. Since there are L incoming/outgoing links, we use an L  L pre-splitting module to provide multicast support to one channel from each group. Overall, we need p pieces of L  L pre-splitting modules. Fig. 7(a) shows the schematic diagram. This

More post-splitting modules can be added for incremental upgrade. Outgoing channels

LFxLF super post-splitting module Post-splitting modules (LxL)

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1 …

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(a) Upgraded node architecture Super Optical post-splitting Wavelength switches modules Wavelength demultiplexers (LFxLF) (LFxLF) multiplexers 1

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it can cost-effectively handle many multicast sessions with small fanout as it adopts the pre-splitting modules.

3.2. Post-splitting design In post-splitting design, we add post-splitting modules after the existing optical switches of the node. For convenience of explanation, we consider the channels at the same wavelength in the node. Since an incoming light beam to a node is only multicast to fibers of distinct outgoing links, each light splitter in the post-splitting modules is only required to have a fanout of L (i.e., the fanout is equal to the number of outgoing links). Since we can flexibly select any available fibers in a link for a light-tree, we group the channels in a similar manner as the pre-splitting design. We design an LF  LF super post-splitting module shown in Fig. 8(a). Each super post-splitting module handles the channels at a particular wavelength. It has q pieces of L  L post-splitting modules, where q is a design choice. If each post-splitting module has s splitting-capable ports, then sq input ports (i.e., input ports F  q + 1 to F of groups

Upgraded node architecture Super Super pre-splitting Optical post-splitting Wavelength modules switches modules Wavelength demultiplexers (LFxLF) (LFxLF) (LFxLF) multiplexers 1

Incoming link 1

2

1

S-Pre

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L  s + 1 to L in Fig. 8(a)) are splitting-capable ports which can split the incoming light beams to at most L beams. To upgrade a unicast node to a multicast-capable node, we add a super post-splitting module after each existing optical switch. Fig. 8(b) shows the upgraded node. When an incoming light beam is to be switched to multiple outgoing links, it is switched to an available splitting-capable port of the super post-splitting module and then it is split and delivered to the desired outgoing links by this module. The post-splitting design can also support incremental upgrading to handle more multicast sessions by incrementally adding more post-splitting modules within each super post-splitting modules. The post-splitting design essentially keeps the original node architecture and components (see Fig. 8(b)), so that the upgrading cost and overhead are small. Furthermore, it can cost-effectively handle a few multicast sessions with large fanout as it adopts the post-splitting modules. 3.3. Pre/post-splitting design In pre/post-splitting design, we add super pre-splitting modules before the existing optical switches and super post-splitting modules after these optical switches. Fig. 9 shows the upgraded node. This design integrates the strengths of both types of splitting modules to handle multicast sessions with small and large fanout. It can also support incremental upgrading to handle more multicast sessions by incrementally adding more splitting modules in the corresponding super module. The pre/post-splitting design essentially keeps the original node architecture and components (see Fig. 9), so that the upgrading cost and overhead are small. Furthermore, it can cost-effectively handle multicast sessions with large and small fanout as it adopts both the pre-splitting and post-splitting modules. 3.4. Discussion and comparison

Incoming link L

2

S-Pre

W

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2

S-Post

F

F

Fig. 9. Pre/post-splitting design for multi-fiber networks. It uses super pre-splitting and super post-splitting modules to upgrade an existing node to a multicast-capable node.

The proposed designs for multi-fiber networks have the same features as the ones for single-fiber networks. For details, please refer to the discussion in Section 2.4. In both the existing and the proposed designs, the essential signal degradation factor is ‘‘splitting’’. If an incoming light beam is split into x light beams to realize multicasting, the splitting ratio is defined to be 1-to-x. A

Table 2 Splitting ratio of the existing and the proposed designs (L is the number of links attached to a node and F is the number of fibers in each link). Designs Proposed designs

Existing designs

Splitting ratio Pre-splitting design Post-splitting design Pre/post-splitting design

1-to-m (where m is a design choice and it is typically very small such as m = 2 in our simulation studies) 1-to-L Upper bounded by 1-to-mL

Design Design Design Design

Upper bounded by 1-to-FL 1-to-FL 1-to-FL 1-to-FL

shown shown shown shown

in in in in

Fig. Fig. Fig. Fig.

