Impairment-aware multicast session provisioning ... - Semantic Scholar

Computer Networks 91 (2015) 675–688

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Impairment-aware multicast session provisioning in metro optical networks T. Panayiotou a,∗, G. Ellinas a, N. Antoniades b, A. Hadjiantonis c a KIOS Research Center for Intelligent Systems and Networks, Department of Electrical and Computer Engineering, University of Cyprus, Nicosia 1678, Cyprus b Department of Engineering Science and Physics, College of Staten Island, CUNY, New York, NY, United States c Department of Engineering, University of Nicosia, Nicosia, Cyprus

a r t i c l e

i n f o

Article history: Received 19 January 2015 Revised 11 August 2015 Accepted 4 September 2015 Available online 16 September 2015 Keywords: Networks Optical communications Multicast routing Network architecture Physical layer

a b s t r a c t This work investigates the problem of designing, engineering, and evaluating metropolitan area transparent optical networks for the provisioning of multicast sessions. Apart from finding the minimum-cost tree and using metrics on the physical performance of the system, namely the Q-factor, this work investigates different node architecture designs including architectures with active and passive splitters and architectures with different receiver and transmitter designs. Different network engineering approaches are also utilized and are used to ascertain whether a multicast connection should be admitted to the network. “Tree balancing techniques” are used for routing the multicast sessions, aiming at maximizing the multicast connections that can be admitted to the network.

1. Introduction Advances in optical wavelength division multiplexing (WDM) networking have made bandwidth-intensive applications widely popular. Clearly, most connections carried over an optical mesh network have been high-bandwidth pointto-point (PtP) connections. However, a number of recent new customer applications have driven the need to support multicast connections, potentially over optical mesh networks. These applications, requiring point-to-multipoint (PtMP) connections from a source node to several destination nodes in the network include video distribution for residential customers, video conferencing between telepresence-equipped rooms for global enterprise customers, video training and

∗

Corresponding author: Tel.: +357 99860778. E-mail addresses: [email protected], [email protected] (T. Panayiotou), [email protected] (G. Ellinas), [email protected] (N. Antoniades), [email protected] (A. Hadjiantonis). http://dx.doi.org/10.1016/j.comnet.2015.09.004 1389-1286/© 2015 Elsevier B.V. All rights reserved.

© 2015 Elsevier B.V. All rights reserved.

e-learning, grid-computing applications, telemedicine applications, etc. Multicasting provides an easy means to deliver messages to multiple destinations without requiring too much message replication. Next-generation networks must have the capability and build-in intelligence to support all types of traffic (unicast, multicast, and groupcast) and all kinds of applications. All-optical multicasting (the assumption in this work is that the network is completely transparent without OEO conversions and thus it has no regeneration points) has been investigated in the research community since the early days of optical networking [1–8], but has only recently received considerable attention from the service providers, mainly because now many applications exist that can utilize the multicasting feature. In these networks, optical splitters can be used to split the incoming signal to multiple output ports, thus enabling a source node to establish connections with multiple destinations by creating a “light-tree”. There exist several routing heuristics for finding the lighttrees; however, for the majority of them there is no consideration on the physical layer constraints. In this work, we

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T. Panayiotou et al. / Computer Networks 91 (2015) 675–688

present “tree-balancing” routing techniques aimed at maximizing the multicast connections which can be admitted to the network. These techniques, that also take into consideration the physical layer impairments (PLIs), are shown to improve the overall blocking probability compared to previous tree routing techniques found in the literature. To investigate whether a multicast connection should be admitted to the network, apart from finding the minimum cost tree, a Q-budgeting approach is used as a metric of the physical performance of the system [9]. Furthermore, the availability of transmitters and receivers is also investigated for the establishment of the multicast connection. The assumption in this work is that a multicast call is accepted into the network only if a working tree can be found that satisfies the physical layer constraints (acceptable BER at all the destinations of the multicast session) and it also has available network resources (available transmitter/receiver and wavelength). This paper extends on the work presented in [11]. Specifically, in [11], several “tree-balancing” techniques that consider the PLIs were initially introduced. However, in that work, no specific multicast-capable node architecture or engineering was assumed; rather, the multicast-capable node architecture was treated as a “black-box”. This work goes one step further, by examining several node architectures and engineering designs utilizing active or passive splitters and different types of transmitters and receivers including every possible combination between fixed and tunable transceivers. A small number of these were first presented in [14] but the work here is greatly expanded and more indepth. Specifically, several transceiver designs are for the first time discussed and evaluated (fixed TXs/tunable RXs, tunable TXs/fixed RXs) and the presentation of the node architectures and network engineering cases is presented in detail. Furthermore, this work expands on the multicast routing algorithms examined, as a number of new and existing algorithms are developed and compared for every node architecture/network engineering presented. The novelty of the work stems from the fact that in the literature most of the work that includes PLIs deals only with unicast connections, whereas this work investigates multicast connections, presenting a complete solution of node architecture design, network engineering, as well as multicast routing algorithms for the case when the PLIs are also considered. Furthermore, it is shown that the proposed algorithms, that take the physical layer constraints into consideration, outperform the rest of the tree routing techniques that either consider only the power budget or route the multicast connections irrespective of the physical layer constraints. This work clearly shows that different engineering of the physical layer produces different multicast group blocking, a strong indicator that a more refined interaction between physical and logical layer is needed for efficient multicast connection provisioning. In Section 2 the physical layer system model used to account for the physical layer impairments is presented. This is followed by the description of different node architecture designs in Section 3 and of various multicast tree routing heuristic algorithms in Section 4. Provisioning approaches for the multicast connections for the impairmentaware case are described in Section 5 and performance results for these schemes for all the routing techniques are

shown in Section 6. The paper ends with some concluding remarks in Section 7. 2. Physical layer system modeling The Bit Error Rate (BER) of the system is the main performance indicator in a fiber-optic digital communication system. However, as the BER is a difficult parameter to numerically evaluate, the required system Q-factor for a target BER is derived instead using Eq. (1) [9,10].

BER =

Q 1 erfc √ 2 2

−Q

≈

e2 √ Q 2π

(1)

The value of the Q-factor can be calculated using Eq. (2) [9–11] and compared to the required performance,

Q=

I1 − I0

σ1 + σ0

(2)

where I0 and I1 represent the received current levels for symbols 0 and 1 respectively and σ i is shown in Eq. (3) [9–11] as the sum of the variances of the thermal noise, shot noise, various components of beat noise, and relative intensity noise (RIN) (σ 0 and σ 1 denote the sum of the variances for the various noise components for symbols 0 and 1 respectively). 2 2 2 σi2 = σth2 + σshot−i + σASE−ASE + σs−ASE−i +

(3)

2 2 σRIN−i + σASE−shot

This approach assumes a baseline system with various receiver noise terms as well as Amplified Spontaneous Emission (ASE) noise. To include other common physical layer impairments such as crosstalk, fiber nonlinearities, distortion due to optical filter concatenation, and Polarization Mode Dispersion (PMD) amongst others, a simple Q-budgeting approach is used as described in [9]. The approach starts from the Q-value for the baseline system and budgets Q-penalties for the various physical layer impairments that are present. The Q-penalty (QdB ) associated with each physical layer impairment in a system is commonly expressed in dB and in this work the following definition is used: QdB = 10 × log(Qlinear ). The Q-penalty is calculated as the QdB without the impairment in place minus the QdB with the impairment present. This approach enables a network designer to calculate the impact of physical layer effects, such as non-linearities, polarization effects, optical crosstalk, as well as aging and safety margins, in the design of an optical network. The values used for this budgeting approach are shown in detail in [11]. The reader should note that when calculating the dB value for fiber nonlinearities (such as cross-phase modulation and four wave mixing), a worst-case value is assumed that covers the cases of varying number of channels on each path based on the work in [9] that included detailed time-domain simulations for the nonlinear effects. It must also be pointed out that amplifier gain control is assumed [12] and that no polarization dependent gain/loss (PDG/PDL) or amplifier ripple are present, thus precluding power instabilities. The formulation used for the calculation of the variances of the different noise components (thermal, shot, various components of beat noise, and RIN noise) can be found in


