Design algorithms for path-level grooming of traffic in WDM metro optical networks

Vol. 7, No. 8 / August 2008 / JOURNAL OF OPTICAL NETWORKING 759

Design algorithms for path-levelgrooming of traffic in WDM metro

optical networks

Srivatsan Balasubramanian and Arun K. Somani*

Department of Electrical and Computer Engineering, Iowa State University,Ames, Iowa 50011, USA

*Corresponding author: [email protected]

Received March 10, 2008; revised June 1, 2008; accepted May 15, 2008;published July 25, 2008 �Doc. ID 93621�

Recent research in new architecture design for wavelength-routed networks isfocused on grooming (aggregation) of traffic at the optical layer. Typically, thisis achieved in three steps: (1) configure the circuit in the form of a path or atree; (2) use optical devices such as couplers or splitters to allow multiple us-ers to share a circuit through point to point (P2P), point to multipoint (P2MP),multipoint to point (MP2P), or multipoint to multipoint (MP2MP); and (3) pro-vide an arbitration mechanism to avoid contention among end users. We com-pare the performance of architectures that aggregate traffic at the path level.Based on extensive simulations, we conclude that, for the studied topologyand traffic, (1) MP2MP outperforms other architectures by multiple orders ofmagnitude in single-hop scenarios, (2) P2P performs the best in multihoptransceiver-constrained scenarios, and (3) P2MP performs the best in multi-hop wavelength-constrained scenarios. © 2008 Optical Society of America

OCIS codes: 060.0060, 060.4265.

1. IntroductionAn optical network consists of optical transceivers interconnected by reconfigurableoptical cross connects. In such a network, there arises a necessity to share resources,namely, wavelengths and transceivers, due to their high cost. The potential to sharearises due to the disparity in channel capacity and demand sizes. Grooming reflectsthe ability of a network to perform traffic aggregation and improve resource sharing.Grooming can be provided within a layer or across layers. The grooming functionalitybuilt into the optical layer is optical grooming (o-grooming) and the grooming func-tionality that is available between the optical layer and the client layer is electronicgrooming (e-grooming). We use the words grooming and aggregation interchangeablyin this paper.

1.A. O-groomingCommercial systems with 128 wavelengths and transmission rates of up to 40 Gbits/sper wavelength have been made possible using state-of-the-art optical technologies todeal with physical-layer impairments. The end-user requests for bandwidth, on theother hand, have been ranging from 155 Mbits/s to 2.5 Gbits/s. Dedicating a wave-length or waveband for each end user will lead to severe underutilization of WDMchannels. Several o-grooming techniques have been researched that provide the abil-ity to efficiently pack several low-speed traffic streams into high-speed bandwidthtrunks: (1) waveband switching, (2) wavelength switching, (3) subwavelength time-slot-level switching, (4) burst switching, (5) flow switching, and (6) packet switching.The o-grooming technique used in an optical network depends on the granularity andtime scale of the switching functionality available in the optical layer.

Waveband-level switching is a technique that is used when the optical-layer switch-ing devices are limited to operation at the coarse granularity of a set of wavelengths.If the set corresponds to all the wavelengths in the fiber, it is called fiber switching.Wavelength-level switching techniques allow circuit-switched sharing of a wavelengthby configuring the optical switch for the lifetime of a connection. For subwavelengthtime-slot-level switching, the wavelength is divided into T fixed time slots and theoptical switching fabric is reconfigured for every k time slots �k=1�T�. Forpacket/flow/burst switching, the optical switching fabric is reconfigured for every

1536-5379/08/080759-24/$15.00 © 2008 Optical Society of America


packet/flow/burst, thereby ensuring that the resources are used only for the time theyare required. The feature common to all the grooming strategies is switch reconfigu-ration at various time scales to enable efficient packing of small requests into high-bandwidth pipes.

Techniques that switch at the time-slot/flow/burst/packet level suffer from the fun-damental limitation that scalable, fast optical switches with low loss and polarizationindependence are either too expensive to fabricate or not practically realizable. Thefocus of this paper is to review some of the recently proposed wavelength-level switch-ing architectures that employ different o-grooming strategies. These architectures donot require switching on the microsecond time scale and use off-the-shelf opticaldevices, yet, through their novel interconnection, allow a wavelength to be shared bymultiple end users (thereby leading to efficient network utilization). Typically, this isachieved in three steps: (1) configure the circuit in the form of a path or a tree; (2) useoptical devices such as splitters or combiners to allow multiple transmitters and/orreceivers to share the same circuit; and (3) provide an arbitration mechanism to avoidcontention among end users of the circuit. In our current work, for a typical networktopology and traffic pattern, we compare the performance of these architectures thataggregate at the path level and identify scenarios where one outperforms the other.

1.B. E-groomingElectronic grooming refers to the techniques in the client layer that are overlaid ontop of a grooming optical layer to carry traffic efficiently. A network that employs elec-tronic grooming capabilities has at least one client node that processes traffic neithersourced nor sunk by it. Although e-grooming may lead to reduced network costs, elec-tronic switching delay is incurred. Due to e-grooming, a connection may have totraverse multiple circuits before reaching the final destination. The design approachesfor e-grooming in the literature can be broadly classified as based on an integer linearprogram (ILP) for static traffic and auxiliary-graph-, network-flow-, matrix-, andclustering-based techniques for dynamic traffic as described in [1]. In this work, weanalyze the interaction between o-grooming and e-grooming capabilities for variousarchitectures that aggregate traffic at the path level based on an auxiliary graphapproach.

The rest of the paper is organized as follows. In Section 2, a taxonomy for the vari-ous optical grooming techniques in circuit-switched networks is provided. In Section 3,the network dimensioning problem is defined and trade-offs made by various architec-tures in terms of network resources used and blocking performance achieved are dis-cussed. Prior work related to this research is presented in Section 4, and a graph-based heuristic for network dimensioning is presented in Section 5. The performanceof various aggregation techniques in a random network topology are evaluated andcompared in Section 6, followed by a summary of the derived conclusions in Section 7.

2. TaxonomyThe various architectures discussed here are based on optical circuit switching (OCS)as they reserve a wavelength and the route for the lifetime of a connection. These dif-ferent flavors of circuit switching [2] do not require rapid reconfiguration of opticalswitches, thereby resulting in a scalable network architecture, but sometimes mayrequire rapidly tunable transceivers. Consider a network topology as a directed graphG�V ,E�, with V as the vertex set and E as the edge set. The circuit �C� in the graph Gis specified by two parameters: (1) the set of links that concatenate to form the circuitand (2) the list of source and sink nodes on the circuit. The circuit could be in the formof a simple path or a tree, and it could have one or more source and sink nodes. Letvo�V be the circuit originating node and vt�V be the circuit terminating node. Thecircuit C carries requests subject to the following two constraints:

Capacity constraint. This specifies that the sum of the request sizes carried by acircuit is at most the wavelength capacity.

Containment constraint. This specifies connection types and possible source andsink nodes on the circuit.

Based on the traffic aggregation strategy specified by the containment constraint,circuit switching can be categorized into the following four classes as shown in Fig. 1:


Point to point (P2P). In this technique, the circuit is configured as a simple path.There is exactly one source and one sink in C, thereby allowing traffic aggregationbetween the originating node �vo� and the termination node �vt� of the simple path.These circuits are called lightpaths (LPs) [3], and the switch architecture that sup-ports low-speed traffic streams directly from client network equipment is called asingle-hop grooming optical cross connect (OXC) [4].

