Reconfiguring multicast sessions in elastic optical networks adaptively with graph-aware deep reinforcement learning

Abstract

With the fast deployment of datacenters (DCs), bandwidth-intensive multicast services are becoming more and more popular in metro and wide-area networks, to support dynamic applications such as DC synchronization and backup. Hence, this work studies the problem of how to formulate and reconfigure multicast sessions in an elastic optical network (EON) dynamically. We propose a deep reinforcement learning (DRL) model based on graph neural networks to solve the sub-problem of multicast session selection in a more universal and adaptive manner. The DRL model abstracts topology information of the EON and the current provisioning scheme of a multicast session as graph-structured data, and analyzes the data to intelligently determine whether the session should be selected for reconfiguration. We evaluate our proposal with extensive simulations that consider different EON topologies, and the results confirm its effectiveness and universality. Specifically, the results show that it can balance the trade-off between the number of reconfiguration operations and blocking performance much better than existing algorithms, and the DRL model trained in one EON topology can easily adapt to solve the problem of dynamic multicast session reconfiguration in other topologies, without being redesigned or retrained.

Full text

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Reconfiguring Multicast Sessions in Elastic Optical
Networks Adaptively with Graph-Aware Deep
Reinforcement Learning
Xiaojian Tian, Baojia Li, Rentao Gu, and Zuqing Zhu, Senior Member, IEEE
Abstract—With the fast deployment of datacenters (DCs),
bandwidth-intensive multicast services are becoming more and
more popular in metro and wide-area networks, to support
dynamic applications such as DC synchronization and backup.
Hence, this work studies the problem of how to formulate and
reconfigure multicast sessions in an elastic optical network (EON)
dynamically. We proposed a deep reinforcement learning (DRL)
model based on graph neural networks (GNNs) to solve the
sub-problem of multicast session selection in a more universal
and adaptive manner. The DRL model abstracts the topology
information of the EON and the current provisioning scheme
of a multicast session as graph-structured data, and analyzes
the data to intelligently determine whether the session should
be selected for reconfiguration. We evaluate our proposal with
extensive simulations that consider different EON topologies, and
the results confirm its effectiveness and universality. Specifically,
the results show that it can balance the tradeoff between the
number of reconfiguration operations and blocking performance
much better than the existing algorithms, and the DRL model
trained in one EON topology can easily adapt to solve the
problem of dynamic multicast session reconfiguration in other
topologies, without being redesigned or retrained.
Index Terms—Optical multicast, Elastic optical networks
(EONs), Network reconfiguration, Deep reinforcement learning
(DRL), Graph neural network (GNN).
I. INTRODUCTION
In recent years, the rising of cloud services and live video
streaming has made multicast services more and more popular
in the Internet [1]. This trend becomes even more remarkable
since 2020, because of the surge in demands for video con-
ferencing and online classroom services during the epidemic.
Meanwhile, due to the fast deployment of datacenters (DCs)
all over the world, the popularity of multicast services can also
be seen in metro and wide-area networks [2], especially for
bandwidth-intensive applications such as DC synchronization
and backup, distributed scientific computing, etc [3]. This
has put great pressure on DC interconnects (DCIs) and made
multicast provisioning in DCIs an attractive research topic.
With the tremendous bandwidth in each optical fiber, optical
networking plays an important role in DCIs, and a latest study
[4] even suggested that an optical-circuit-switched architecture
could be more scalable and cost-effective for regional DCIs
X. Tian, B. Li and Z. Zhu are with the School of Information Science and
Technology, University of Science and Technology of China, Hefei, Anhui
230027, P. R. China (email: zqzhu@ieee.org).
R. Gu is with the School of Information and Communication Engineering,
Beijing University of Posts and Telecommunications, Beijing 100876, China.