1(b) [4] 1(c) [14] 1(d) [15] 1(e) [16]

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Table 3 Necessary components for upgrading using the simulation settings in Section 5 (i.e., L = 4, m = 2, s = 2, p = 1, q = 1). (a) Single-fiber network. (b) Multi-fiber network with 10 fibers per link. Design

Necessary components per wavelength Active components

Passive components

(a) Pre-splitting design

 8 optical gates

 4 1  2 light splitters  4 2  1 light combiners

Post-splitting design

 8 optical gates

 2 1  4 light splitters  2 3  1 light combiners, and 2 2  1 light combiners

Pre/post-splitting design

 12 optical gates (the node has only 4 outgoing fibers, so it can accommodate at most 2 multicast sessions and hence one pre-splitting module with m = 2 and one post-splitting module with s = 1 are sufficient)

 4 1  2 light splitters, and 2 1  4 light splitters  7 2  1 light combiners

Existing design shown in Fig. 1(b)

For 10 wavelengths:  40  42 optical switch (equivalently, about 1271 2  2 optical switches using 3-stage Clos architecture)  4  4 optical switch

For 10 wavelengths:  2 1  2 light splitters

Existing design shown in Fig. 1(c)

 16 optical gates  16 2  1 optical switches

 4 1  4 light splitters

Existing design shown in Fig. 1(d)

 16 optical gates

 4 1  4 light splitters  4 4  1 light combiners

Existing design shown in Fig. 1(e)

 4  6 optical switch  4 2  1 optical switches  8 optical gates

 2 1  4 light splitters

(b) Pre-splitting design

 8 optical gates

 4 1  2 light splitters  4 2  1 light combiners

Post-splitting design

 8 optical gates

 2 1  4 light splitters  2 3  1 light combiners, and 2 2  1 light combiners

Pre/post-splitting design

 16 optical gates

 4 1  2 light splitters, and 2 1  4 light splitters  2 3  1 light combiners, and 6 2  1 light combiners

Existing design shown in Fig. 1(b)

For 10 wavelengths:  400  402 optical switch (equivalently, about 43655 2  2 optical switches using 3-stage Clos architecture)  4  4 optical switch

For 10 wavelengths:  2 1  2 light splitters

Existing design shown in Fig. 1(c)

 1600 optical gates  1600 2  1 optical switches

 40 1  40 light splitters

Existing design shown in Fig. 1(d)

 1600 optical gates

 40 1  40 light splitters  40 40  1 light combiners

Existing design shown in Fig. 1(e)

 40  42 optical switch (equivalently, about 1271 2  2 optical switches using 3-stage architecture)  40 2  1 optical switches  80 optical gates

larger splitting ratio (i.e., a larger x) would result in weaker optical signal which may need amplification. Table 2 shows the splitting ratio of the existing and the proposed designs. Compared with the existing designs, the proposed designs have mild and smaller splitting loss and hence they need lower amplification cost. For example, if we use the simulation settings in Section 5, the pre/post-splitting design has a splitting ratio of at most 1-to-8 while the existing design shown in Fig. 1(c) has a splitting ratio of 1-to-40. On the other hand, we could apply the multicast routing and wavelength assignment algorithms that take the physical layer impairments into account (e.g., see [5,36] and the references therein), and adopt optical ampli-

 2 1  40 light splitters Clos

fiers or regenerators when it is necessary (e.g., see [9,17,37,38]). 4. Cost analysis In this section, we carry out a cost analysis, showing that upgrading using our designs is more cost-effective than replacement (i.e., replacing the existing unicast optical switches by new multicast-capable optical switches). To upgrade a unicast node to a multicastcapable node, there are two cost factors: (i) the cost of the necessary optical components, and (ii) the manpower cost of upgrading.