Multipoint to multipoint (MP2MP). In this technique, each circuit can have mul-tiple source nodes and multiple sink nodes. In [5], the circuit, called a light trail (LT),is configured as a simple path. The containment constraint allows aggregation ofrequests of type (vi, vj) for any node vj that is downstream of node vi in circuit C. Atevery node along the circuit, the signal passes through a splitter, a shutter, and a com-biner. The splitter and the combiner are attached to a receiver and a transmitter,respectively. At the splitter, a part of the signal power is tapped by the receiver forlocal processing while the rest of the signal passes to the shutter. The shutter is asimple mirror-based optical attenuator that is configured to either block or let thewavelength pass through. If the node is the last or the first node of the circuit, theshutter is configured in the off position, isolating this wavelength from the rest of thenetwork. For all intermediate nodes, the shutter is in the on position, letting the sig-nal pass through. The signal, if not blocked by the shutter, travels through the com-biner before exiting the node. The combiner allows the intermediate nodes to transmiton the circuit while no upstream node is transmitting, and the access is regulatedthrough an arbitration protocol. The splitter allows transmission originated by anysource to be broadcast to any node downstream to it. Based on the address informa-tion in the transmission, the downstream nodes may choose to either ignore the trans-mission or process the information further. A LT with optical time-division-multiplexing (OTDM) capabilities is discussed in [6]. In [7], the circuit is configured inthe form of a tree and is referred to as a clustered light trail (CLT). A CLT has mul-tiple sources and sinks, and the containment constraint for this technique allows foraggregation of requests of type (vi, vj) for any node vj that is downstream of any nodevi on the tree, C.

Point to multipoint (P2MP). In this technique, a circuit has exactly one source nodebut one or more sink nodes. In [8], C is configured as a simple path. The circuit cancarry requests of type (vo, vi) for any node vi that is downstream of the circuit origi-nating node vo in C. This aggregation is made possible through a drop-and-continuefeature [8], similar to a LT, and differs in that the combiners are absent in the inter-mediate nodes of the circuit. We call this architecture a source-based light-trail (SLT).Since there is only one source per circuit, an internal queueing and scheduling policyat the originating node is sufficient to regulate medium access. A SLT with OTDMcapability on the source node is called a super lightpath (SLP) and is dicussed in [9].In [10], C is configured as a tree and is called a light tree (LTR). The requests sup-ported by C are of type (vo, vi), where vo is the root node of the tree and vi refers to itsleaf nodes. The signals from the source are distributed to the various destinations byusing multicast-capable wavelength-routing switches. As explained in [4], the rootnode uses the tree to communicate with all the leaf nodes in a time-multiplexed man-ner. A LTR with OTDM capability on the root node is called a super light tree (SLTR)and is discussed in [11].

P2P

Path

OCS

Path Tree

MP2MP

LT CLT

LT/OTDM

P2MP

LTR

Path Tree

MP2P

TWINDLT

Path Tree

SLTLPSLP

Fig. 1. The different flavors of optical circuit switching (OCS) include the following ar-chitectures: lightpath (LP) [3,4], destination-based light-trail (DLT) [12,18], time-domain wavelength-interleaved networking (TWIN) [13], source-based light-trail (SLT)[8], super lightpath (SLP) [9], light tree (LTR) [10], super light tree (SLTR) [11], lighttrail (LT) [5], light trail with OTDM (LT/OTDM) [6], and clustered light trail (CLT) [7].


Multipoint to point (MP2P). In this technique, each circuit has multiple sourcenodes but one sink node. In [12], C is configured as a simple path. This techniqueallows the circuit terminating node vt to sink requests of type (vi, vt) for any node vithat is upstream of vt in the linear path C. Each of these sources can communicatewith the terminating node of the circuit through a unidirectional bus-based mediumaccess protocol. We call this architecture a destination-based light trail (DLT). In [13],C is configured as a tree. This method allows the circuit to aggregate requests of type(vi, vo), where vo is the root node of the circuit and vi is any nonroot node in the tree.Each source is equipped with a high-speed tunable laser, and each destination isassigned a unique wavelength. When a source has traffic to a destination, the sourcetunes to the wavelength specific to the destination and transmits. Each intermediatenode routes the traffic solely based on the wavelength.

We propose a two-tier model for the metropolitan networks in [2], which bringstogether the various circuits that aggregate at the path level. The metro network con-sists of a set of rings in the first tier (called the metro edge) with each ring having ahub node. The hubs in turn are connected in the second tier to form a ring or a meshnetwork (called the metro core). The traffic pattern in the metro edge is hubbed,whereas in the core networks the traffic pattern is meshed. We propose a SLT- (for col-lection) and a DLT- (for distribution) based coarse WDM (CWDM) ring architecture formetro edge networks and a LT- and a LP-based ring/mesh WDM architecture formetro core networks. The downstream trail is used for the hub (central office) totransmit data to all the other nodes (access points) on the bus/ring and the upstreamtrail is used for the access points to transmit data to the hub.

In LPs and SLTs, scheduling of all packets is done internally on the circuit convenornode, and hence no arbitration is required among network nodes. The control planefor LPs is simple to manage, but the number of options available for sharing is less.SLTs, DLTs, and LTs require burst mode receivers to accommodate packets that arrivewith different optical power and phase alignments. Due to distributed medium accessprotocol (MAC) in LTs and DLTs, the propagation delays in the feedback loop, theguard band requirements for synchronization, and the requirement to achieve coordi-nation across multiple nodes, the control plane becomes more complex. The differentarchitectures differ in the trade-offs made in terms of hardware and software require-ments, performance, and control complexity.

3. Network Dimensioning ProblemThe network dimensioning problem in the context of dynamic traffic can be defined asfollows. Given the physical topology, a fixed number of wavelengths per link �W� anda fixed number of transceivers per node �X� identify the most economical route andwavelength assignment of an incoming request so as to maximize the probability ofaccepting future requests. If the client layer is equipped with electronic traffic groom-ing (TG) capabilities, connections may go through several optical-electrical-optical(OEO) conversions (and hence multiple hops) before reaching the final destination. IfTG capabilities are absent, connections reach the destination with a single hop. Torefer to an architecture with TG capability in the client layer, we suffix the architec-ture name with the letters TG. In our work, using a unified framework, we solve thedimensioning problem for eight architectures—LP, SLT, DLT, and LT and their respec-tive counterparts that are capable of full electronic grooming, LP-TG, SLT-TG, DLT-TG, and LT-TG—and compare their performance.

The performance of these architectures for an example four-node network with onewavelength per link and three transceivers per node is shown in Fig. 2. Let Ci refer tothe ith call in a sequence of five call arrivals. Each call has a bandwidth requirementof two units and the capacity of the wavelength is ten units. The resource require-ments for all the networks are shown in Fig. 2.

This example brings to light the trade-offs involved in o-grooming. Thougho-grooming increases aggregation capability, it comes with a price that we call aggre-gation penalty. There are two kinds of aggregation penalties—bandwidth penalty andtransceiver penalty. Due to these penalties, even if packing of requests into circuitsare done in the ideal way, transceiver or wavelength utilization of 100% is not achiev-able if there is more than one source or sink in a circuit. For instance, consider theDLT-TG circuit (say, T) in Fig. 2(g) that carries two connections—1 to 3 and 2 to 3. A


total of three communication units are used—a receiver on node 3 and a transmittereach on nodes 1 and 2. The wavelength is capable of filling only a maximum of tenunits of transmitter capacity and ten units of receiver capacity. By tuning a secondtransmitter to accept C2, the circuit has a total of 20 units of transmitter capacity, ofwhich 10 units will remain unusable. The network has a total transceiver capacity of240 units (3 transmitters and 3 receivers for each of the 4 nodes), of which 4.16%�10 units� is unusable, and this is called the transceiver penalty (scaled by the net-work transceiver capacity). The bandwidth penalty arises because C3 locks up twounits of bandwidth on the entire wavelength, that is, including link (1,2). This band-width locking beyond the connection span is required since the circuit, by intentionaldesign, does not support optical packet-level switching. The total bandwidth con-sumed on all the links of the network is 18 units (6 units for C5 and 4 units each forC1, C3, and C4). The bandwidth penalty (scaled by the total consumed bandwidth) is11.11%. The bandwidth and transceiver penalties are not incurred for LP networkssince they have exactly one source and sink.