[10] while realistic parameters of industry receivers are utilized. The sum of these variances for symbols 0 and 1 can then be calculated using Eq. (3) and the Q-factor is evaluated by substituting into Eq. (2). The received current levels (Ii ) for symbols 0 and 1 are given by Eq. (4) where Pout represents the linear signal power at the receiver end, X represents the extinction ratio, r is the responsivity of the receiver, and pi represents the eye opening-level for symbols 0 and 1.

10X/10 Ii = 2 × r × Pout × × pi 1 + 10X/10

(4)

The modeling based on the Q-performance of the connection is used during the provisioning phase to decide whether a multicast connection should be admitted to the network or rejected [13]. In an optical network there are effects that are inter-depended to the number of channels present at each instance in the system (optical crosstalk, cross-phase modulation, four wave mixing are some examples) and there are others that only depend on the one channel under investigation. The modeling used in this work allows for the case where the Q-constraint is applied for new calls only, with the above calculation done for these new calls. To conclude, based on this methodology, if any of these tests fail, meaning that the Q-factor for any path on the calculated tree is below a predetermined threshold, then the new call will be blocked. 3. Node architecture designs In this section various node designs are studied. The architectures presented below were designed to support multicast connections in transparent optical networks. The criterion was, apart from the transparent components, to keep the cost of these architectures low, to design architectures that can be built with commercially available components, as well as architectures that can handle effectively the physical layer impairments (PLIs) present. During the network engineering, real component specification were assumed on which the Q-factor modeling is also based. These architectures as described and analyzed have not been previously proposed by other author groups. For example, several multicast-capable architectures utilizing optical splitters can also be found in the literature [15], without however considering the insertion losses of the splitters and the engineering of the node at the physical layer. Note that the term “engineering” in this work is defined as a methodology for basically executing a power budget and accounting for all the power penalties of the physical layer effects that impact the performance of the path under consideration. In this work, the performance of the network is first examined for two different cases of multicast-capable nodes, namely based on active or passive splitters, and then the performance of the networks is examined for different types of transmitters and receivers including every possible combination between tunable and fixed transceivers. The network performance is further examined for multiple multicast routing heuristic algorithms. Note that the main difference between the two types of architectures is that with passive splitters, power is split as many times as the fanout of the node and controllable semiconductor optical amplifiers (SOAs) are used as gates to “cut-off” power at outputs where the signal is not destined for, whereas with active splitters

λ1,λ

2

2

,...,

λ

1 . . . . . . . ,..., . λ . M

Mx1 fiber switch

1X(M+1) splitter

DMUX

λ1,λ

677

MUX

λ1 N

λ

. .

2

. . λ N .

. . . . VOA

SOA

λ1 N

PRE-AMP

λ

2

. λ .N .

. . . . . .

POST-AMP

Fig. 1. Node architecture consisting of passive splitters, optical switches, attenuators, and amplifiers.

the power is split as many times as the fanout of the nodes in the multicast tree found via the multicast routing heuristics. 3.1. Passive vs. active splitting designs Fig. 1 shows the generic node architecture with its splitting capabilities as is used throughout this work. In this design, N wavelengths are assumed at each input fiber and M inputs/outputs per node are shown. Optical demultiplexers/multiplexers are used to separate the wavelengths at the input and then to combine them at the output. Optical splitters are used to split the optical power and SOAs (acting as gates) are needed for blocking signals from appearing at unwanted output ports (in the case of passive splitting). All SOAs are controlled in an intelligent manner to avoid clashing at the same output/same wavelength of the switch. Note that the SOAs (that act as gates) will not be required in the case of active splitting, and this is the only difference between the node architectures with passive and active splitters in terms of components. Input optical amplifiers (pre-amps) are utilized to compensate for the loss in the optical fiber segment preceding the node, whereas output optical amplifiers (postamps) are used to compensate for the node loss (these are typically Erbium Doped Fiber Amplifiers (EDFAs)). Variable optical attenuators (VOAs) are also utilized to equalize the power prior to entering the output EDFAs (post-amps) for better performance and for the handling of polarization depended gain (PDG). The M × 1 Microelectromechanical Systems (MEMS)-based optical switches are used for guiding a signal wavelength from any input port to a specific output port. For simplicity, only a few switch interconnection lines are shown in the figure. 3.1.1. Network engineering for active vs. passive splitters designs As pointed out, the architectures utilizing active and passive splitters are investigated first, followed by the examination of a number of different transceiver designs. While the network engineering is specifically described for the active and passive splitter designs, it is also applied with small variations to the different transceiver designs. The network engineering variations regarding every presented node design appear (where appropriate) throughout the rest of the paper. For the active and passive splitters designs the network is engineered as follows: +3 dBm power is launched into

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T. Panayiotou et al. / Computer Networks 91 (2015) 675–688 Table 1 Typical component losses in the node. Component

Losses in dB

Mux/Dmux [16] VOA [17] Splitter SOA [18] Switch [19]

3 0.5 10 × log(fanout) 0.6 1

1X(M+1) splitter

DMUX

λ1 λ2

λ 1 , λ 2 ,..., λ N

.

G < 13 13 < G ≤ 15 15 < G ≤ 17 17 < G ≤ 20 G > 20

7 6.7 6.5 6 5.5

λ2 λ

PRE-AMP

. .

. . .N

. .

POST-AMP

. .

SOAs

(NXM) TXs

1X(M) splitter RX TX

λN

TX

λ2

λ1

TX

λ1

λN

RX

RX

λ

λ1

2

RX

λ

N

RX

RX

λ2

λ1

NXM

Fig. 2. Case 1: Node design for fixed TXs/RXs.

each span of optical fiber, with the pre-amplifiers designed to increase power to 6 dBm coming into the optical node, and post-amplifiers are set for bringing the power back to 3 dBm as the signal is launched into the next fiber span. The above shifting of optical gain to the pre-amp improves the overall node noise figure. Insertion losses for multiplexers/demultiplexers, switches, SOAs, and VOAs are based on commercially available components and typical values for these are shown in Table 1. Noise figures (NFs) for the preand post-node EDFAs are calculated from a look-up table containing information obtained from realistic commercial amplifier designs, and depend on the amplifier gain taken at each time (Table 2). Insertion loss is calculated based on the worst-case scenario, considering passive or active splitters, and the amplifier gain is determined for such a worst-case scenario. This worst-case scenario is in this work limited by the maximum loss that a signal can experience passing through a given node. In particular, the determining factor is the node splitting loss, which varies depending on the node fanout and is maximized in nodes that split the signal power the maximum number of times. In the network used in this work for simulation purposes, the maximum fanout of any node is six, and by adding one more for local add/drop purposes the maximum power split that is used becomes seven. Based on the above, the maximum node loss can be calculated by Eq. (5) as,

NodeLoss = DmuxL + SplittingL + SOAL + SwitchL + VOAL + MuxL

VOAs

SOAs

λ1

M

NF

. . . .