T.K.C. Chan et al. / Computer Networks 55 (2011) 2005–2021

2015

Table 4 Necessary components for upgrading as a function of the system and design parameters L, F, m, s, p and q. Design

Necessary components per wavelength Active components

Passive components

Pre-splitting design

 mpL optical gates (m and p are design choices and they are typically small such as m = 2 and p = 1 in the simulation studies in Section 4)

 pL 1  m light splitters  pL m  1 light combiners

Post-splitting design

 sqL optical gates (s and q are design choices and they are typically small such as s = 2 and q = 1 in the simulation studies in Section 4)

 qs 1  L light splitters  q(L-s) (s+1)  1 light combiners, and qs s  1 light combiners

Pre/post-splitting design

 (mp+sq)L optical gates

 pL 1  m light splitters and qs 1  L light splitters  pL m  1 light combiners, q(L-s) (s+1)  1 light combiners, and qs s  1 light combiners For W wavelengths:  s 1  m light splitters

Existing design shown in Fig. 1(b)

For W wavelengths:  WLF  (WLF+s) optical switch  sm  sm optical switch

Existing design shown in Fig. 1(c)

 (LF)2 optical gates  (LF)2 2  1 optical switches

 LF 1  LF light splitters

Existing design shown in Fig. 1(d)

 (LF)2 optical gates

 LF 1  LF light splitters  LF LF  1 light combiners

Existing design shown in Fig. 1(e)

 LF  (LF + s) optical switch  LF 2  1 optical switches  sLF optical gates

 s 1  LF light splitters

4.1. Cost of the necessary optical components To make an objective analysis, we measure the cost in terms of the components required for upgrading. To distinguish the total cost required, we observe two properties: (i) the cost essentially depends on the active components required because active components are much more costly than passive components, and (ii) for the active components involved (i.e., optical switches and optical gates), an optical switch is much costly than an optical gate because an optical gate is just a 1  1 on/off switch. Table 3 compares the optical components required by our designs and the existing designs using the simulation settings in Section 5 (i.e., a node has L = 4 incoming/outgoing links, each fiber has W = 10 wavelength channels, m = 2, s = 2, p = 1 and q = 1). We see that our designs have significantly lower cost than the existing designs especially for multi-fiber networks. It is because our designs can reuse the existing components and this reuse is especially significant for multi-fiber networks. For example, when each link has 10 fibers, Table 3(b) shows that the pre/post-splitting design requires only 16 optical gates and hence it has significantly lower cost than the existing designs shown in Fig. 1(b)–(e). In general, Table 4 compares the necessary optical components as a function of the system and design parameters.

 The existing designs involve the following steps: (i) removing the existing optical switches, (ii) adding the multicast-capable switches, and (iii) making some simple re-connections. Figs. 10 and 11 show the upgrading processes for the pre-splitting design and an existing design respectively. We see that the upgrading steps of our design and the existing design are simple and have about the same overhead. Therefore, our designs and the existing designs require small and about the same manpower cost. 4.3. Overall cost and cost-effectiveness Our designs have significantly lower cost because: (i) the cost of the necessary optical components is significantly lower (see Tables 3 and 4) as the existing components can be reused, and (ii) the manpower cost of upgrading is small and about the same as that of the existing designs (e.g., see Figs. 10 and 11). Our designs are more cost-effective because they have significantly lower cost while they (post-splitting design and pre/post-splitting design) have essentially the same performance as the existing designs (as demonstrated in Section 5). 5. Simulation and results

4.2. Manpower cost of upgrading To integrate the new optical components into the node, the manpower cost depends on the necessary steps which are given below:  Our designs involve the following steps: (i) adding the pre-splitting and/or post-splitting modules, and (ii) making some simple re-connections.

We conduct computer simulation to evaluate and compare the proposed upgrading designs. 5.1. Simulation models and experiments We compare our designs (i.e., upgrading unicast nodes to multicast-capable nodes) with the existing designs (i.e., replacing unicast nodes by multicast-capable nodes

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Original node Optical Wavelength switches Wavelength Incoming demultiplexers (NxN) multiplexers fibers 1 λ1

Outgoing fibers 1

λ2

2

λ2

2

2

…

(c)

…

λ

2

…

…

Pre

…

N

…

N

…

W

λ2

Pre

…

λ

2

…

…

Pre

…

…

…

… N

2

…

λ2

Outgoing fibers 1

Step 3 for upgrading Pre-splitting Optical Wavelength modules switches Wavelength (NxN) Incoming demultiplexers (NxN) multiplexers Outgoing fibers fibers 1 1 Pre λ1

…

Step 2 for upgrading Pre -splitting Optical modules switches Wavelength Wavelength Incoming demultiplexers (NxN) (NxN) multiplexers fibers 1 Pre λ1 Pre

N

(b)

(a)

2

…

λW

N

N

2

…

…

…

…

…

…

…

…

…

λW

N

Step 1 for upgrading Optical switches Wavelength Wavelength Incoming demultiplexers (NxN) multiplexers Outgoing fibers fibers 1 1 λ1

N

W

(d)

Fig. 10. Upgrading process for the pre-splitting design. (a) The original node. (b) Step 1: disconnect the wavelength demultiplexers from the optical switches. (b) Step 2: add the pre-splitting modules. (c) Step 3: connect the pre-splitting modules to the wavelength demultiplexers and the optical switches.