4. Prior WorkThe RingO project in [12] introduces a MP2P aggregation mechanism in a ring archi-tecture for metro applications. The authors describe a proof-of-concept network thathas nodes with a tunable transmitter and a fixed receiver. To communicate with anode, data are sent on a wavelength dedicated for that node. Each wavelength istapped on every node and is used for discerning activity on the wavelength. Packetsfrom multiple sources headed for the same destination are scheduled appropriately toavoid collisions. The authors of [14] extend the ideas in [12] to introduce the MP2Paggregation architecture in mesh networks. They provide an ILP formulation forstatic network design [15] and a heuristic for MP2P aggregation [14]. Under statictraffic scenarios, the transceiver requirements of MP2P is studied in [16], and thecosts of P2P and MP2P are compared in [17]. A dual-bus architecture is proposed in[18], and a protocol for accessing the bus is dealt with in [18].

The LT architecture that uses a MP2MP strategy is introduced for metro networksin [5]. Simple MAC protocols for this architecture are discussed in [5,19,20]. The fiber-level and wavelength-level switching architectures for a LT are described in [21,22],respectively. Heuristics are developed for static network design in single-hop LT ringnetworks [23] and mesh networks [22,24,25]. Dynamic network dimensioning algo-rithms for LT mesh networks are developed in [26–28] and for SLT mesh networks in[8]. Protection and restoration schemes for LT ring networks [28,29] and LT mesh net-works [24] are also designed. LT-based network prototypes are demonstrated in[30–33]. A variant of this architecture called bus-LSP along with a heuristic algorithmto design optimal layouts is discussed in [34] in the context of generalized multiproto-col label switching (GMPLS) networks.

The static network design problem for a SLT-based model called lighttours is dis-cussed in [35]. The authors of [35] argue that lighttours is superior to a LT with the

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

ArchLP

DLT

SLT

LT

LP-TG

DLT-TG

SLT-TG

LT-TG

T1

2

1

2

2

3

2

3

R1

1

2

2

2

2

3

3

(e) LT(a) Requests (b) LP (c) DLT (d) SLT

(i) LT-TG(f) LP-TG (g) DLT-TG (h) SLT-TG (j) Summary

C1C2 C3

C4C5

A1

2

2

3

2

4

3

5

Fig. 2. (a) Request sequence. (b) Only C1 is accepted. (c) Only C1 and C3 are accepted.(d) Only C1 and C2 are accepted. (e) Only C1, C2, and C3 are accepted. (f) Only C1 and C5are accepted. (g) Only C1, C3, C4, and C5 are accepted. (h) Only C1, C2, and C5 are ac-cepted. (i) All connections are accepted. (j) Resource requirements of variousarchitectures.


assumption that the medium access protocol provided in [5] does not allow for mul-tiple simultaneous connections on a LT, whereas lighttours is capable of the same.However, the work in [20] introduces a slotted synchronous model that allows for mul-tiple simultaneous connections on the channel and is similar to the protocol proposedin [35]. Hence, the argument provided in [35] is not valid in the context of the proto-col proposed in [20]. In this paper, we do not make any assumptions about the arbitra-tion protocol used by the different architectures.

In our current work, we use an auxiliary graph approach [26] to solve the multihopdesign problem for networks that do path-level aggregation of traffic in optical net-works (also abbreviated as PLATOONs) similar to the approach used in [36]. MultihopLT network dimensioning was first investigated in [27] through a graph-basedapproach. In both the graph-based approaches, for each physical node in the network,a number of vertices are introduced in the auxiliary graph to model the state of thenetwork. In [27], the number of vertices introduced in every wavelength layer is pro-portional to the number of physical links, whereas in our model, it is proportional onlyto the number of physical nodes. Our model is applicable for any path-level aggrega-tion strategy, unlike the earlier work that models only light trails. The authors of [27]focused only on the service provisioning aspects. The contribution of this work is tocompare the performance of various path-level aggregation strategies based on manydifferent metrics. We identify two issues that are inherent in the traffic aggregationstrategies—bandwidth penalty and transceiver penalty. These factors help us under-stand and reason out the differences in performance among different architectures.None of the existing work in the literature that we are aware of compares all the men-tioned architectures under different resource-constrained scenarios. Using our model,we are able to identify and reason out scenarios for which one architecture would out-perform the other, while such conclusions are not made in any previous work.

5. Auxiliary Graph ModelIn this section, we introduce an auxiliary graph approach and outline the steps of thealgorithm. Next, we describe the virtual topology representation for traffic aggrega-tion and provide the rules based on which the auxiliary graph is generated. Wedevelop the algorithm for LT-TG (referred to as trails in this section) though it will beshown that, with minor modifications in the virtual topology representation, otherarchitectures can be modeled as well. Subsequently, we identify the grooming policyand assign costs to network resources to achieve the required objectives. Finally, weillustrate the heuristic with an example six-node network.

5.A. Auxiliary Graph ApproachThe basic idea behind our model is as follows. We design an algorithm that takes traf-fic request T�s ,d ,m , ta , te� as input, where m is the value of the subwavelengthrequest between the source s and destination d, ta is the arrival time, and te is theending time. An auxiliary graph is obtained based on the current network state takinginto account the availability of grooming switches, transceivers, wavelengths, andtheir respective costs. The cost of resources are fixed based on a chosen groomingpolicy. Using a simple Dijkstra’s algorithm, the shortest route is identified between sand d that can accommodate the request m. The concatenation of links in the shortestroute constitutes the physical route and the wavelength assignment for the request. Ifsuch a route does not exist, the required network resources may not be available tocarry the call, and the call is blocked. Otherwise, the network state is modified toreflect the resources consumed by the current request and the algorithm proceeds tohandle the next traffic request. We assume that all nodes in the network maintain anup-to-date database of resource usage in the network.

5.B. Virtual Topology RepresentationA generic auxiliary-graph-based model to solve the dimensioning problem is describedin [2] and the virtual topology representation is described here. The virtual topologylayer (VTL) captures the reachability information in the network. Each node has twolayers and both layers have a transmitter node and a receiver node. The layers arecalled busy and idle layers. A transmitter (receiver) unit in the busy layer is alreadyprovisioned for a circuit, which means that there is at least one connection in the cir-


cuit that is being sourced (sunk) by this node. A transmitter (receiver) unit in the idlelayer is not provisioned yet but can be possibly tuned into the circuit. The two-layermodel is explained using the following example.

Consider the physical topology shown in Fig. 3(a) with no electronic grooming capa-bilities. Initially, there are no calls in the network and hence the VTL has no links.Consider a call that arrives between node 0 and node 1. The call is routed along thelink 0–1, arc C is created, and the residual capacity of the circuit is calculated. Con-sider a call that arrives now between node 0 and node 2. The call is routed along thelinks 0–1–2 on a different wavelength. The reachability information corresponding tothe circuit containment set is captured in the VTL as shown in Fig. 3(b). For a LT cir-cuit, arcs A, B, and D are introduced. If the circuit is a SLT, only arcs A and D areintroduced. If the circuit is a DLT, only the arcs A and B are introduced. If it is sim-ply a LP circuit, A alone is introduced.

5.C. Auxiliary Graph GenerationThe physical topology of a network can be represented by a graph G��V� ,E��, where V�is the node set and E� is the link set. The auxiliary graph corresponding to the physi-cal graph is defined as G�V ,E�, where �V� is the number of vertices introduced to rep-resent the node set and �E� is the number of edges introduced to describe the networkstate.