λ 1 , λ 2 ,..., λ N

Gain in dB

MUX

. .

λ.. N

1 . . . . . .

Table 2 NF values of the EDFAs [20].

(2xM)x1 fiber switch

(5)

where DmuxL , SplittingL , SOAL , SwitchL , VOAL , and MuxL are the insertion losses in dB of the Dmux, the splitter, the SOA, the switch, the VOA, and the Mux respectively. Substituting the values for the loss of the above components that were given in the previous section and assuming the maximum splitting explained above, the total node loss in this case will be 16.6 dB. Based on this, VOAs are engineered to set the total power of each signal to a specific worst-case value so that power equalization is achieved at the input of the post-EDFAs. It is assumed that the EDFAs

have their own gain control mechanism, so that in the case when not all signals are present at each output, this ensures correct amplification. Here, VOAs take into account the total power (Tp ) as defined in Eq. (6).

Tp = Ps + (rASE × Bofilter )

(6)

where Ps is the signal power in Watts, rASE is the ASE noise spectral density, and Bofilter is a typical nominal optical bandwidth of 12.5 GHz. At the destination nodes, a pre-amplifier is assumed with noise figure of 4.5 dB and a gain such that the total input power is at −4 dBm. 3.2. Transmitter/receiver designs Another constraint related to the physical layer apart from the Q-budgeting approach is now introduced, namely the transmitter/receiver availability. The modeling used in this work allows for the Q-factor calculation to be performed for any new call and in addition it examines if any available transmitters and receivers exist for that call. This means that even if the Q-value for every path on the calculated tree is above the predetermined threshold (i.e., the path is acceptable), the new call will be blocked if there are no available transmitters or receivers for the desired wavelength or for any other alternate wavelength. The network engineering is presented in this paper only for the cases of fixed transmitters/fixed receivers and tunable transmitters/tunable receivers. Due to space limitations, the remaining two scenarios of fixed transmitters/tunable receivers and tunable transmitters/fixed receivers are only presented through their corresponding performance in the results section. 3.2.1. Case 1: fixed transmitters/receivers This case assumes a fixed number of transmitters and receivers. For each source/destination node their total number is assumed to be the number of working wavelengths N times the degree of the node M, as shown in Fig. 2. The figure clearly shows that on the transmitting side 1 × M splitters are needed for each transmitter, followed by M gates, in order to be able to turn the signal off for any unwanted output


1X(M+1) splitter

DMUX

λ1 λ 2

λ 1 , λ 2 ,..., λ N 1 . . . . . . λ 1 , λ 2 ,...,..

(M+1)x1 fiber switch

λ1,λ

. .

. λ .N .

1 . . . . . . . ,..., . . M

. . VOA

λ

λN

λ

M

λ

PRE-AMP

1

λ1,λ

. .

2

. . N .

. .

POST-AMP

. .

M SOAs (Mx1) switch 1X(M) splitter

2

. .

TX

λ

N

TX

λ2

TX

λ1

RX

λ

N

RX

λ

2

2

1

λ1

N

λ

MUX

. .

2

. . λ N .

. . . . VOA

λ

λ1

N

λ

. .

2

. . λ N .

PRE-AMP

. .

POST-AMP

. .

M SOAs 1X(M) splitter

RX

λ

λ

,...,

(2XM)x1 fiber switch

1X(M+1) splitter

DMUX

MUX

679

(MXN) X (0.5XMXN) RX

switch

switch

(MXN) X (0.5XMXN) TX

λ 1 / λ 2 / .. / λ Ν

TX

RX

TX λ 1 / λ 2 / .. / λ Ν λ 1 / λ 2 / .. / λ Ν

RX

λ 1 / λ 2 / .. / λ Ν

Fig. 3. Case 2: Node design for fixed TXs/RXs a second approach. Fig. 4. Node design for tunable TXs/RXs. Table 3 Typical MEMS switch losses (switch size K × L) [19]. Size

Losses in dB

K × L ≤ 25 25 < K × L ≤ 36 36 < K × L ≤ 56 56 < K × L ≤ 68 68 < K × L ≤ 80 80 < K × L ≤ 100 K × L > 100

1 1.5 2.2 3 3.7 4.5 5

port (for the case of passive splitting), while on the receiving side, N × M optical receivers are available directly connected to these gates. 3.2.2. Case 2: fixed transmitters/receivers— a second approach This case presents a slight variation of the aforementioned Case 1, by assuming that the number of the fixed transmitters/receivers equals the number of working wavelengths in the system. This assumption relies on the fact that some of the traffic will be pass-through traffic (typically this is approximately 75% of the traffic) and not all connections will originate or terminate at every node. The only difference from Case 1 is that the number of transmitters/receivers is now decreased to one transmitter/receiver per wavelength. As shown in Fig. 3, M × 1 optical switches are now needed at the receivers so as to direct the dropped wavelengths to the desired optical receiver destinations. Corresponding losses for these kind of optical switches will depend on the port size with typical values shown in Table 3 when these switches are implemented using MEMS technology. 3.2.3. Case 3: Tunable transmitters/receivers This case assumes that both transmitters and receivers are tunable and thus their available number is now equal to the number of wavelengths in the system N. The number of transceivers is set in such a way so as to permit the simultaneous utilization of all distinct wavelengths on the same fiber link if all the constraints are met for the specific connections passing through that link (wavelength continuity con-

straint and Q-factor considerations). Clearly, if the number of transceivers used was less than the number of available wavelengths that would limit the performance of the network, as connections would be blocked due to the unavailability of transceivers and not of wavelengths. As shown in Fig. 4, a switch is needed at both the receiver and transmitter sides with an add/drop capability of 50% on the total number of working wavelengths. This is a realistic percentage of wavelengths to be accessed in a system at each given node. As a result, the dimensions of such a switch will be (N × M) times (0.5N × M) and its loss will depend on its size with typical losses shown in Table 3. Note that in Table 3 K and L refer to the number of inputs and outputs of the switch respectively (K = N × M and L = 0.5N × M). 3.2.4. Network engineering for transmitter/receiver designs For the various node architectures considered in this work, the signal launched power into the fiber is now set to +5 dBm, and each node’s EDFA is assigned a realistic noise figure (NF) depending on its gain (Table 2), with the gain of each pre-amplifier compensating the loss of each preceding fiber span (the fiber attenuation in this analysis is considered to be 0.3 dB/km). The gain of each post-amplifier compensates for the actual node loss and is engineered based on the worst-case insertion loss through the node. The output powers of the pre- and post-amplifiers are now set at +7 dBm to further improve the overall node NF. The worst-case insertion loss is limited either by the maximum splitting loss in the case of fixed transmitters/receivers (Cases 1 and 2), or by the maximum loss of the transmitter’s switch in the case of tunable transmitters/receivers (Case 5). For example, if the maximum node degree in the network is 6 and the number of wavelengths per fiber is 32, the maximum times the power is split is 7, to account for the add/drop ports (8.5 dB loss), while the maximum size of the transmitter’s switch (K × L > 100 in Table 3 for a switch with K input and L output ports) for the tunable transmitters/receivers case corresponds to a maximum transmitter switch loss (TXL ) of 5dB. Thus, the worst-case insertion loss in the tunable case is given by NodeLoss = TXL + SplittingL + SOAL + SwitchL + VOAL + MuxL where the