Manuscript received on May 9, 2021.
than a natural packet-switched network. More promisingly, the
advances on the flexible-grid elastic optical networks (EONs)
can further improve the performance of optical switching on
spectrum-efficiency, adaptivity and application-awareness [5–
7]. Note that, for bandwidth-intensive and long-lasting applica-
tions (e.g., DC backup), realizing multicast directly in the op-
tical domain has the benefits such as less bandwidth/protocol
overheads and easier to obtain large throughputs [8]. The
agility of EONs would further promote these benefits, which
motivated people to study how to provision multicast services
in EONs and proposed various algorithms [9–14].
Meanwhile, the semi-permanent optical layer in telecommu-
nication networks might not adapt to the dynamic applications
and traffic in DCIs [15]. Therefore, a dynamic optical layer
with fast reconfiguration speed is desired. For instance, the
standardization effort in [16] suggested that to properly support
inter-DC communications, a dynamic optical network should
be reconfigurable within a few milliseconds. Following this
trend, researchers have considered different dynamic operation
scenarios for EONs, e.g., the reconfiguration to accommodate
time-varying unicast traffic [17, 18], spectrum defragmentation
[19], lightpath restoration [20], and spectrum retuning for
bulk data transfers [21]. The dynamic nature of the multicast
services in DCIs determines that each multicast session might
also need to be updated consistently to maintain the optimality
of its service provisioning scheme (i.e., the one that consumes
the least spectrum resources) [22]. For example, during a one-
to-many DC backup, each destination DC joins the multicast
session when the data of its interest starts to be transferred,
and it will leave the session when its data transfer is done.
The problem of how to formulate and reconfigure multicast
sessions in EONs dynamically was previously studied in [22].
Specifically, the authors divided the problem into two sub-
problems, i.e., session selection and session reconfiguration,
and designed algorithms to solve them. The session selection
algorithm finds the most “critical” multicast sessions whose
provisioning schemes waste the most spectrum resources
when being compared with the optimal ones (i.e., off their
optima the most), to reconfigure. After the sessions have
been selected, they can be reconfigured with either full or
partial rearrangements in the session reconfiguration, to free up
unnecessary spectrum usages. Note that, the reconfiguration of
multicast sessions should be evaluated from two perspectives,
i.e., the number of reconfiguration operations and overall
blocking probability of multicast sessions. Specifically, by
invoking more reconfiguration operations, we generally can

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readjust the provisioning schemes of multicast sessions better
to save more spectrum resources, and thus a lower blocking
probability will be get in the future. Hence, to maximize
the efficiency of the reconfiguration, we should use the least
reconfiguration operations to achieve the largest reduction on
blocking probability. However, to the best of our knowledge,
how to optimize this tradeoff has not been fully explored yet.
We can see that in the reconfiguration of multicast ses-
sions, the sub-problem of session selection is more relevant
to the aforementioned tradeoff. Nevertheless, the heuristic
approaches developed in [22] (i.e., the D-/Q-value based
selection strategies) cannot universally adapt to dynamic EON
environments, and the problem of how to select between them
and determine their key parameters can only be tackled in an
empirical manner. This motivates us to revisit the sub-problem
in this work. Note that, deep reinforcement learning (DRL) can
obtain statistically optimal solutions for complex and time-
varying problems without explicit programming [23]. Hence,
we try to replace the heuristic approaches for session selection
with a DRL-based algorithm, and expect that it can balance
the tradeoff between the number of reconfiguration operations
and blocking probability better.
Note that, in order to select multicast sessions in an EON
to reconfigure, we need to process data in graph structure,
which can hardly be handled well by the neural networks
(NNs) in linear structures. This is because certain important
information buried in the graph-structured data can be lost,
and the DRL models with NNs in linear structures need to be
redesigned and retrained when the EON’s topology changes.
Fortunately, graph neural networks (GNNs) [24] can fulfill
the requirements much better, as they can operate directly on
graph-structured data to understand the complex relations in
it for the applications related to networks [25].