Node model. In G, each node comprises W+3 layers with each layer including aninput port and an output port. Layers 1 through W are the wavelength layers (WLs),layer W+1 and layer W+2 are the trail layers (TLs) or the VTL described in Subsec-tion 5.B, and layer W+3 is the grooming layer (GL).

Network model. G is a graph with �2W+6�V� vertices and is generated as follows.Let Vy

i,k refer to the yth port on layer k at node i. Let y=1 refer to the input port andy=0 refer to the output port. Eight different types of edge are inserted into the auxil-iary graph based on the network state.

• E-grooming edge: If the network has e-grooming capabilities, for each node i,there is an edge introduced from the input port to the output port of the groom-ing layer. That is,

�V1i,W+3,V0

i,W+3� � E ∀ i � V�. �1�

For modeling networks with no e-grooming capabilities, the e-grooming edge isnot introduced.

• Wavelength link edge: If a free wavelength k exists on the link �i , j�, an edge isintroduced between the output port of wavelength layer k on node i and the inputport of wavelength layer k on node j. That is,

�V0i,k,V1

j,k� � E ∀ �i,j� � G�,

wavelength k is free on �i,j�. �2�

The capacity of this edge is the capacity of a wavelength.

2

1

00

1

2A

BC

D

Fig. 3. (a) Three-node LT network. (b) Virtual topology after connection from node 0 tonode 2 is set up on trail {0,1,2}. Shaded nodes are on the RX side while the rest are onthe TX side. Circles are in the busy layer and boxes are in the idle layer of the virtualtopology.


• Circuit edge: Let z denote a communication unit on a node with z=0 referring toa transmitter and z=1 referring to a receiver. Let Tt refer to the tth circuit in thenetwork. If i�Tt, node i is active on the trail. Define At

z�i�=1 if i�Tt and node i’szth communication unit is active on Tt, 0 if i�Tt and node i’s zth communicationunit is idle on Tt, and −1 otherwise. Let It�j� refer to the location of node j in cir-cuit Tt. Four kinds of edges are introduced for LT networks based on the follow-ing conditions:

�V0i,W+1,V1

j,W+1� � E, for some circuit t carried in G,

∀i,j: At0�i� = 0, At

1�j� = 0, It�j� � It�i�, �3�

�V0i,W+1,V1


∀i,j: At0�i� = 0, At

1�j� = 1, It�j� � It�i�, �4�

�V0i,W+2,V1


∀i,j: At0�i� = 1, At

1�j� = 0, It�j� � It�i�, �5�

�V0i,W+2,V1


∀i,j: At0�i� = 1, At

1�j� = 1, It�j� � It�i�. �6�

Equation (6) states that if i’s transmitter unit is active on t, j’s receiver unit isactive on t, and j is downstream of i on trail t, an edge is introduced from the out-put port of layer W+2 on node i to the input port of layer W+2 on node j. Simi-lar interpretations can be extended for the other equations as well. The capacityon all these edges is the residual capacity of trail t. The above-mentioned equa-tions are true only for LT and LT-TG networks. For modeling other networks, thefollowing constraints need to be added along with Eqs. (3)–(6). For modeling SLTand SLT-TG networks, include the additional constraint that i should be the con-vener node for trail t. For modeling DLT and DLT-TG networks, include the addi-tional constraint that j should be the end node for trail t. For modeling LP andLP-TG networks, include the constraint that i should be the convener node and jshould be the end node for trail t.

• Mux edge: There is an edge introduced between the output port of layer W+3 onnode i to the output port of layer W+2 on node i:

�V0i,W+3,V0

i,W+2� � E ∀ i � V�. �7�

• Demux edge: There is an edge introduced between the input port of layer W+2on node i to the input port of layer W+3 on node i:

�V1i,W+2,V1

i,W+3� � E ∀ i � V�. �8�

• Receiver edge: If there is at least one free receiver available at node i, two typesof arc are introduced. First, there is an edge introduced from the input port ofevery WL at node i to the input port of the GL at node i. Second, an edge is intro-duced between the input port of layer W+1 at node i to the input port of the GLat node i:

�V1i,k,V1

i,W+3� � E ∀ i � V�, k � �1, . . . ,W�, �9�

�V1i,W+1,V1

i,W+3� � E ∀ i � V�. �10�

• Transmitter edge: If there is at least one free transmitter available at node i, twotypes of arc are introduced. First, there is an edge introduced between the outputport of the GL at node i to the output port of every WL at node i. Second, thereis an edge introduced between the output port of the GL at node i to the outputport of layer W+1 at node i:

�V0i,W+3,V0

i,k� � E ∀ i � V�, k � 1, . . . ,W, �11�


�V0i,W+3,V0

i,W+1� � E ∀ i � V�. �12�

• Wavelength bypass edge: There is an edge from the input to the output port ofeach wavelength layer at node i:

�V1i,k,V0

i,k� � E ∀ i � V�, k � �1, . . . ,W�.

Each edge �i , j� in the auxiliary graph is associated with a tuple �ci,j ,wi,j�, where ci,jrefers to the residual capacity of the edge and wi,j refers to edge’s weight or cost. Thecapacity of a wavelength edge is the capacity of a wavelength. The capacity of a trailedge is the residual capacity of the trail. For others, the capacity is infinity. The trailedges carry information pertaining to its routing and wavelength assignment (RWA).In the VTL, multiple edges could exist between two vertices, but the cost of theseedges may differ based on their RWA.

5.D. Auxiliary Graph AlgorithmThe input to the reachability graph algorithm shown in Fig. 4 is the current networkstate in the form of the auxiliary graph generated as mentioned above. The methodtakes a call T�s ,d ,m , ta , te� and runs a shortest-route algorithm on the auxiliary graph

STEP 1: Generate a request T (s, d,m, ta, te).

STEP 2: Identify the list S of calls in the network that are scheduled to leave before ta.

STEP 3: Consider a call s ∈ S.

STEP 4: Remove the call from the network. Update the transceivers consumed by this call on all thenodes in its route and the wavelengths used by this call on all the links in its route. If the number oftransmitter units available on a node just became nonzero, an edge needs to be introduced betweenthe output port of the GL on this node to the W input ports of the WLs on this node. An edgeis also introduced between the output port of the GL on this node to the output port of layer W + 1on this node. Repeat the procedure with the receiver units modifying appropriate arcs on appropriate nodes.

STEP 5: Update all the trails that carried this call to make it consistent with Eqs. (3)–(6). Update theproperty tuple (ci,j , wi,j) and trim the trails to free wavelength links, if possible.

STEP 6: Remove call s from list S. If S is empty, proceed to STEP 7; otherwise return to STEP 3.

STEP 7: Delete the edges in G whose residual capacity is less than m since they cannot carry this call.

STEP 8: Find the shortest route P from the output port of the GL layer on node s to the input port of theGL layer on node d based on the grooming policy.

STEP 9: If P does not exist, drop the call and return to STEP 1.

STEP 10: If P exists, decompose P into two sets N and O, where N is the list of new trails to be createdand O is the list of old trails to be updated to carry this call.

STEP 11: For n ∈ N , the wavelength link edges used by the call are removed. Trail edges are introduced inG based on Eqs. (3)–(6). Update the cost and residual capacity of the trail edges. Update the transceiverusage on all the nodes of the trail.

STEP 12: For every element o ∈ O, update the transceiver status on all the nodes of the trail and maketrail edges consistent with Eqs. (3)–(6). Update the residual capacity of the trail edges.