680


maximum splitting loss for the add channels is now calculated assuming that the maximum times the power is split is 6, which is the maximum node degree. In general, the worst-case scenario in any case is given by NodeLoss = P max[(DmuxL + SplittingL + SOAL + SwitchL + VOAL + MuxL ), A (TXL + SplittingL + GATEL + SwitchL + VOAL + MuxL )], where P SplittingL is the splitting loss for the pass-through channels, and SplittingAL is the splitting loss for the add channels. Again, the noise figure of the p-i-n receiver’s pre-amplifier is assigned a value of 4.5 dB with a gain that is adjusted so as to bring the signal power to −4 dBm. It must also be pointed out that the Q-value is calculated under the same assumptions as described previously for the case of passive versus active splitters. The reader should note that the additional components utilized in these architectures compared to multicastincapable nodes are banks of splitters, SOAs (used as gates), and VOAs. To achieve the broadcast and select functionality in this work, a combination of SOAs as gates and fiber switches was utilized (keeping the switch sizes small and thus limiting the losses). Clearly, other designs can also be used to achieve this functionality; for example, a design with only MEMS switches can be utilized. However, such an approach would require much larger MEMS switches with increased losses and with slower reconfiguration times. The choice of SOAs in particular for the proposed design was made because SOAs have been improving tremendously lately as a technology and their cost has significantly gone down; as such, the original waveguide-based switching vision with SOAs as fast-acting gates that can provide also some gain to compensate for the switching fabric is appropriate for the fast switching scenarios. Furthermore, between the five architectures compared in this work, the only differences between them are at the TX/RX sides (in some cases tunable TXs/RXs are used and in others fixed TXs/RXs are used, always in combination with splitters, SOAs, and smallsized switches). Between these architectures, clearly the ones using tunable TXs/RXs are more costly, however, the small increase in cost is offset by the additional flexibility and functionality provided by these architectures.

4. Routing heuristic algorithms for multicast connections with physical layer impairments The typical approach for multicast communication is to build a multicast tree rooted at the source and spanning all the destinations in a given multicast group. Usually, a cost is assigned to each link of the network, and the objective is to determine the tree of minimum cost. This is the well-known Steiner Tree problem in graph theory, which is known to be NP-complete when the multicast group has more than two members [1]. Thus, constructing costeffective light-trees (finding cost-effective trees along with the wavelength assignment problem for these trees) is also an NP-complete problem. Several heuristics have been developed for the Steiner Tree problem that take as input a graph G = (V, E ) representing the network (fiber links are represented by set of edges E and network nodes are represented by set of vertices V), a source node s ∈ V, a destination set D = [d1 , d2 , . . . , dn ] ⊆ V, and distance costs assigned to each

edge e ∈ E. The output of the heuristic is a tree T spanning the set s ∪ D [23]. Even though the Steiner Tree (ST) heuristic algorithm [2] seems to be efficient as far as the resources of the network are concerned (in terms of total number of links required for building the ST tree) it does not account for any physical layer constraints. Shortest path-based tree (SPT) heuristic algorithms [21], that combine a number of independent shortest paths from source to each destination, also do not account for any physical layer constraints but nevertheless they have the ability to improve the Q-factor at the tree destinations, since they tend to keep the destinations as close (in distance) to the source as possible. By doing this, they tend to decrease the attenuation loss and the signals now pass through a smaller number of optical amplifiers. However, they also tend to increase the total number of links used in the tree, thus utilizing more network resources. To reduce the total number of links on the tree, a variation of the heuristic is utilized that enables the links that are already added to the tree to be reused by the next iteration of the algorithm (Optimized Shortest Paths Tree (OSPT) heuristic [22]). More specifically, when a single shortest path from the source to a destination node is calculated, the initial graph G is updated by setting a cost equal to zero (0) for the links that correspond to the shortest path. This way, these links have a greater probability of being reused in the calculation of a next shortest path, thus reducing the total cost of the tree. Finally, the Minimum Hop Tree (MHT) heuristic algorithm is a modification of the ST heuristic which aims at decreasing the number of hops from the source to the destination nodes. Consequently, the number of amplifiers the signal passes through decreases and so does the ASE noise. Also, the number of total links used in the tree is decreased. However, the attenuation loss is increased as the algorithm does not account for the actual distances between the nodes. The implementation of the MHT heuristic is the same as the ST heuristic, having as the only difference the fact that the ST heuristic (where the link weights represent physical distance (in km)), at each iteration, adds to the tree the destination node that is closer to the already created tree in terms of physical distance (attempting to minimize the impact of the noise added to the signal at each EDFA (higher gain at the EDFAs is required for compensating for the fiber losses of longer distances, leading to higher additive noise)), while the MHT heuristic adds to the tree the destination node that is closer to the currently constructed tree in terms of the number of link hops. Since the ST heuristic appears repeatedly throughout the paper, its pseudocode is given in Algorithm 1. Clearly, several heuristic algorithms exist for solving the multicast routing problem [2,22,24–26]. However, these heuristics do not account for the physical layer impairments encountered by the multicast connections. Furthermore, when the physical layer constraints are introduced when solving the multicast routing problem, only the power budget is typically considered [27,28]. Thus, to implement multicast routing with physical layer constraints, new multicast routing heuristics are needed. Different multicast routing heuristic algorithms that also account for the physical layer impairments are described analytically in this section, that utilize “balancing” techniques for calculating the tree.


681

Algorithm 1 Steiner Tree (ST) heuristic.

Algorithm 2 BLT_Q.

Input: A graph G = (V, E ) representing the network, a source node s ∈ V , a destination set D = [d1 , d2 , . . . , dn ] ⊆ V , and link weights, representing the physical distance, assigned to each edge e ∈ E. Output: A tree T spanning the set [s, D].

Input:Agraph G = (V, E ) representing the network, a source node s ∈ V , a destination set D = [d1 , d2 , . . . , dn ] ⊆ V , distance costs (in km) assigned to each edge e ∈ E and a Q-tolerance value qtolerance . Output: A tree T spanning the set s ∪ D such that the Q-factor for every destination node ∈ D is above or equal to qtolerance .

1: 2: 3: 4: 5: 6: 7: 8: 9: 10:

T ←s k←0 while k < n do Calculate all shortest paths from nodes ∈ T to destination nodes ∈ D Choose the shortest path amongst them and add it to tree T Identify node d j ∈ D last added to tree T Remove destination node d j from D k←k+1 end while return T

1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12:

4.1. Balanced light-tree with Q-tolerance (BLT_Q) heuristic algorithm Initially, the algorithm finds a shortest-path tree T using the ST heuristic, that spans the source and the destination nodes for each multicast group. This algorithm then extends the BLT approach, which only takes into account the power budget when constructing the tree [27], by taking into consideration the Q-factor as well. In particular, BLT_Q is based on the minimum acceptable Q-factor. Considering that the tolerance Q-factor value for each path is q, this algorithm tries to maximize the Q-factor only at those destination nodes where its value is lower than q. Specifically, prior to the balancing part of the algorithm, an initial tree T is created in which the Q-factor is calculated for every destination node in the tree by utilizing the Qbudgeting approach described in Section 2. Then BLT_Q performs delete/add operations on the paths of the initial tree T based on the Q-factor of the destination nodes. Let u be a node with unacceptable Q-factor, and let z be the node with the maximum Q-factor in T. The main idea behind BLT_Q is to delete node u from T, and add it back to the tree by connecting it to node z in the path from source s to node z. This results in an increase of the Q-factor of node u, but it also reduces the Q-factor of all nodes below node z in the tree. This pair of delete/add operations is performed only if it does not reduce the Q-factor of any node beyond that of node u. Thus, after each iteration of BLT_Q, the Q-factor of the node with a value below the tolerance Q-value is increased. The algorithm also ensures that while the Q-factor of some other node(s) is decreased, it does not decrease beyond the tolerance Q-value. The balancing part of the algorithm terminates, if after a number of iterations the minimum Q-value for all destination nodes is higher than the Q-tolerance value, or if two successive iterations fail to increase the minimum Q-factor. The pseudocode of the BLT_Q heuristic is described in Algorithm 2 while its computational complexity is calculated as O(n|V|2 ) according to results presented in [29,30]. Note that the complexity of the

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begin Find initial tree T spanning the destination set D ⊆ V using the Steiner Tree (ST) algorithm i←1 Calculate the Q-factor for all destination nodes ∈ D in T q ←minimum Q-factor of T while i > 0 do if q ≥ qtolerance then i←0 else T ← T U ← Set of leaf nodes with minimum Q-factor Z ← Set of destination nodes with maximum Qfactor In G, compute all shortest paths from every node in set Z to every node in set U Choose the shortest path, pz,u , among them, where z ∈ V and u ∈ U w ← the first node in the path from u to s in T such that w ∈ D or w has a fanout > 1 Delete from T the path from w to u Add pz,u to T Calculate the Q-factor for all destination nodes ∈ D in T q ← minimum Q-factor of T if q > q then T ← T q ← q else i←0 end if end if end while return T

conventional Steiner Tree (ST) heuristic is also O(n|V|2 ) [29]. However, BLT_Q assumes that a ST tree is already constructed before balancing, contributing to an increased execution time for the BLT_Q heuristic. Figs. 5 and 6 show an illustrative example of the balancing procedure of the BLT_Q heuristic, assuming that q is the Q-tolerance value. Specifically, Fig. 5 shows a currently constructed tree T consisting of five destination nodes. The algorithm first identifies the destination nodes with Q-value below q and the destination nodes with the maximum Qfactor values. In this example, it is assumed that node d2 is the node with a Q-value below q and d4 is the maximum Qfactor node. Subsequently, according to Fig. 6, BLT_Q removes node d2 from the tree, as well as all the intermediate nodes and links from node d5 to node d2 , and adds it back to the tree by connecting it via a shortest path originating from the

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maximum Q-factor node, d4 . Note that, in this example it is assumed that with the addition of node d2 back to the tree, via path (d4 − k − d2 ), the Q-factor of d2 is increased, while the Q-factor of the rest of the destination nodes in the tree does not decrease below q. As pointed out, BLT_Q increases only the Q-factor of the tree nodes that their Q-value is below a tolerance value, e.g., q. Thus, the choice of different q values has an impact on the creation of the trees. Specifically, if q is set to ∞, then the BLT_Q heuristic will try to return a tree with the best possible average Q-factor. However, that will also increase the total number of links on the tree. In order to keep the number of links on the tree low and therefore the number of wavelengths used low, it is best to choose a q value equal to the acceptable Q-factor at the receiver (Q-threshold). As the BLT_Q algorithm tends to create trees that have more breadth than depth it decreases the attenuation loss. It also decreases the number of optical amplifiers that the signal passes through, thus decreasing the ASE noise. In contrast, even though the BLT algorithm that accounts only for power budget constraints creates trees that split the signal power the minimum number of times, it tends to create trees that have more depth than breadth, increasing the attenuation loss and the signals now pass through a larger number of optical amplifiers, thus increasing the ASE noise. 4.2. Max degree tree (MDT_F) heuristic algorithm Similar to the BLT heuristic, the MDT_F heuristic algorithm was also developed that accounts only for the power budget constraint (other physical layer impairments such as ASE noise, crosstalk, PMD, etc. are not considered). It tries to control the splitting losses at the nodes by not allowing the construction of trees that have nodes with fanout greater

than a predetermined value F. In this way, losses at the splitting nodes are reduced. However, this approach is appropriate only for network engineering with active splitters, since with passive splitter engineering losses at the splitters cannot be controlled by the algorithm but only by the network topology. In other words, if MDT_F was utilized in a network where node architectures with passive splitters were assumed, the average node degree of the MDT_F tree would have been reduced but the splitting losses would still depend only on the fanout of the network nodes in the physical topology, due to the fixed splitting capabilities of the passive splitters. The worst-case scenario for MDT_F is based on the maximum splitting loss that a signal encounters passing through a node. The idea behind MDT_F is to sequentially add shortest paths to T from a list of sorted shortest paths, examining whether or not the max degree criterion is kept. If with the addition of a new shortest path the max degree criterion is violated, the path is deleted and the next shortest path is selected from the list. The list of paths is sorted based on the cost of the paths in ascending order and one list per destination node is calculated. The performance of the MDT_F heuristic algorithm depends greatly on the F parameter. When F = 1, MDT_F creates trees with serial connected nodes, since the maximum fanout of the nodes must be one. A very small value for F may not be desired as only a long path is created with many hops and therefore the signal has to pass through a large number of amplifiers. On the other hand, a large number for F creates trees that have more breadth than depth, and the total number of links in the tree is increased. Also, note that if a different value of F is used for each node in the network, then the algorithm can be used in optical networks with sparse light splitting since multicast-incapable nodes can be accounted for by letting F = 1 for these nodes. The basic steps of the MDT_F heuristic are described as pseudocode in Algorithm 3 while its computational complexity is calculated as O(n|V|2 ) [29,30]. 4.3. Drop-and-continue tree (DAC) heuristic algorithm Another multicast routing heuristic developed, called the Drop-and-Continue (DAC) heuristic algorithm, works as the MDT_F heuristic when F = 1. The idea behind DAC is the creation of a tree where the signal is not split as it passes through the nodes of the tree, unless that node is a destination [31,32]. The algorithm starts with connecting the source with the destination node that yields the minimum cost path. Then, the last node added to the tree chooses a destination from the remaining destinations in set D, based on the shortest path criterion, and adds it to the tree. The same procedure is followed until all destinations are added. This approach creates trees where the nodes are connected together in a serial way, and it tends to create very long paths, thus minimizing the splitter losses at the intermediate nodes. However, the number of amplifiers the signal passes through is increased, particularly when the size of the multicast group is large compared to the total number of nodes in the network. The pseudocode of MDT_F is slightly modified for the DAC heuristic algorithm and is described in Algorithm 4. Its complexity is again calculated as O(n|V|2 ) according to work presented in [29,30].