In this work, we propose a DRL model based on GNNs
to solve the sub-problem of multicast session selection in a
more universal and adaptive way. The DRL model takes the
topology information of the EON and the current provisioning
scheme of a multicast session as the input, abstracts them as
graph-structured data, and analyzes the data to intelligently
determine whether the multicast session should be selected for
reconfiguration. We evaluate the proposed graph-aware DRL
model with extensive simulations that consider different EON
topologies. The simulation results confirm the effectiveness
and universality of our proposal, and show that it can balance
the tradeoff between the number of reconfiguration operations
and blocking probability much better than the existing heuris-
tic approaches, without empirical parameter adjustments.
The rest of the paper is organized as follows. Section II
briefly surveys the related work. We describe the network
model and operation principle of the dynamic reconfiguration
of multicast sessions in EONs in Section III. The graph-aware
DRL model for session selection is designed in Section IV, and
we discuss its performance evaluations in Section V. Finally,
Section VI summarizes the paper.
II. RELATED WORK
Multicast in the optical domain has been studied since the
inception of wavelength-division-multiplexing (WDM) net-
works, and Sahasrabuddhe et al. [8] first came up with the
concept of light-tree for it. One can refer to the survey in
[26] for a complete review of optical multicast in fixed-grid
WDM networks. The proposals of flexible-grid EON [5–7]
considered to leverage bandwidth-variable transponders (BV-
Ts) and bandwidth-variable switches (BV-WSS’) to manage
the spectrum allocation in the optical layer with a fine granu-
larity of 12.5GHz or even less, and thus can make the optical
layer more spectrum-efficient and adaptive. Meanwhile, the
flexible spectrum management in EONs transforms the well-
known routing and wavelength assignment (RWA) problem in
WDM networks into a more complex one, i.e., the routing and
spectrum assignment (RSA) [27]. Hence, the provisioning of
optical multicast should be revisited for EONs.
In [9], the authors proposed two multicast-capable RSA
(MC-RSA) algorithms for EONs and analyzed their perfor-
mance. Liu et al. [12] improved the performance of MC-RSA
by leveraging layered auxiliary graphs. Nevertheless, these two
studies did not consider the adaptive modulation-level selec-
tion in EONs. The multicast provisioning with impairment-
aware routing, modulation and spectrum assignment (RMSA)
was addressed in [11], where the authors designed two integer
linear programming (ILP) models and a few heuristics. Then,
the multicast-capable RMSA (MC-RMSA) algorithms to sup-
port distance-adaptive transmissions were developed in [13].
The authors of [14] introduced light-forest to further improve
the performance of MC-RMSA and proposed a polynomial-
time approximation algorithm. In addition to algorithmic con-
tributions, people have also leveraged the idea of software-
defined EON (SD-EON) to experimentally demonstrate the
control plane operations for optical multicast in [28].
However, the aforementioned studies all assumed that the
optical switches are multicast-capable (MC) (i.e., supporting
light-splitting). Note that, MC optical switches usually have
complicated architectures and thus can be relatively expensive
[26]. Therefore, it might not be cost-effective to build an
EON with them, since the majority of the communications
in the EON will still be for unicast services. This issue can
be addressed by realizing multicast with multicast-incapable
(MI) optical switches, i.e., establishing a logic light-tree for
each multicast session with multiple unicast lightpaths [10].
Specifically, the study in [10] proposed a spectrum-flexible
member-only relay (OL-M-SFMOR) scheme for this purpose.
Another benefit of realizing multicast with MI optical
switches is that the multicast sessions can be reconfigured in
a local and easier manner. This is because the multicast with
MC optical switches has the restriction that all the branches of
a light-tree should have the same spectrum assignment, while
this is not required by the OL-M-SFMOR scheme [10]. In [22],
the authors studied how to formulate and reconfigure multicast
sessions dynamically, assuming that OL-M-SFMOR is used in
an EON built with MI optical switches. Nevertheless, as we
have already explained, the algorithms proposed in [22] for
multicast session selection still have a few drawbacks, which
motivate us to revisit the sub-problem in this work and try to
solve it better with a novel graph-aware DRL model.
Previously, Li et al. [29] designed a deep neural network
(DNN) to predict the performance of multicast light-trees.