STEP 13: If the number of free receivers on any node in the path P becomes zero, remove the receiver edgefrom the W input ports of the WLs on this node to the input port of the GL on this node. Also, remove thereceiver edge that goes from the input port of layer W + 1 on this node to the input port of the GL on thisnode. Repeat the procedure with the transmitter unit modifying appropriate arcs on appropriate nodes.

STEP 14: Return to STEP 1.

Fig. 4. Auxiliary-graph-based traffic grooming heuristic.


from the output port of the GL on node s to the input port of the GL on node d. Theroute generated by Dijkstra’s algorithm could be one of the following: (a) a direct trailfrom source to destination, (b) a concatenation of multiple trails, (c) a concatenation ofmultiple wavelength links, or (d) a concatenation of trails and wavelength links.Choices (b) and (d) arise only when e-grooming is present. If a source-to-destinationroute exists, the call is accepted, the route and wavelength are assigned, the auxiliarygraph is updated, and the algorithm proceeds to handle the next request. Otherwise,the call is blocked. The running time of this setup algorithm is O��E�log�V�� since wechose heap implementation of shortest paths due to its simplicity. If a call is to be torndown, the residual capacity of the corresponding trail is updated and the trail isdimensioned accordingly. If required, the trail is torn down and the correspondingwavelength links are freed.

5.E. Cost ModelThis auxiliary graph model can achieve various objectives using different groomingpolicies. The cost of the links in the auxiliary graph is specified based on the groomingpolicy. We choose a dynamic policy that assigns the unused transmitter and receiveredges at a very high cost, while the cost of the wavelength edge passing through linki is given by WEi=�Ti, where Ti is the number of circuits passing through link i and� is empirically chosen based on simulations. Although the transceiver consumption islimited by the high cost of the transceiver edges, the wavelength link cost does loadbalancing and reduces wavelength consumption as well. We use the adaptive groom-ing policy in our algorithm.

The current algorithm does not take into account the requirements of burst modereceivers and guard band synchronization, which are necessary for all architecturesexcept LP and LP-TG. Future work in this field could take these into account whileevaluating network costs.

5.F. Illustrative ExampleWe describe the auxiliary graph generation procedure using a single-wavelengththree-node unidirectional LT-TG ring {0,1,2} with the ring direction specified by thearc (0,1). All the connections have half the capacity of the wavelength and hence up totwo connections can share one wavelength. Initially, no trail has been set up in thenetwork. Let Cs,d

i refer to the ith connection in the sequence of dynamic arrivals,where the connection is to be established between s and d. Assume that a connectionC0,2

1 arrives at the network. This request can be routed through the available freewavelength links on the route T1= �0,1,2� shown in Fig. 5(a). As a result, free wave-

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length links (V00,1, V1

1,1) and (V01,1, V1

2,1) are removed and a trail edge (V00,3, V1

2,3) isintroduced in G.

The newly established trail can accommodate the request (0,1) or (0,2) or (1,2) inthe future. The trail edge that was just introduced in the auxiliary graph offers con-nectivity in the graph to support only the request (0,1) in the future. To include theadditional reachability information, two additional edges (V0

0,3, V11,2) and (V0

1,2, V12,3)

are introduced in the VTL as seen in Fig. 5(b). The three trail edges are identifiedwith the same trail and the capacity of the edges is assigned to be the residual capac-ity of the trail. The properties (such as capacity) of all three edges are updated asmore requests are set up or existing requests are torn down on the trail. Assume thatanother connection C1,2

2 arrives at the network. This request can be routed on theresidual capacity of the existing trail T1 and requires that a new transmitter on node1 be activated. Since the state of the transmission unit of node 1 on trail T1 haschanged, the trail edge (V0

1,2, V12,3) is removed and a new edge (V0

1,3, V12,3) is introduced.

The residual capacity on all the trail edges is updated. Let us now consider two cases.In the first case, C1,2

2 leaves before C0,21 . The transmitter on node 1 is again idle on

the trail. Hence, the edge (V01,3, V1

2,3) is removed, the edge (V01,2, V1

2,3) is added, makingit consistent with Eq. (5) and the capacity on all the edges are updated. If C0,2

1 leavesbefore another connection arrives, all the trail edges are removed and the originalwavelength links are replaced. In the second case, C0,2

1 leaves before C1,22 , and the

wavelength link (0,1) in the trail T1 is free. Control plane signaling is used to dimen-sion the trail, and T1 is modified to {1,2}. The trail edges (V0

0,3, V12,3) and (V0

0,3, V11,2) are

removed, and the wavelength edge (V00,1, V1

1,1) is added as observed in Fig. 6(a). Now,a new connection C0,2

3 arrives. The connection can be carried from node 0 to node 1using the just freed wavelength link (0,1), creating a new trail T2= �0,1�, and can thenbe electronically groomed by node 1 to be multiplexed along with trail T1 to reachnode 2. This activates the transmitter on node 0 and the receiver on node 1. Hencenew trail edges (V0

0,3, V11,3) are added and the wavelength edge (V0

0,1, V11,1) is removed

as seen in Fig. 6(b).

6. Performance EvaluationWe first state some of the assumptions made in our simulations. Subsequently, we dis-cuss some performance metrics of interest. Finally, we present discussions and obser-vations based on single-hop and multihop simulation results.

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Fig. 6. (a) Connection from node 0 to node 2 is torn down. Connection from node 1 tonode 2 remains. (b) New connection from node 0 to node 2 is admitted. New trail {0,1} isset up and connection groomed through node 1.


6.A. Simulation AssumptionsWe evaluated the performance of these networks with respect to various performancemetrics of importance. We make the following assumptions. Every link in the networkis assumed to have two fibers and the same wavelength can be used in the forwardand reverse direction. Wavelength conversion is not present in the network. The traf-fic requests are primarily requiring subwavelength capacity. Suppose a link has10 Gbits/s capacity and a connection request capacity in units of 1 Gbits/s, then itcan be abstracted as a link having a capacity of ten units and requests being in unitsof ones.

We assume that call arrivals are Poisson distributed and call holding times areexponentially distributed (whose average value is normalized to unity). The requestsare uniformly distributed among all node pairs. The observed results are averagedand reported as such. The results obtained for LP, SLT, DLT, LT, LP-TG, SLT-TG,DLT-TG, and LT-TG are described for a random network of 40 nodes, 121 links, and adiameter of 8 which is typically the size of a medium-sized metro core network. ForTG networks, we assume the overlay interconnection model and that all nodes arecapable of full electronic grooming.

The call sizes are 1, 2, 3, and 4 units, and individual granularities have equalcapacity arrival rates [1]. We use the Waxman graph model with parameters � and �[37] to generate random topologies. The simulations are done using discrete eventsimulation techniques for a series of 106 call arrivals. There are W wavelengths perfiber and X transceiver pairs per node. The observed results are averaged andreported in this section.

6.B. Performance MetricsWe study many of the following performance metrics described below.

Connection related. (1) Average number of connections, (2) average physical hoplength per connection, (3) average virtual hop length per connection, (4) connectionblocking probability per granularity, (5) connection blocking probability, (6) capacityblocking probability, and (7) service provisioning time.

Circuit related. (1) Average number of circuits, (2) average number of connectionsper circuit, and (3) average circuit length.

Network related. Network-related metrics can be divided as wavelength related ortransceiver related. The wavelength-related metrics are (1) average number of wave-length links used, (2) average total wavelength bandwidth used, (3) wavelength-packing fraction (fraction of the wavelength carrying traffic), (4) linkwise distributionof capacity used, and (5) bandwidth penalty. The transceiver-related metrics are (1)average total number of transceivers used, (2) average capacity of transceivers used,(3) transmitter-to-receiver usage ratio, (4) nodewise distribution of transceiver usage,and (5) transceiver penalty. In the rest of this section, we describe some of the high-lights of our results.