Step 1 for upgrading

Originalnode Optical Wavelength switches Incoming demultiplexers (NxN) fibers 1 λ 1

N

N

(a)

(b)

Step 2 for upgrading SaD Wavelength switches Incoming demultiplexers (NxN) fibers λ 1 1

N

λ

2

2

W

…

N

λ

Wavelength multiplexers Outgoing fibers 1

…

2

…

2

…

(c)

SaD Wavelength switches Incoming demultiplexers (NxN) fibers λ 1 1

…

W

…

λ

Wavelength multiplexers Outgoing fibers 1

2

…

…

… N

Step 3 for upgrading

…

λ

2

…

N

2

…

2

Wavelength multiplexers Outgoing fibers 1

…

W

2

…

…

…

…

…

λ

N

2

Wavelength Incoming demultiplexers fibers 1

…

λ

2

Wavelength multiplexers Outgoing fibers 1

N

(d)

Fig. 11. Upgrading process for the existing designs (e.g., the designs in [14–16]). (a) The original node. (b) Step 1: remove the existing optical switches. (b) Step 2: add the split-and-delivery (SaD) switches. (c) Step 3: connect the SaD switches to the wavelength multiplexers and demultiplexers.

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where these multicast-capable nodes adopt the existing designs), showing that upgrading is preferable to replacement. We generate a sequence of requests for new sessions based on a Poisson process with arrival rate k. The duration of each session is exponentially distributed with mean 1/l. We conduct three simulation experiments for comprehensive performance evaluation: (1) In the first simulation experiment, we simulate an individual node which uses each of the proposed and existing designs. Let the node have four incoming links and four outgoing links. Each session comes into any incoming link of the node with equal probability, and it goes to k randomly selected outgoing links of the node with probability Pk where Pk follows a truncated geometric distribution with parameter a for 1 6 k 6 K [39,40]:

Pk ¼

ð1  aÞak1 ; 1  aK

for 1 6 k 6 K

ð1Þ

and K is the maximum fanout. When a session has only k = 1 outgoing link, it is a unicast session and

the ratio of multicast sessions R is equal to 1  P1 = (a  aK)/(1  aK). Practically R is not large (say, R 6 0.2) because multicast traffic volume is typically smaller than unicast traffic volume. When each link has one fiber (i.e., single-fiber networks), we consider light, medium and heavy traffic at 0.002, 0.02 and 0.2 Erlangs respectively, and let m = 2 and s = 2 (where m is the fanout of the light splitters in the pre-splitting module and s is the number of splitting-capable ports in the post-splitting module). When each link has 10 fibers (i.e., multi-fiber networks), we consider light, medium and heavy traffic at 10, 20 and 40 Erlangs, respectively, and let each super pre-splitting module have a 4  4 pre-splitting module with m = 2 and each super post-splitting module have a 4  4 post-splitting module with s = 2. (2) In the second simulation experiment, we simulate an entire network in which the nodes use each of the proposed and existing designs. The network is the NFSNET with 14 nodes and 21 bi-directional links [41]. Each session originates from any node of the network with an equal probability, and it has k randomly selected destination nodes with probability

Ali-Deogun [16] Non-blocking [14,15]

100

Blocking probability

40 Erlangs

10-1

20 Erlangs Ali-Deogun design [16]

10-2

10

-3

Pre-splitting Post-splitting Pre/post-splitting

Pre-splitting and post-splitting designs similar blocking probability the non-blocking design

10 Erlangs

Pre/post-splitting design has nearly the same blocking probability as non-blocking designs

10-4 0

0.05

0.1

0.15

Ratio of multicast sessions

0.2

R

(a)

Ali-Deogun [16] Non-blocking [14,15]

100

Blocking probability

40 Erlangs

10-1

Pre-splitting Post-splitting Pre/post-splitting

20 Erlangs Ali-Deogun design

10-2

Pre-splitting design

10 Erlangs

10-3 Post-splitting design Pre/post-splitting design Non-blocking design

10-4 0

0.05

0.1

0.15

Ratio of multicast sessions

0.2

R

(b) Fig. 12. Blocking probability of the proposed and existing designs in the first simulation experiment with one fiber per link. (a) Maximum fanout K is 2. (b) Maximum fanout K is 4.