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However, the DNN still uses a linear architecture, which is
not good at processing graph-structured data, and the topic
was not on multicast reconfiguration. Due to its promising
performance on processing graph-structured data, GNN has
attracted great attention nowadays [25], especially for the
complex optimizations in networks [30, 31].
III. PROBLEM DESCRIPTION
In this section, we explain the network model and operation
principle of the dynamic multicast reconfiguration in EONs.
A. Network Model
The topology of an EON for DCI is modeled as a directed
graph G(V, E ), where Vand Eare the sets of DCs and fiber
links, respectively. Here, similar to the case in [22], we assume
that the EON is built with MI optical switches. On each link
e∈E, there are Ffrequency slots (FS’), each of which has a
bandwidth of 12.5GHz. The BV-Ts that terminate each fiber
link are assumed to be the sliceable ones [32], which means
that as long as there are sufficient spectrum resources on a
link, its BV-Ts can always be sliced to facilitate the requested
lightpath transmissions.
We model each multicast session as M R(s, D, b, t), where
s∈Vdenotes the source, Drepresents the set of destinations,
bis the bandwidth demand in Gbps, and tstands for its life-
time. In this work, we consider a dynamic EON environment
that each multicast session M R(s, D, b, t)can come and leave
on-the-fly, and during its life-time t, the DCs in Dcan change
over time too. Hence, when a new multicast session first
comes in, we leverage the OL-M-SFMOR scheme in [10]
to set up several lightpaths for establishing a logic light-
tree, such that each destination in Dcan receive bGbps
from the source sthrough one or more lightpaths. Here, each
lightpath for serving the multicast session can only start and
end at its member nodes (i.e., those in s∪D) for saving
BV-Ts, according to the principle of OL-M-SFMOR [10].
As the optical signal is only transmitted all-optically on each
lightpath, the RSA schemes of different lightpaths in the logic
light-tree are independent, i.e., the spectrum assignments on
different branches of the light-tree can be different.
After the initial provisioning of the multicast session, the
DCs in Dcan change over time. Then, when a DC leaves
the session or a new DC joins in, the lightpaths in the logic
light-tree are updated, still with OL-M-SFMOR. Nevertheless,
this might gradually degrade the optimality of the logic light-
tree, the RSA schemes of certain lightpaths in it can be sub-
optimal and waste spectrum resources. Therefore, we need to
reconfigure the multicast session adaptively from time to time.
B. Dynamic Reconfiguration of Multicast Sessions
We use Algorithm 1 to explain the operation principle of
dynamic formulation and reconfiguration of multicast sessions
[22]. Lines 2-10 explains how to formulate multicast sessions
dynamically. Then, the reconfiguration of multicast sessions is
triggered periodically to maintain the optimality of the logic
light-trees of in-service multicast sessions. Here, we need to
solve two sub-problems for the reconfiguration, i.e., session
selection (Line 12) and session reconfiguration (Line 13). The
session selection needs to find the most “critical” multicast
sessions whose logic light-trees are off their optima the most,
to reconfigure. The session reconfiguration rearranges the logic
light-trees of the selected sessions to save spectrum resources,
which can be done with either full or partial rearrangements
[22]. Specifically, the full rearrangement recalculates the logic
light-tree of each selected session with OL-M-SFMOR, while
the partial rearrangement only chooses certain lightpaths in
the logic light-tree of each selected session to reconfigure,
according to the average cost of the lightpaths in it1.
Algorithm 1: Dynamic provisioning of multicast sessions
1while the EON is operational do
2for each newly-arrived session M Ri(s, D, b, t)do
3try to set up a logic light-tree for it with
OL-M-SFMOR;
4if the light-tree cannot be established then
5mark M Rias blocked;
6end
7end
8for each existing session M Rj(s, D, b, t)do
9if thas been expired then
10 remove M Rjand free its resources;
11 end
12 if Dhas changed then
13 update its logic light-tree with
OL-M-SFMOR;
14 end
15 end
16 if it is the time to reconfigure multicast sessions then
17 select existing multicast sessions to reconfigure;
18 reconfigure the selected multicast sessions;
19 end
20 end
Throughout the aforementioned process, we need to balance
the tradeoff between the number of lightpath reroutings and
overall blocking probability of multicast sessions. It can be
seen that the sub-problem of session selection is more relevant
to this tradeoff. Hence, in the following, we first review the
D-/Q-value based selection strategies designed in [22], analyze
their drawbacks, and then explain the principle of our graph-
aware DRL based selection algorithm.