Let � be the performance metric that holds the value �i during interval ti, which isthe time period between the ith event (connection arrival or departure) and the�i+1�th event. Let T be the total time of the simulation. The average value of � iscomputed as �avg=�i�i* ti /T. Though we study many different metrics, we presentonly a few results due to space constraints. Detailed results can be found in [2].

6.C. Single-Hop ResultsIn this subsection, we compare the performance of LP, SLT, DLT, and LT architecturesand assume that electronic grooming capabilities are not available in the client layer.We study three random networks, N1, N2, and N3, with 20, 30, and 40 nodes, respec-tively (see Fig. 7). Since the results obtained were similar in nature, we report obser-

Net α β N L D

N1 0.4 .25 20 63 5

N2 0.4 .15 30 90 7

N3 0.4 .1 40 121 8

Network W X R

N1 20 15-19 450-550

N2 27 16-20 450-550

N3 21 15-19 450-550

Net W X R

N1 15-19 20 450-550

N2 18-26 21 450-550

N3 13-21 20 450-550

(a) (b) (c)

Fig. 7. (a) Random graph parameters for single-hop simulations. N, nodes; L, links; D,diameter. Provisioned resources for (b) the transceiver-limited scenario and (c) thewavelength-limited scenario.


vations for the N2 network. For each topology, we study two scenarios—thewavelength-limited scenario and the transceiver-limited scenario. For a wavelength-(transceiver-) limited scenario, we provide plenty of transceivers (wavelengths) toensure that the number of wavelengths (transceivers) alone is critical for network per-formance.

6.C.1. Blocking PerformanceThe capacity blocking probability metric is shown for the wavelength-constrained sce-nario in Fig. 8(a) with X=21 and R=450 erlangs (E). As the wavelength increases,there is a significant improvement in blocking performance for all networks. LTs showthe best performance, while LPs show the worst performance. SLTs and DLTs showsimilar performance and are positioned between LTs and LPs. This is because LTshave more aggregation choices than SLTs and DLTs, which in turn have more choicesthan LPs. SLTs and DLTs have identical aggregation choices, and hence they showsimilar performance.

The blocking performance for the transceiver-constrained scenario is reported inFig. 8(b) with W=27 and R=450 E. The performance trends are similar, and thereexists a few orders of magnitude difference between LTs and LPs in transceiver-limited systems as well. The blocking performance is studied as a function of load forX=20 and W=27 (figure not shown). As the load increases, blocking increases gradu-ally. The blocking performance is more sensitive to change in load at low loads than athigh loads. For the rest of the single-hop results, the reported metrics were studied asa function of load, with W=27 and X=20.

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Fig. 8. (a) Blocking performance as a function of W for X=21 and L=450 E. (b) Block-ing performance as a function of X for W=27 and L=450 E.


6.C.2. Carried BandwidthCarried bandwidth is the total bandwidth in the network that is consumed to supporta given carried load. For a specific carried load, the lesser the required carried band-width, the better the performance. Figure 9(a) plots the carried bandwidth normalizedto the total capacity in the network as a function of offered load. A LT carries themaximum load due to its increased aggregation choices. The carried load is high, theaverage circuit lengths are high, and hence the consumed bandwidth is also high. ALP, on the other hand, carries the least load and hence consumes the least networkbandwidth. At 450 E, LTs and LPs consume approximately 11.5% and 10.2% of thetotal capacity in the network, respectively. With this small difference in bandwidthconsumption, LTs achieve four orders of magnitude performance improvement overLPs as seen in Fig. 8(b). As the offered load increases, the carried load also increases,thereby increasing the carried bandwidth.

The effective carried bandwidth is the carried bandwidth normalized by the mini-mum required bandwidth for a specified offered load and is presented in Fig. 9(b). Tocalculate the minimum required bandwidth for a specified load, it is assumed thatevery accepted call is routed along the shortest route. The bandwidth consumed byLTs is just 20% more than the minimum required value for the observed loads. LPsconsume the least bandwidth in excess of the minimum bandwidth because they carrythe least load for a given offered load. For all architectures, as the load increases,deviation from the minimum value increases.

6.C.3. Circuit and Connection LengthsThe average circuit length and average connection length are shown as a function ofload in Fig. 10(a). In general, the average circuit length increases with load and satu-

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(Ratio)

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Fig. 9. When X=20 and W=27, (a) carried bandwidth as a function of load and (b) ef-fective carried bandwidth as a function of load.


rates at some load. Initially, as the load increases, circuits with longer lengths areestablished since wavelengths become unavailable along shorter routes. However, asthe load increases further, fewer connections get accepted due to increase in blocking,and hence the increase in circuit length is more subtle. When all wavelength links areexhausted, the network stops accepting connections and hence the circuit lengthssaturate. For low offered loads, the carried load is maximum for a LT due to itsincreased aggregation choices, and hence LTs have the highest average circuit length.However, beyond a load of approximately 520 E, SLTs and DLTs have longer circuitlengths than LTs despite LTs carrying the maximum load. Due to reduced aggregationchoices, SLTs and DLTs need longer circuits to carry traffic at high loads. A LP is satu-rated for the specified offered loads and shows the lowest circuit length.

The average connection length for a LT is approximately 20% in excess of the aver-age path length (at 450 E), whereas for a SLT and a DLT, it is approximately 15% inexcess of the same. The trends here are similar to those observed for average circuitlengths with the exception that the average connection lengths are greater than theaverage circuit lengths. The average connection length can be computed by weighingeach trail length by the number of connections in the trail. Since longer trails arelikely to have more connections, they are likely to be weighted more, and hence aver-age connection lengths are greater than average circuit lengths.

6.C.4. Bandwidth PenaltyThe bandwidth required to carry a connection can be logically construed to be of threeparts: B , B , and B . B is the minimum required bandwidth to carry the connec-

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Fig. 10. When X=20, W=27, and the network average path length is 3.17, (a) averagecircuit length and average connection length as a function of load (subscript ct and solidcurves refer to the former, while subscript cn and dotted curves refer to the latter) and(b) bandwidth penalty and penalty ratio as a function of load (subscript bp and solidcurves refer to the former, while subscript pr and dotted curves refer to latter).

min p cr min


tion assuming no resource constraints. Bp is the bandwidth consumed due to thegrooming penalty. Bcr refers to the fact that the connection may not always follow theshortest route due to the limited availability of resources or due to routing policy. Con-sider an example linear circuit A1−A2−A3−A4−A5, which among other connections,carries a connection of unit size from A1 to A3. Also, assume that there exists a linkfrom A1 to A3 on the physical topology. Here Bmin=1, since any connection from A1 toA3 will require a minimum of one hop. The connection locks up bandwidth on thelinks, �A3,A4� and �A4,A5�, and hence Bp=2. The remaining difference is attributedto constrained resources along the shortest route or to the routing policy and Bcr=1.

The bandwidth penalty, normalized to the total carried capacity, is computed as afunction of load in Fig. 10(b). A LP supports only source–destination aggregation andhence does not have multiplexing penalties. For the studied loads, the bandwidth pen-alty is a minimum of 15% in a LT, whereas it is a minimum of 9% in a SLT or DLT.Since bandwidth penalty is a significant percent of the total carried bandwidth, itaffects performance. As the load increases, the total carried capacity also increases.The penalty also increases due to increased multiplexing such that the ratio of band-width penalty to carried capacity increases.

The penalty ratio is defined as the ratio of Bp to Bp+Bcr, expressed as a percentage.The ratio is as high as 85% (at 450 E) for a LT in Fig. 10(b). This suggests that, inLTs, of the network bandwidth required in excess of the minimum required band-width, the bandwidth penalty has a much greater role to play than constrainedresources or routing policy. Since the aggregation choices are limited for SLTs andDLTs, lesser aggregation happens and the bandwidth penalty is only up to a maxi-mum of 70% (at 450 E). As the load increases, the bandwidth penalty increases. How-ever, the bandwidth consumed due to constrained resources (or routing policy)increases even more rapidly due to higher carried load. Hence, the penalty ratiodecreases with increase in offered load.