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Algorithm 3 MDT_F. Input: A graph G = (V, E ) representing the network, a source node s ⊆ V , a destination set D = [d1 , d2 , . . . ., dn ] ⊆ V and distance costs (in km) assigned to each edge e ∈ E. Output: A tree T spanning the set s ∪ D such that every node ∈ T has a fanout of at most F . If no such a tree exists, the algorithm returns T = ∅. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23:

begin S←s T ←s k←n while k > 0 do Find set P consisting of all shortest paths from node(s) ∈ S to destination node(s) ∈ D. Sort shortest paths in P based on their cost, with the shortest path among them placed first on the list. Let l be the number of shortest paths in P. i←1 while i ≤ l do Identify shortest path pi ∈ P. if With the addition of pi to T the fanout of nodes in T does not exceed F then Add pi to T Identify destination node d j last added to T . Remove destination node d j from D. Add destination node d j to S. else i←i+1 end if end while k←k−1 end while return T

Algorithm 4 DAC. Input: A graph G = (V, E ) representing the network, a source node s ∈ V , a destination set D = [d1 , d2 , . . . , .dn ] ⊆ V and distance costs (in km) assigned to each edge e ∈ E. Output: A tree T spanning the set s ∪ D such that every node ∈ T has a fanout of at most 1. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15:

begin T ←s k←0 v←s while k < n do Find set P consisting of all shortest paths from node v to destination node(s) ∈ D. Sort shortest paths in P based on their cost, with the shortest path among them placed first on the list. Identify shortest path p among the paths in P. Add p to T Identify destination node d j last added to T . Remove destination node d j from D. v ← dj k←k+1 end while return T

Fig. 7. Flowchart of the IA–MC–RWA algorithm.

5. Impairment—aware provisioning of multicast connections For each multicast request that randomly arrives, the impairment-aware multicast routing and wavelength assignment (IA–MC–RWA) algorithm first solves the routing problem by finding a multicast tree that can accommodate the request utilizing any of the algorithms described in Section 4 and then tries to assign a wavelength for that tree based on the first-fit wavelength assignment technique [24] (note that a single multicast connection request occupies a full wavelength). More precisely, the IA–MC–RWA algorithm attempts to assign to the tree the first wavelength with available transmitters and receivers. Multicast requests are blocked if there is no available wavelength for the entire tree either due to the transmitters/receivers constraint or due to the unavailability of a route. If a wavelength assignment is possible, the Q-factor at each destination on the tree is evaluated according to the Q-budgeting approach described in Section 2. The multicast request is blocked if there is at least one destination on that tree with a Q-value that falls below a predetermined threshold value and there is no alternate wavelength assignment possible. Otherwise, a new wavelength assignment is implemented and the heuristic is repeated. Fig. 7 shows the flowchart describing the aforementioned IA–MC– RWA methodology. The reader should note that in this work only static multicasting is assumed as this is in line with the large amount of work in the literature that considers that the entire multicast tree is provisioned/unprovisioned as a whole and not dynamically (i.e., nodes cannot join and leave the multicast session along its duration). However, as dynamic multicasting is also important for certain applications where end-users can join and leave a multicast session dynamically, it is currently being considered as future work to complement the work presented in this paper.

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T. Panayiotou et al. / Computer Networks 91 (2015) 675–688 Table 4 Network statistics. Number of nodes Number of links Average distance Maximum distance Minimum distance Average node degree Minimum node degree Maximum node degree Diameter

50 98 (196 arcs) 60 km 100 km 20 km 3.92 3 6 305 km/6 hops

6. Performance results To evaluate the performance of the different node architectures, network engineering, and multicast routing algorithms, a network is used that meets the characteristics of a metro network in terms of average distance lengths, density, and number of nodes. The engineering of the network, as well as the Q-factor modeling, reflects the characteristics of the specific network (e.g., maximum splitting losses, maximum link distance, etc.). Further, the network is large enough so as to allow the multicast routing algorithms to work with different multicast group sizes, and dense enough in order to allow the investigation of the impact of the different multicast routing algorithms proposed on the network performance. Summarized information of the network utilized is shown in Table 4. Note that the Matlab tool was used for the simulations described in this section. A dynamic traffic model is used where multicast sessions arrive at each node according to a Poisson process and the holding time is exponentially distributed with a unit mean, for a network load of 100 Erlangs (with the mean arrival rate of the Poisson process set at λ = 100 and the mean departure rate set at μ = 1). Multicast requests were randomly generated (randomness refers to the member of nodes in the multicast group) and each request was associated with the appropriate arrival and departure times that were generated according to the predefined parameters of the Poisson process. In this work, a Q-threshold of 8.5dB is assumed, corresponding to a BER of 10−12 . In order to determine the Q-value for each call, a baseline system Q-value is first calculated based on the signal and noise terms assuming 10Gbps bit rate, a pre-amplified p-i-n photodiode, and a WDM system with 32 wavelengths spaced at 100 GHz. Externally modulated transmitters and standard NRZ modulation is assumed.

Also, note that no Forward Error Correction (FEC) is assumed in this work. In each simulation 5000 requests were generated for each multicast group size for a total of 40, 000 multicast requests and the results were averaged over five simulation runs. The blocking probability was calculated for each simulation run while varying the multicast group size. The reader should note that the variance of the averaged values over the simulation runs was not significant. Specifically, it is of the order of 10−2 for the maximum multicast group size assumed (25 member nodes) while as the multicast group size reduces, the variance goes to 0. For the evaluation of the blocking probability, the IA–MC–RWA of Fig. 7 is assumed for every node architecture/engineering and for every multicast routing technique described above. The first set of simulations deals with the question of what type of splitters should be used in the optical nodes, namely active or passive, as well as the choice of the routing heuristic on the operation of the network. Fig. 8 (a) illustrates the simulation results (for all heuristic algorithms considered) for the blocking probability versus the multicast group size when a number of multicast algorithms are implemented assuming node engineering with active splitters and Fig. 8 (b) shows the blocking probability versus the multicast group size assuming passive splitters (for a subset of the algorithms that exhibit reasonable blocking results). From Fig. 8 (a), it is initially clear that some of these heuristics exhibit very high blocking probability (such as DAC, MHT, etc) and are thus not considered further in the results that follow. Also, from both figures it is shown that the Steiner Tree heuristic (multicast tree with the minimum cost based on shortest path calculations) and the BLT algorithm that only takes power budget constraints into consideration exhibit much higher blocking probabilities than the proposed BLT_Q algorithm, for both active and passive cases. Note that BLT_Q is examined for the two extreme cases; for the case where the Q-tolerance value was set to ∞ (BLT_Q_∞) and for the case where the Q-tolerance value was set to be equal to the Q-threshold (BLT_Q_8.5). Results of both passive and active cases show that BLT_Q_8.5 performs better than BLT_Q_∞, an indicator that a tolerance Q-value higher than the acceptable Q-factor forces the algorithm to find trees with shorter paths, leading to trees utilizing a larger number of links. On the other hand, a tolerance Q-value lower than the acceptable Q-factor is not examined as this will result to the creation of trees with insufficient Q-factor at the destination nodes (these trees will eventually be blocked).

Fig. 8. Blocking probability versus multicast group size for network engineering with (a) active splitters and (b) passive splitters.

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Fig. 11. Blocking probability due to TXs/RXs versus multicast group size for network engineering with fixed transmitters/receivers (Case 1).


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Fig. 9. Blocking probability versus multicast group size for network engineering with fixed transmitter/receivers (Case 1).