The D-value of a logic light-tree is actually the hop-count
of its longest-destination branch [22]
D(T) = max [hops(s→d),∀d∈D],(1)
where Tis the light-tree for multicast session M R(s, D, b, t)
and hops(·)returns the hop-count of a routing path. With the
definition in (1), the D-value based selection (DTS) strategy
first calculates the average D-value of all the in-service multi-
cast sessions, and then selects those whose D-values are larger
1Here, the cost of a lightpath was defined in [22], which depends on the
lightpath’s spectrum usage and the number of hops of its routing path.

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than the average value to reconfigure. As DTS only considers
the branch lengths of each logic light-tree but does not address
the overall tree structure or the spectrum assignment on the
links, it might not always select the most critical sessions to
reconfigure.
The Q-value of a logic light-tree considers the overall tree
structure and the spectrum assignment on its links [22]
Q(T) = hops(T∗)·hidx(T∗)
hops(T)·hidx(T),(2)
where T∗is the logic light-tree that is calculated with OL-
M-SFMOR based on the current network status, and hidx(·)
returns the highest index of the used FS’ on a light-tree. With
(2), the Q-value based selection (QTS) strategy first chooses
a threshold Qlb , and then selects those whose Q-values are
smaller than Qlb to reconfigure. Although QTS considers more
information of a logic light-tree than DTS, the information
is still somehow limited, and the value of Qlb can only be
determined empirically, which is rather difficult in a dynamic
EON or for EONs with various topologies.
To address the issues of DTS and QTS, this work proposes
to select multicast sessions in a self-adaptive manner with
graph-aware DRL. More specifically, the DRL model takes the
topology information of the EON and the current provisioning
scheme of a multicast session as the input, abstracts them
as graph-structured data, and analyze the data with GNNs to
intelligently determine whether the multicast session should be
selected for reconfiguration. Meanwhile, after offline training,
the DRL model is also trained in the online manner to make
sure that it can optimize its decision-making automatically and
adaptively according to the reward feedbacks from a dynamic
EON environment, i.e., its effectiveness and universality can
be guaranteed without empirical parameter adjustments.
IV. GRAPH-AWARE DRL BASED APPROACH
This section elaborates on our graph-aware DRL model for
multicast session selection. Note that, to determine whether
a multicast session should be selected for reconfiguration or
not, we need to process graph-structured data (i.e., the tree
topology and the spectrum usages on its links). This task is
suitable for GNNs, because NNs in linear structures normally
only deal with the data in Euclidean domains well [25].
A. System Architecture
We still assume that the EON for DCI is operated by lever-
aging software-defined networking (SDN), which means that
the control plane consists of a centralized controller to handle
the tasks for network control and management (NC&M). Our
graph-aware DRL model obtains the information about the
EON and the multicast sessions in it from the controller, and
selects the most critical sessions to reconfigure.
Fig. 1 explains the operation principle of the graph-aware
DRL model, and its work-flow is illustrated with step num-
bers. Dynamic requests regarding multicast sessions (i.e., new
multicast sessions and changes on in-service sessions) are first
processed by the request handler, which dispatches them to
both the traffic engineering database (TED) and the service
Network Status
Feature
Engineering
Traffic Engineering Database
StateState
State
Action
Service
Provisioning
Session
Reconfiguration
Reward
Calculation
Network Status
A-GNN C-GNN
Action
Evaluation
DRL Agent
Periodical
Trigger
Experience
Buffer
Reward
Online
Training
Update
Global GNN
Gradient
Parameters
Dynamic
Requests
New Multicast
Sessions
Destinations
Join/Leave
Sessions
Action
Request Handler
Topology
In-Service
Multicast
Sessions
In-Service
Lightpaths
Historical
Multicast
Sessions
10
11
12
13
9
8
7
6
6
5
5
5
4
3
2
2
1
Fig. 1. Architecture and operation principle of our graph-aware DRL model.