Fig. 13. Blocking probability of the proposed and existing designs in the first simulation experiment with 10 fibers per link. (a) Maximum fanout K is 2. (b) Maximum fanout K is 4.

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Pk where Pk follows a truncated geometric distribution with parameter a for 1 6 k 6 N  1 [39,40] (i.e., Pk = (1  a)ak1/(1  aN1)). When a session has only k = 1 destination node, it is a unicast session and the ratio of multicast sessions R is equal to 1  P1 = (a  aN1)/(1  aN1). For single-fiber networks, we consider light, medium and heavy traffic at 0.01, 0.1 and 1 Erlangs, respectively. For multi-fiber networks, we consider light, medium and heavy traffic at 40, 60 and 100 Erlangs respectively. The node parameters are the same as that in the first simulation experiment. We apply the algorithm proposed in [42] to determine the Steiner tree (multicast tree) for each multicast session. (3) In the third simulation experiment, we study how to select the number of splitting modules of each type. We consider multi-fiber networks under a traffic load of 10 Erlangs and R = 0.2. In the above experiments, all the switch ports of the nodes are used. When a new session cannot be set up because of insufficient free resources, this session is blocked. We adopt the

Fig. 14. Blocking probability of the proposed and existing designs in a network environment in the second simulation experiment with one fiber per link. (a) Restricted fanout of each node equals 2. (b) Unrestricted fanout of each node.

blocking probability as a performance metric and it is equal to a/A where A is the total number of sessions generated and a is the number of sessions blocked. We measure the blocking probability in simulation until its 95% confidence interval has a relative width of 0.5% or smaller (i.e., measurement is stopped when (B2  B1)/B1 < 0.005 where B1 is the lower endpoint and B2 is the upper endpoint of the 95% confidence interval of the blocking probability). 5.2. Simulation results Fig. 12 shows the blocking probability of the proposed and existing designs in the first simulation experiment with one fiber per link. When K = 2, Fig. 12(a) shows that the proposed and existing designs have about the same blocking probability. When K = 4, Fig. 12(b) shows that our designs (except the pre-splitting design) and the existing designs have about the same blocking probability, while the pre-splitting design has larger blocking probability. For example, when the traffic load is 0.002 Erlangs and R = 0.2, the blocking probabilities of the pre-splitting, postsplitting, pre/post-splitting designs, the non-blocking designs in [14,15] and the design in [16] are 3.95  102, 1.07  103, 1.07  103, 1.07  103 and 1.07  103, respectively. These results reveal the following properties: (i) Upgrading is preferable to replacement because our designs (pre/post-splitting design and post-splitting design) give essentially the same performance as the existing designs but our designs involve significantly lower cost because they reuse the existing node components. (ii) Among our three designs, the pre/post-splitting design gives the best performance while it has the largest complexity, while the post-splitting design is the most costeffective because its blocking probability is close to that of the pre/post-splitting design but its complexity is significantly lower. Fig. 13 shows the blocking probability of the proposed and existing designs in the first simulation experiment with 10 fibers per link. When K = 2, Fig. 13(a) shows that the proposed designs have about the same blocking probability as the non-blocking designs [14,15], while the Ali– Deogun design [16] has significantly larger blocking probability. When K = 4, Fig. 13(b) shows that the post-splitting design and the pre/post-splitting design have about the same blocking probability as the non-blocking designs. These results reveal the following properties: (i) Upgrading is preferable to replacement because our designs (pre/ post-splitting design and post-splitting design) give essentially the same performance as the non-blocking designs [14,15] and better performance than the Ali–Deogun design [16] but our designs involve significantly lower cost because they reuse the existing node components. (ii) The post-splitting design is the most cost-effective because its blocking probability is very close to that of the pre/postsplitting design and the non-blocking designs [14,15] but its complexity is significantly lower. Figs. 14,15 show the blocking probability of the proposed and existing designs in a network environment in the second simulation experiment. We observe the same properties in a network environment: (i) Upgrading is preferable to replacement because our designs (pre/post-