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The overall simulation results show that there is no particular gain when using active splitters instead of passive splitters, at least for the worst-case engineering scenario that was presented in Section 3 above. This is due to the fact that VOAs are utilized to attenuate the total power of each signal to a predetermined value that is calculated based on the worst-case signal power scenario. It must be noted here that active splitters are not commercially available as of yet and even when they do become mainstream, their cost and increased control complexity will still tip the scale towards their passive counterparts. As a result, the rest of this work assumes passive optical splitters at the multicast-capable optical nodes. The rest of the figures present simulation results for the blocking probability versus the multicast group size when a number of multicast routing heuristic algorithms are used assuming different network engineering scenarios. In particular, Fig. 9 assumes the Case 1 scenario (fixed transmitters/receivers), Fig. 12 assumes the Case 2 scenario (fixed transmitters/receivers— second approach), and Fig. 13 assumes the tunable transmitters/receivers scenario. (Plots for Case 3 (tunable transmitters and fixed receivers) and Case 4 (fixed transmitters and tunable receivers) are omitted in this paper as they present results very similar to the results of Cases 2 and 5 respectively.) Blocking in all cases can be due to the Q-factor or the unavailability of resources (wavelengths and/or transmitters/receivers). The break-down of the results for two of the cases (Cases 1 and 5) are also presented. Specifically, for Case 1, Fig. 10 shows blocking only due to Q and Fig. 11 shows blocking only due to the unavailability of TXs/RXs. Similarly, for Case 5, Fig. 14 shows blocking only due to Q and Fig. 15 shows blocking only due to the unavailability of TXs/RXs. The break-down of the results for the rest of the cases is omitted as the blocking probability is mainly limited by the unavailability of TXs/RXs. Specifically for Cases 2, 3, and 4, both the blocking probability due to

Fig. 12. Blocking probability versus multicast group size for network engineering with fixed transmitter/receivers (Case 2).


Fig. 10. Blocking probability due to Q versus multicast group size for network engineering with fixed transmitters/receivers (Case 1).

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Q and the blocking probability due to the unavailability of wavelengths was found to be close to 0. The reader should note that all these architectures are comparable in terms of cost and capacity. Their cost differences are due to the different assumptions made for the TXs/RXs designs. In general, tunable transceivers are more expensive than fixed. However, as will be shown next, in order for the fixed transceivers to achieve an acceptable performance, their numbers are larger compared to the tunable transceivers case. Simulation results show that the blocking probability is greatly reduced in the case of fixed TXs/RXs (Fig. 9), since in this case the blocking probability due to Q (Fig. 10) is not significant, compared to the rest of the cases examined. Specifically, in the fixed TX/RX case the worst-case node loss is less compared to the cases with tunable components (Cases 3 − 5), where switches are also used in the design of the add/drop ports. Additionally, in the case of fixed TXs/RXs (Case 1) there is more flexibility in the network to assign wavelengths to the multicast connections as there are more TXs/RXs available for wavelength assignment (e.g., in the case of tunable TXs/RXs only 50% of the possible input ports can be dropped at the same time). The results also show that the BLT_Q_8.5 heuristic performs the best for all network engineering cases as it tends to create trees that have more breadth than depth, limiting

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Fig. 14. Blocking probability due to Q versus multicast group size for network engineering with tunable transmitter/receivers (Case 5).

the blocking due to Q. OSPT is the second best heuristic as it tends to push the destination nodes closer to the source node compared to the other routing heuristics but it also tends to increase the total number of the links in the lighttree (increasing the blocking probability due to unavailability of wavelengths). The case of fixed transmitters/receivers (but with some limitations on their numbers) whose performance is illustrated in Fig. 12, as well as the case of tunable transmitters/fixed receivers (not shown here but with results very similar to the results shown in Fig. 12), exhibited the highest overall blocking probability among all cases. For these cases there is also no difference in terms of performance when different routing techniques are utilized. This is due to the fact that for these two cases blocking is mainly caused due to the lack of receivers rather than due to Q or due to the unavailability of wavelengths. Thus, the proposed routing techniques that have an advantage in terms of physical layer impairments (PLIs) are performing similar to the ones that do not take the PLIs into consideration. Furthermore, comparing the performance results for the designs for Case 3, Case 4 (with results that are omitted in this paper but that are very similar to the results shown in Fig. 13), and Case 5, one can deduct that it is more important to have more available receivers than transmitters for multicast connectivity, as the blocking probability for Cases 4 and 5 was significantly lower compared to Case 3. Note that in order for the architectures to be comparable, for all the cases that tunable TXs and/or RXs are assumed, the number of tunable TXs and/or RXs is assumed to be equal to the number of wavelengths while only 50% of the possible input/output ports can be used at the same time. In general, the blocking probability for some engineering cases is impractically high, especially for large multicast group sizes. Specifically, the blocking probability for Cases 2

and 3 is limited by the number of available receivers (equal to the number of wavelengths in these architecture designs). Note, however, that for the simulations performed in this work only 32 wavelengths are utilized, whereas many more wavelengths per fiber are considered today. A small number of wavelengths is chosen in order to avoid extensive running times; however, this tends to cause a significant blocking probability due to the unavailability of resources, something that in practice can be avoided if a larger number of wavelengths is utilized (in current networks WDM systems of up to 128 wavelengths can be deployed). Furthermore, in practical terms the multicast group sizes would be small (in general the multicast applications would have a small percentage of the network nodes as destinations), thus also reducing significantly the blocking probability values. Nevertheless, these results are shown in this work in order to demonstrate the impact of the different architecture/engineering scenarios to the algorithms and the system performance. Such results can be very useful to network engineers and designers when considering which architecture or network engineering scenario to use during the design and operation of their network. In order to ascertain the performance of the multicast routing heuristics when the multicast group size is not fixed but the multicast calls are of varying multicast group size, another simulation scenario was examined. Specifically, the blocking probability versus the averaged multicast group size was generated for a fixed network load of 100 Erlangs. Note that the rest of the simulation parameters remain the same as before. For each simulation point of an averaged multicast group size k, multicast requests were generated with their group size being uniformly distributed among the set of numbers [k − 2, k − 1, k, k + 1, k + 2]. Then, once the multicast group size was specified, the member nodes of the group were randomly chosen among the network nodes. Figure 16 shows the blocking probability versus the averaged multicast group size for the ST, BLT, BLT_Q_8.5, and OSPT heuristic algorithms and for the fixed node design scenario (Case 1) that exhibited the best performance compared to the rest of the architecture/engineering scenarios. The results clearly show that as the averaged multicast group size increases the blocking probability also increases, with the BLT_Q_8.5 heuristic algorithm that considers for the PLIs performing the best compared to the rest of the multicast routing heuristic algorithms developed for comparison purposes. Note that the performance results of the heuristic algorithms shown in Fig. 16 are very close to the results of Fig. 9, where

Fig. 15. Blocking probability due to the unavailability of TXs/RXs versus multicast group size for network engineering with tunable transmitter/receivers (Case 5).