provisioning module. As explained in Algorithm 1, the service
provisioning module serves the dynamic requests and updates
their provisioning results in the TED. Then, the reconfiguration
of multicast sessions is triggered periodically, and it starts
from TED sending the current network status to the feature
engineering module, which abstracts the network status to a
state that consists of graph-structured data. The DRL agent
uses two GNNs, i.e., the actor GNN (A-GNN) and critic GNN
(C-GNN), to analyze the state of each in-service multicast
sessions and select certain sessions to reconfigure.
Next, the action from the DRL agent (i.e., the selected
multicast sessions) is forwarded to the session reconfiguration
module, which works with the service provisioning module to
reconfigure the selected sessions. After this, the TED sends
the new network status to the reward calculation module to
obtain the reward of the last action conducted by the DRL
agent. Then, we organize the state, action and reward as a
training sample, and store it in the experience buffer. When
enough entries of experience have been accumulated, the
online training module invokes a training process to update
the global GNN, which in turn updates the parameters of the
A-GNN and C-GNN in the DRL agent accordingly.
B. Preprocessing of Data
To prepare the input to the graph-aware DRL model, we
abstract the topology information of the EON and the current
provisioning scheme of a multicast session as graph-structured
data G(V, ˜
V , E , ˜
E), where Vand Estill represent the sets
of DC nodes and fiber links in the EON, respectively, while
˜
Vand ˜
Edenote the features of the nodes and links in V
and E, respectively, regarding the current provisioning scheme
a multicast session M R(s, D, b, t). Specifically, according to
the current logic light-tree Tof M R, we classify the nodes

5
in Vinto 5categories, i.e., the source s, destinations in D,
intermediate node on Tthat used to be a destination, normal
intermediate node, and nodes that are not on T. Then, the
feature of a node v∈Vcan be described with a corresponding
vector ˜v∈˜
V, with one-hot coding. Here, we use 5bits to
represent the aforementioned node categories, respectively. For
instance, if we have a node v=s, its feature vector ˜vshould
be [1,0,0,0,0], or if the node vis a destination, its feature
vector ˜vshould be [0,1,0,0,0]. On the other hand, the feature
of a link e∈Eis defined as ˜e=f
F, where fis the number of
unused FS’ on link eand Fis the total number of FS’ there.
Here, for simplicity, we do not consider distance-adaptive
modulation selection, and assume that all the lightpaths in each
logic light-tree use the lowest modulation level (i.e., BPSK).
Note that, if we need to consider distance-adaptive modulation
selection, the only difference is that we should let our DRL
model learn the relation between the transmission distance of
a lightpath and the number of FS’ that it uses. Hence, when
preprocessing the graph-structured data of G(V, ˜
V , E , ˜
E), we
need to include the length of each fiber link as an attribute,
modify the feature of each link in Eand ˜
Eaccordingly, and
redesign the GNNs in the DRL model to accommodate the
changes. This will be considered in our future work.
C. Structure of GNN
We design the GNNs used in our DRL model based on
graph convolutional network (GCN) [33]. The GCN takes the
graph-structured data G(V, ˜
V , E , ˜
E)as the input, and performs
two types of operations on the data, i.e., the message transfer
and information reduction. For the two types of operations,
we define two functions as follows. The message function
calculates the message to be sent from node vto node u
msg(v , u) = ˜v·˜e, v, u ∈V, e = (v, u)∈E, (3)
where nodes vand uare connected with a link e= (v, u)in
G(V, ˜
V , E , ˜
E). The reduction function reduces the messages
that each node in Vreceives from its neighbors.
rdu(v) = X
{u:(u,v)∈E}
msg(u, v ), v ∈V. (4)
Then, we send {rdu(v),∀v∈V}through a linear network
in the GCN to obtain the new feature vector of v, and the
transfer function from layer-lto layer-(l+ 1) is defined as
˜v(l+1) =σ(W·rdu(l)(v) + b),(5)
where Wand bdenote the weight matrix and bias of the linear
network, respectively, σ(·)is the nonlinear transfer function,
and rdu(l)(v)represents the reduced information for node v
obtained in layer-lof the linear network.