Another metric of interest is multiplexing gain, which refers to the average numberof connections sharing a circuit. It is observed that a LT has the maximum number ofconnections multiplexed per circuit, followed by a SLT and a DLT, with a LP havingthe least multiplexing capability (figure not shown). At high loads, when a circuit isset up, there is a good chance of another call arriving at the network to be multiplexedonto the same circuit since the calls are arriving at a rapid rate. Hence, as the loadincreases, gain increases.

6.C.5. Wavelength Link UsageA metric that captures the efficiency of packing is the number of wavelength linksused for a given offered load as reported in Fig. 11(a). A wavelength link is said to betouched if it is being used to carry some traffic. For a specified carried load, the lowerthe wavelength link usage, the better the performance. As the load increases, thenumber of wavelength links used increases. A LT uses the minimum number of wave-length links despite carrying the maximum load. It is observed that a LP touchesapproximately 50% of the wavelength links (at 450 E) in the network to carry a band-width of just over 10% of the total capacity in the network, showing that the packingis fractional.

A loose lower bound on the required number of wavelength links is the number ofwavelength links required to carry the traffic when it traverses the shortest routes.The required number of wavelength links normalized to the minimum required wave-length links is effective wavelength links (figure not shown). A LT consumes a maxi-mum of 450% in excess of the minimum required wavelength links (at 450 E). Thedeviation from the minimum is large only because the bound is loose. As the loadincreases, the aggregation capability increases, and hence the deviation from theminimum value decreases.

6.C.6. Transmitter UsageTransmitter usage is defined to be the number of transmitters used (touched) normal-ized by the number of transmitters in the network. For a specific carried load, the lessthe transmitter usage, the better the performance. For a specific offered load, a SLThas the minimum transmitter usage as observed in Fig. 11(b) since it uses a source-based aggregation technique. A DLT, on the other hand, uses transmitters rapidly,


thereby leading to the highest transmitter usage. A LP, with its source–destinationaggregation performs better than a DLT. Though a LT has more aggregation choicesthan a SLT, a LT tries to conserve both transmitters and receivers and hence performsslightly worse than a SLT. A loose lower bound on the required number of transmit-ters is Xmin=�i��j�Ti,j /C��, where Xmin is the minimum number of transmittersrequired in the network, T�i , j� is the traffic from i to j, and C is the wavelength capac-ity. The total number of transmitters used normalized to the minimum required trans-mitters is the effective number of transmitters (figure not shown). A SLT, which per-forms the best, is approximately 210% in excess of the minimum. The effectivenumber of transmitters reduces with load because the increased grooming capabilityat high loads leads to more efficient consumption of transmitters. Although a DLT per-forms poorly in transmitter consumption, it achieves the best receiver consumptionsince it performs destination-level aggregation. The ratio of transmitter-to-receiverusage is analyzed in Fig. 12(a). SLTs use 30% more receivers than transmitters, andDLTs use 25% more transmitters than receivers. For a SLT, the ratio increases withload. This is because, as the load increases, due to increased aggregation, transmitterusage does not increase as much as receiver usage.

6.C.7. Transceiver PenaltyThe transceiver penalty (TP) scaled by the network transceiver capacity is evaluatedas

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Fig. 11. (a) Required wavelength links expressed as a percentage of the total wave-length links in the network as a function of load when X=20 and W=27. (b) Transceiverusage expressed as a percentage of the total number of transceivers in the network as afunction of load when X=20 and W=27.


TP =100 � ��t

T�Ntxt + Nrx

t � − 2 � T�

2 � X,

where Ntxt is the number of transmitters on the tth trail, Nrx

t is the number of receiv-ers on the tth trail, T is the number of trails, and 2�X is the sum of the number oftransmitters and receivers in the network. TP is shown in Fig. 12(b). The transceiverpenalty increases with load due to increased aggregation capabilities at higher loads.Due to transceiver penalty, approximately 12% of the total transceiver capacity is lostfor LTs (at 450 E). Approximately 7% of the total transceiver capacity is lost for SLTsand DLTs (at 450 E). This corresponds to transmitter capacity loss in DLTs andreceiver capacity loss in SLTs. LPs do not suffer from transceiver penalties.

6.D. Multihop ResultsThe auxiliary graph approach is used to compare network performance under bothnetwork interconnection models—the overlay model and the integrated model. For theoverlay model, when a call arrives, it is first routed on the virtual topology. If the callcannot be accommodated, a request is made to the optical layer where, if there aresufficient wavelength links available, the call is accepted. Two e-grooming policieswere used for the integrated model—one that minimizes the number of virtual hopstaken by a connection and another that minimizes the number of physical hops takenby a connection. Eight architectures—LP, SLT, DLT, LT, LP-TG, SLT-TG, DLT-TG, andLT-TG—were compared in our work. We report results for the overlay model since thederived conclusions were similar in nature for both, though the observations for theoverlay model were more pronounced. The simulation parameters are specified in Fig.13. For each topology, the wavelength-limited and transceiver-limited scenarios were

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Fig. 12. (a) Ratio of transmitter-to-receiver usage when X=20 and W=27. (b) Trans-ceiver penalty as a function of load for X=20 and W=27.


studied. We describe the results obtained for the 40-node N3 network here since theother topologies yielded similar conclusions.

The capacity blocking performance as a function of X is shown in Fig. 14(a) for atransceiver-limited system. The blocking performance as a function of W for awavelength-limited system is reported in Fig. 14(b). We make the following observa-tions from the figures. (1) For transceiver limited systems, LP-TG outperforms LT-TG,SLT-TG, and DLT-TG by many orders of magnitude. (2) For wavelength-limited sys-tems, LT-TG, SLT-TG, and DLT-TG outperform LTP-TG by many orders of magnitude.(3) For both wavelength- and transceiver-limited systems, SLT-TG, DLT-TG, andLT-TG, show similar performance. We reason out these observations in the rest of thesection.

6.D.1. Wavelength-Constrained ScenariosTo explain the observations, we note the following. In our algorithm, for a circuit pass-ing through N nodes, the number of edges introduced in the VTL is O�1� for LP-TG,

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N2 20 10-14 450-550

N3 19 14-18 450-550

Network W X R

N1 12-16 20 450-550

N2 14-19 18 450-550

N3 12-16 25 450-550

(a) (b) (c)

Fig. 13. (a) Random graph parameters for multihop simulations. Provisioned resourcesfor (b) the transceiver-limited scenario and (c) the wavelength-limited scenario.

1e-06

1e-05

1e-04

0.001

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14 14.5 15 15.5 16 16.5 17 17.5 18

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Blocking

Probability

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LP-TGSLT-TGDLT-TGLT-TG

1e-06

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0.001

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12 12.5 13 13.5 14

CapacityBlockingProbability

Wavelengths

LPSLTDLTLT


(a)

(b)

Fig. 14. (a) Capacity blocking probability as a function of X with W=19 and load=450 E. (b) Capacity blocking probability as a function of W with X=25 and load=450 E.


O�N� for SLT-TG and DLT-TG, and O�N2� for LT-TG. Since the number of edges intro-duced is maximum for LT-TG, the density of the VTL is the highest for LT-TG and thelowest for LP-TG. Due to the low density of LP-TG VTL, its diameter is large and theconnectivity is low. In the overlay model, the route is first found on the VTL. Due tolow reachability, the route takes many hops to reach the destination and hence mayrequire many wavelength links. In wavelength-limited systems, consuming manywavelength links is detrimental to performance and hence LP-TG performs poorly. Tocorroborate this, we observed in [2] that the average virtual hop lenth for LP-TG ismore than that observed for LT-TG. Also, the average circuit length and connectionlength is higher for LP-TG despite carrying a lower load than LT-TG. This confirmsthat LP-TG experiences a more fractional packing and longer routes due to the sparsevirtual topology.