Fig. 16. Blocking probability versus averaged multicast group size for network engineering with fixed transmitter/receivers (Case 1). Table 5 Q-threshold for different BER values (Eq. 1). 10−8 7.48


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that a more refined interaction between physical and logical layer is needed for multicast connection provisioning. Specifically, from the performance results it is clear that a design of a multicast-capable optical cross-connect utilizing passive splitters will not affect the network performance (compared to an active splitters’ design where the node has control on the splitting of the signal) and that the design of the node in terms of the choice of transmitters and receivers significantly affects the blocking probability. Also, the choice of the routing algorithm greatly impacts the network performance, with the proposed BLT_Q heuristic algorithm outperforming all the rest. Current work focuses on dynamic multicasting where end-users can join and leave a multicast session dynamically. Furthermore, the presence of a small number of regenerators and their placement problem is currently being investigated as a topic of future work. References

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Fig. 17. Blocking probability versus multicast group size for network engineering with fixed transmitter/receivers (Case 1). The BLT_Q heuristic is examined for different Q-thresholds.

the multicast group size is kept fixed for every simulation point. Finally, the blocking probability versus the multicast group size, for different Q-thresholds, is also evaluated, but only for the BLT_Q heuristic that it is shown to perform the best, among all the multicast routing heuristic algorithms developed. Also, only the fixed node design scenario (Case 1) is considered, as it is the one that exhibited the best performance compared to the rest of the architecture/engineering scenarios. Table 5 shows the Q-thresholds assumed in accordance to each target BER (given by Eq. 1). Results in Fig. 17 clearly illustrate that the blocking probability of the BLT_Q heuristic increases as the multicast group size increases, and as the Q-threshold is set at higher levels. This is reasonable, as a higher Q-threshold value limits the optical signal reach, thus causing a larger number of calls to be blocked due to insufficient Q-factor at the receiver end. 7. Conclusions This work expands on our previous work presented in [11] where novel “light-tree balancing techniques” to investigate the problem of provisioning multicast sessions in metropolitan all-optical networks were first introduced. In this work the impact of node design/network engineering on the design of the multicast routing algorithms is shown, especially when the physical layer impairments (via the Q-factor) are taken into consideration. It is demonstrated via simulation that different engineering of the physical layer produces different multicast group blocking, a strong indicator

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[22] A. Khalil, A. Hadjiantonis, G. Ellinas, M. Ali, Pre-planned multicast protection approaches in WDM mesh networks, in: Proceedings of the 31st European Conference on Optical Communication (ECOC), Glasgow, Scotland, 2005. [23] S.L. Hakimi, Steiner’s problem in graphs and its implications, Networks 1 (1971) 113–133. [24] Y. Sun, et al., Multicast routing in all-optical wavelength-routed networks, SPIE Opt. Netw. Mag. 2 (4) (2001) 101–109. [25] G.S. Poo, Y. Zhou, A new multicast wavelength assignment algorithm in wavelength-routed WDM networks, IEEE J. Select. Areas Commun. 24 (4) (2006) 2–12. [26] J. Wang, X. Qi, B. Chen, Wavelength assignment for multicast in alloptical SEM networks with splitting constraints, IEEE/ACM Transac. Netw. 14 (1) (2006) 169–182. [27] Y. Xin, G.N. Rouskas, Multicast routing under optical layer constraints, Proc. IEEE Infocom. 4 (2004) 2731–2742. [28] M. Ali, J.S. Deogun, Power-efficient design of multicast wavelength routed networks, IEEE J. Select. Areas Commun. 18 (10) (2000) 1852– 1862. [29] H. Takahashi, A. Matsuyama, An approximate solution for the Steiner problem in graphs, Math. Japon. 24 (1980) 573–577. [30] E.W. Dijkstra, A Note on two problems in connexion with graphs, Numer. Math. (1959) 269–271. [31] M. Ali, J.S. Deogun, Cost-effective implementation of multicasting in wavelength-routed networks, IEEE/OSA J. Lightwave Technol. 18 (12) (2000) 1628–1638. [32] R. Lin, W.D. Zhong, S. Bose, M. Zukerman, Multicast traffic grooming in tap-and-continue WDM mesh networks, IEEE/OSA J. Opt. Commun. Netw. 4 (11) (2012) 918–935. Tania Panayiotou received her diploma degree in computer engineering from the University of Patras, Greece in 2005 and the Ph.D degree in computer engineering from the University of Cyprus in 2013. She is currently a research fellow at KIOS Research Center for Intelligent Systems and Networks of the University of Cyprus. Her research interests include computer networks, telecommunications and optical networks with emphasis on routing/grooming and protection of multicast and groupcast connections on all-optical and translucent optical networks with physical layer constraints. Her research has been funded by the Research Promotion Foundation (RPF) of Cyprus, by the University of Cyprus and the KIOS Research Center for Intelligent Systems and Networks. She is a member of the IEEE and the author or co-author of several publications in leading peer-reviewed journals and conferences. Georgios Ellinas holds B.S., M.S., M.Phil.,and Ph.D. degrees in electrical engineering from Columbia University. He is currently an associate professor and the Chair of the department of electrical and computer engineering at the University of Cyprus. Prior to joining the University of Cyprus, he was an associate professor of electrical engineering at the City College of the City University of New York (2002–2005). Before joining academia, he was a senior network architect at Tellium (2000–2002) and a senior research scientist in Telcordia Technologies’ (formerly Bellcore) Optical Networking Research Group, where he performed research for the DARPA-funded Optical Networks Technology Consortium (ONTC), Multiwavelength Optical Networking (MONET), and Next Generation Internet (NGI) projects from 1993 to 2000. He has coauthored two books on optical networking and more than 170 journal and conference papers and is also the holder of 29 patents on optical networking. His research interests are in the areas of optical architectures, routing and wavelength assignment algorithms, fault protection-restoration techniques in arbitrary mesh optical networks, optical access networks, hybrid opticalwireless access networks, access networks, and intelligent transportation systems.

Neophytos Antoniades received the B.S., M.S., M. Phil and Ph.D. degrees all in electrical engineering from Columbia University, NY, NY.His Ph.D. work at Columbia University focused on modeling of optical components and WDM fiber optic communication systems and networks. During his industrial career with Bell Communications Research (Bellcore) and Corning Inc. Dr. Antoniades’ research activities included design, engineering, and prototyping support of next generation Wavelength Division Multiplexing (WDM) optical systems and networks, modeling of transmission impairments and research on new computer modeling techniques. During his tenure at Bellcore he contributed to the construction of the first experimental prototype multi-wavelength optical networks (MONET and ONTC) based on large-scale US governmentsupported research projects. He is now a professor in the Engineering Science and Physics Department at The College of Staten Island, The City University of New York where he joined in September of 2003. His current research interests include access and metro fiber optic communication systems with a strong research focus on the use of fiber optic technologies for system implementations in avionics platforms. He is a senior member of the IEEE and a member of the Photonics society and has been a technical committee member of various conferences and workshops in the telecommunications field as well as a frequent reviewer in all major peer reviewed journals in the field. He currently holds two US patents and is the author or co-author of over eighty publications in leading peer-reviewed journals and conferences. He is also the author of several book chapters in the field of optical communications, a book on computer simulation as well as a children’s book.

Antonis Hadjiantonis received the BEEE and MEEE from the City College of New York in 1998 and 2000. In 2005 and 2006 he earned the M.Phil. and Ph.D. degrees, both in electrical engineering from the City University of New York (CUNY). He has been a founding member of the Next Generation Networking Group (NGNG) at the City University of New York, and, while there, he was heavily involved in funded research projects in the areas of IP/WDM network overlaying, traffic grooming, optical access networks and control and management of optical networks. After his return to Cyprus, he was employed as a senior researcher with SignalGenerix Inc. (2005–2007) where he worked on various research proposals and funded projects on optical networks. Since 2006, he is an assistant professor with the Department of Engineering at the University of Nicosia. He has been the coordinator of an RPF-funded project and is currently involved in three other RPF-funded projects (in one as coordinator) in the general field of optical communication technologies involving Metro Access solutions, physical impairments in optical network design and Radio over Fiber architectures. His research output includes more than 30 journal and conference proceeding publications in the area of optical networking. His research interests include vertical integration in multi-layer networking environments, routing and signaling algorithms in optical networks, and optical access network survivable architectures.