After several layers of GCNs, we introduce a pooling layer
to aggregate the processed graph-structured data and get a
vector for representing it. Specifically, we select the pooling
layer that averages the feature vectors of each node as
˜
G=1
|V|X
v∈V
˜v(k),(6)
where ˜
Gis the obtained vector, |V|is the number of nodes in
V, and kis the number of GCN layers. Finally, we send ˜
Gto
go through several linear layers, for getting the final output.
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Fig. 2. Training of DRL model in A3C framework.
D. Design of Graph-aware DRL Model
We design the four basic elements of the DRL model as
•Agent: The DRL agent is based on the asynchronous
advantage actor-critic (A3C) framework [34], which uses
multiple pairs of A-GNN and C-GNN for parallel online
training in several threads. For each pair of A-GNN and
C-GNN, the A-GNN provides an action policy π(S)
based on the state Sin graph structure, and chooses the
appropriate action according to the policy π(S). The C-
GNN is responsible for learning the value of state Sand
evaluating the action from A-GNN based on it.
•State: The state Scontains the topology information
of the EON and the current provisioning scheme of a
multicast session, and it is just the graph-structured data
G(V, ˜
V , E , ˜
E)obtained by the data preprocessing.
•Action: The action is modeled with a binary variable
a,i.e., if the multicast session should be selected for
reconfiguration, we have a= 1, and a= 0, otherwise.
•Reward: We define the reward as follows
r=−k1·Nre +k2·[slots(T)−slots(T∗)]
+k3·[cuts(T)−cuts(T∗)] ,(7)
where k1,k2and k3are the positive coefficients for
normalization, Nre represents the number of lightpath
reroutings to reconfigure the multicast session, Tand
T∗denote the logic light-trees for the multicast session
before and after the reconfiguration, respectively, slots(·)
returns the number of FS’ used by a logic light-tree, and
cuts(·)returns the number of spectrum cuts [19] caused
by a logic light-tree. Hence, the reward in (7) decreases
with the number of lightpath reroutings, and increases
with the spectrum usage and spectrum cuts saved by
the reconfiguration. In other words, by maximizing the
reward, our graph-aware DRL model tries to invoke the
smallest number of lightpath reroutings on a multicast
session to achieve the largest savings on spectrum usage
and spectrum cuts.

6
As shown in Fig. 2, we duplicate the A-GNN and C-GNN
into several copies, use one copy as the global GNN, and put
each of the others in a training thread to expedite the training
process. Specifically, each training thread uses its A-GNN and
C-GNN to interact with an EON environment independently
to obtain training samples. In the iterative manner, the global
GNN collects the gradients generated by the training threads,
leverages them to update the parameters of its A-GNN and
C-GNN, and synchronizes the updated parameters to the A-
GNNs and C-GNNs in the training threads. As each thread
is trained independently to obtain the gradients, the major
benefit of this approach is that it effectively reduces the
correlations among training samples. Meanwhile, the multi-
thread training can make full use of available computing
resources to accelerate the online training.
Algorithm 2 explains the training process in a thread in
detail, where we use Tto record the number of training
iterations, and Tmax is the upper-limit on training iterations.
Lines 3-9 use the local A-GNN and C-GNN of the thread
to interact with its own EON environment, for collecting
training samples. Then, when enough training samples have
been collected, Lines 11-17 perform one iteration of the
training. Specifically, the gradients are first calculated locally
with the obtained training sample (Lines 11-13), then they are
forwarded to the global GNN (Line 14), and finally the thread
updates the parameters of its A-GNN and C-GNN according
to the feedback from the global GNN and prepares itself for
the next iteration of training (Lines 15-17).