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Fig. 15. Blocking probability of the proposed and existing designs in a network environment in the second simulation experiment with 10 fibers per link. (a) Restricted fanout of each node equals 2. (b) Unrestricted fanout of each node.

splitting design and post-splitting design) give essentially the same performance as the non-blocking designs but our designs involve significantly lower cost because they reuse the existing node components. (ii) The post-splitting design is the most cost-effective because its blocking prob-

ability is very close to that of the pre/post-splitting design and the non-blocking designs [14,15] but its complexity is significantly lower. Fig. 16 shows the sensitivity results in the third simulation experiment. In general, when more splitting modules

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support multicast communication. We proposed three designs (namely, pre-splitting, post-splitting and pre/postsplitting) to tackle this problem. In general, these designs have: (i) small upgrading cost because they retain and use the existing node components while adding the necessary components, and (ii) small upgrading overhead because they essentially keep the original node architecture. In particular, the pre-splitting and post-splitting designs are simpler and involve lower upgrading overhead, while the pre/post-splitting design gives smaller blocking probability and achieves better cost-effectiveness by suitably selecting the number of splitting modules of each type. Acknowledgment We sincerely thank the anonymous reviewer for his/her in-depth review and valuable suggestions. References

Fig. 16. Sensitivity of the number of splitting modules of each type in the third simulation experiment. (a) Maximum fanout K is 2. (b) Maximum fanout K is 4.

(including pre-splitting and post-splitting) are used, the blocking probability is smaller because more splitting modules can better support multicast sessions. In particular, suitable combinations of pre-splitting and postsplitting modules can result in lower blocking probability. For example, when K = 2 (see Fig. 16(a)), the blocking probability of using 5 pre-splitting and 2 post-splitting modules is 1.26  103, which is lower than the blocking probabilities of using other combinations of 7 splitting modules. Since pre-splitting modules can effectively handle many multicast sessions with small fanout and post-splitting modules can effectively handle a few multicast sessions with large fanout, a suitable combination based on the traffic pattern can result in better performance. Given the traffic characteristics and the total number of splitting modules to be used because of cost consideration, the network designer can select a suitable number of splitting modules of each type to achieve the smallest blocking probability. 6. Conclusions In this paper, we addressed a new problem in optical multicast: how to upgrade the existing unicast nodes to

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Tony K. C. Chan received the B.Sc. degree from the City University of Hong Kong in 1991, the M.Sc. degree from the Hong Kong Polytechnic University in 1997, and the Ph.D. degree from the Hong Kong Baptist University in 2005. In 1993–2002, he worked in the IT industry in Hong Kong. In 2002–05, he pursued his Ph.D. degree. Then he was a Research Fellow, conducting research on networking and multimedia systems. He is currently with the Emperor Group which is a listed company in Hong Kong and is developing advanced IT systems for financial trading.

Yiu-Wing Leung received his B.Sc. and Ph.D. degrees from the Chinese University of Hong Kong in 1989 and 1992 respectively. His Ph.D. advisor was Prof. Peter T.S. Yum. Now he is a Professor in the Department of Computer Science of the Hong Kong Baptist University, Hong Kong. He has been working on two main research areas: (1) networking and multimedia, and (2) cybernetics and systems engineering. He has published over 70 journal papers in these areas.

Gaoxi Xiao received the B.S. and M.S. degrees in Applied Mathematics in Xidian University, Xi’an, China, in 1991 and 1994, respectively, and the Ph.D. degree from Department of Computing, the Hong Kong Polytechnic University, in 1999. From 1994 to 1995, he was with the Institute of Antenna and Electromagnetic Scattering of Xidian University. In 1999, he worked as a postdoctoral fellow at Department of Electronic Engineering, Polytechnic University, Brooklyn, NY. In 1999– 2001, he worked as a visiting scientist in the Center for Advanced Telecommunications Systems and Services (CATSS), University of Texas, Dallas. Since October 2001, he has been working in the Division of Communication Engineering, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, and now he is an Associate Professor. His research interests include WDM optical networking, wireless networking, algorithm design and analysis, and complex systems and networks.