To corroborate this reasoning, we present the following observations for an offeredload of 450 E, for which trends can be found in [2]. We observe that average virtualhop length for LP-TG is 2.5, which is approximately 13.7% more than that observedfor LT-TG. The average circuit length of LP-TG is approximately 3, which is approxi-mately 36.36% in excess of the average circuit length of LT-TG. This difference isattributed to the larger aggregation capabilities of LT-TG. It is also seen in Fig. 15(a)that, the average connection length assumed by LP-TG is approximately 40% higherthan LT-TG, SLT-TG, and DLT-TG despite carrying lesser load than other e-groomingarchitectures. LP-TG consumes approximately 50% more wavelength links thanLT-TG, SLT-TG, and DLT-TG despite carrying lesser load as shown in Fig. 15(b). Thisconfirms that LP-TG experiences a more fractional packing and longer routes due tothe sparse virtual topology.

0.8

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Averagevirtualhops

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5

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6

6.5

7

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460 480 500 520 540

AverageConnectionLength

Load

LPSLTDLTLT


(a)

(b)

Fig. 15. For the wavelength-constrained scenario, (a) average connection length as afunction of load with X=25 and W=15 and (b) required wavelength links as a percent-age of the total wavelength links in the network as a function of load with X=25 andW=15.


6.D.2. Transceiver-Constrained ScenariosWe reason out why SLT-TG, DLT-TG, and LT-TG systems perform poorly intransceiver-constrained systems. In overlay systems, the virtual topology is firstsearched to route the call. Due to significant density of the virtual topology in SLT-TG,DLT-TG, and LT-TG, chances of finding an edge between the source and the destina-tion of the call is high. However, the communication units on the source and destina-tion may not already be provisioned to route the call, and hence transceiver penalty isincurred. In transceiver-constrained systems, penalty on an already precious resourceleads to LT-TG, SLT-TG, and DLT-TG performing poorly. To explain why SLT-TG,DLT-TG, and LT-TG show identical performance, it is to be noted that improvement inperformance due to e-grooming dominates the performance improvement due too-grooming, making o-grooming gains a second-order effect. LT-TG has more choicesin o-grooming than SLT-TG and DLT-TG. However, the bandwidth and transceiverpenalties are also increased due to increased o-grooming choices in LT-TG. Theimprovement in performance due to increased o-grooming is offset by the bandwidthand transceiver penalties, thereby leading to similar performance for all three archi-tectures. To corroborate this reasoning, we note that in [2], the transceiver penalty ofLT-TG is approximately 100% more than what is observed for SLT-TG and DLT-TG,whereas it is zero for LP and LP-TG, and underutilization of an already preciousresource leads to poor performance.

To corroborate this reasoning, we study transceiver penalty as a function of load inFig. 16(a). It is noted that the transceiver penalty of LT-TG is approximately 100%more than what is observed for SLT-TG and DLT-TG. At low loads, LT shows lower

0

2

4

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18

460 480 500 520 540

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Penalty

(%)

Load

LPSLTDLTLT


0

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1

1.5

2

2.5

3

3.5

460 480 500 520 540

BandwidthPenalty(%)

Load

LPSLTDLTLT


(a)

(b)

Fig. 16. For the transceiver-constrained scenario, (a) transceiver penalty as a functionof load with W=19 and X=15 and (b) multiplexing bandwidth penalty as a function ofload with W=19 and X=15.


transceiver penalty than LT-TG, but it overshoots LT-TG at high loads. The rapidlyincreasing penalty trend in LT is due to its increased multiplexing tendency withincreasing loads. There are more ways in which a call can be accommodated in a net-work with e-grooming capabilities. Due to this, the possibility of multiplexing an extracommunication unit on an existing circuit (tune in) is lower, thereby leading to a moregradual increase in transceiver penalty as compared with the non-e-groomed LT.

To explain why SLT-TG, DLT-TG, and LT-TG show identical performance in all sce-narios, note that the performance improvement due to o-grooming is a second-ordereffect as compared with e-grooming. LT-TG has the most choices in o-grooming, butthe bandwidth and transceiver penalties are also increased due to increasedo-grooming choices in LT-TG. The improvement in performance due to increasedo-grooming is offset by the bandwidth and transceiver penalties, thereby leading tosimilar performance for all three architectures. To corroborate this, the bandwidthpenalty as a function of load is studied in Fig. 16(b). The bandwidth penalty incurredby LT-TG is seen to be 70% more than SLT-TG and DLT-TG, showing that, in the pres-ence of e-grooming, increased aggregation capabilities may not always lead to perfor-mance improvement.

The wavelength-packing fraction of the transceiver-constrained system as a func-tion of load is plotted in Fig. 17(a). The wavelength-packing fraction is defined as theaverage fraction of a wavelength that is used to carry traffic. It is seen that LT-TG hasa higher wavelength-packing fraction than SLT-TG, DLT-TG, and LP-TG. It appearsthat LT-TG should perform better than LP-TG. However, it is important to note thatthis metric does not account for the fact that some parts of the carried bandwidth ina wavelength are actually not useful and are simply bandwidth penalty. We subtract

0.1

0.2

0.3

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460 480 500 520 540

WavelengthPackingFraction

Load

LPSLTDLTLT


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0.4

0.5

0.6

0.7

0.8

460 480 500 520 540

EffectivePackingFraction

Load

LPSLTDLTLT


(a)

(b)

Fig. 17. For the transceiver-constrained scenario, (a) wavelength-packing fraction as afunction of load with W=19 and X=15 and (b) effective wavelength-packing fraction asa function of load with W=19 and X=15.


the bandwidth penalty from used bandwidth to study the effective wavelength-packing fraction, which is shown in Fig. 17(b). It is seen that when useful bandwidthalone is considered, LP-TG performs better than LT-TG, DLT-TG, and SLT-TG, andLT-TG performs the worst. This clearly shows that bandwidth penalty degrades theperformance of LT-TG and along with transceiver penalty is responsible for LT-TGperforming poorly.

7. ConclusionsThe path-level aggregation techniques have a significant effect on network perfor-mance. Based on the current work, we conclude the following. If the network topologyis an optical ring, DLTs can be used for collecting traffic from the nodes to the hub,while SLTs can be used for distributing traffic from the hub to the nodes. For single-hop mesh networks, LTs outperform LPs by multiple orders of magnitude, with SLTsand DLTs somewhere in between. SLTs consume more receivers, while DLTs consumemore transmitters. If transmitters are more expensive than receivers, performance ofSLTs can be improved by asymmetrically provisioning more receivers on the nodethan transmitters. For multihop transceiver constrained mesh networks, LP-TG out-performs other architectures. For multihop wavelength-constrained mesh networks,SLT-TG is a compelling choice, since SLT-TG has performance similar to LT-TG butdoes not need distributed arbitration. Bandwidth penalty and transceiver penalty arethe price to be paid apart from additional hardware and software for using trafficaggregation techniques. Based on the results obtained, we feel that path-level aggre-gation techniques can achieve cost-effective optical network deployment in the metrospace.

Acknowledgments

This research was funded in part by National Science Foundation grants CNS0434872 and 0626741, the Information Infrastructure Institute at Iowa State Univer-sity (ICUBE), and the Jerry R. Junkins Endowment.

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Design algorithms for path-level grooming of traffic in WDM metro optical networks