V. PERFORMANCE EVALUATION
In this section, we conduct extensive numerical simulations
to evaluate our proposed approach based on graph-aware DRL.
A. Simulation Setup
The simulations use the four topologies in Fig. 3 for the
EONs for DCIs, to confirm the universality of our proposal in
terms of topologies. The capacity of each fiber link is assumed
to be F= 100 FS’, where each FS has a bandwidth of
12.5GHz to deliver 12.5Gbps throughput. For each multicast
session M R(s, D, b, t),sand Dare randomly selected from
the nodes in the EON, Dcontains [2,5] destinations initial-
ly, the bandwidth demand bis uniformly distributed within
[50,200] Gbps, and the life-time tfollows the exponential
distribution with an average of 500 time-units. As the multicast
sessions are dynamic, we generate new multicast sessions
according to the Poisson traffic model, and for each in-service
multicast, destinations can join or leave dynamically during
its life-time. Specifically, the service time of each destination
follows the exponential distribution, and it leaves its multicast
session when the service time expires, while new destinations
are generated with the Poisson distribution. In Section V-E,
we will change the settings mentioned above and run more
simulations to further verify the universality of our proposal.
The reconfiguration of multicast sessions is invoked every
100 time-units, and this interval is empirically set. The sim-
ulations compare our proposal based on graph-aware DRL
with the heuristics for session selection in [22] (i.e., DTS and
Algorithm 2: Training process of a thread
1T= 0;
2while T < Tmax do
3if it is the time to reconfigure multicast sessions then
4for each in-service multicast session M Rido
5get state Siof M Ri;
6put Siinto the A-GNN to get an action ai;
7apply aito the EON environment;
8calculate reward ri;
9push {Si, ai, ri}to experience buffer;
10 end
11 end
12 if experience buffer is full then
13 reset the gradients as 0;
14 calculate the loss with A-GNN and C-GNN using
the training samples in experience buffer;
15 get the gradients with the loss;
16 send the gradients to the global GNN;
17 update the parameters of A-GNN and C-GNN
according to the feedback from the global GNN;
18 empty the experience buffer;
19 T=T+ 1;
20 end
21 end
QTS), and consider both the partial and full rearrangements
for session reconfiguration. To ensure sufficient statistical
accuracy, we average the results from 5independent runs to
obtain each data point.
B. Training Performance
We first evaluate the training performance of our DRL
model. Note that, the DRL model needs to first go through
the offline training that optimizes its parameters initially, to
make it suitable for being put into online operation/training.
Hence, we study the performance of the offline training in
this subsection, and will consider that of the online opera-
tion/training in subsequent ones. Figs. 4(a) and 4(b) show how
the average number of lightpath reroutings per session and
blocking probability change in the training process, respec-
tively, for the case in the NSFNET topology with the traffic
load at 25 Erlangs. For comparisons, we also plot the results
from DTS-based and QTS-based algorithms in Fig. 4. Here,
all the algorithms assume that full rearrangement is used to
reconfigure the selected multicast sessions, and thus they are
labeled with “-F”. In the following, the algorithms labeled with
“-F” and “-P” mean that they accomplish multicast session
reconfiguration with the full and partial rearrangements in [22],
respectively. Meanwhile, for QTS-based algorithms, we can
choose their thresholds on Q-value for session selection (i.e.,
Qlb), and thus they are also labeled with their Qlb values. For
instance, the QTS-P-0.8in Fig. 4 means that the multicast
reconfiguration uses QTS to select multicast sessions with
Qlb = 0.8, and reconfigures them with partial rearrangement.
The results in Fig. 4(a) show that compared with QTS-P-
0.8, DTS-P achieves a lower blocking probability by invoking

7
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(a) 14-node NSFNET topology
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26 27
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(b) 28-node US Backbone (USB) topology
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(c) 32-node European Backbone (EUB) topology
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(d) 20-node random topology (RT)
Fig. 3. EON topologies used in simulations.
much more lightpath reroutings per session. Meanwhile, after
being trained with more than 5,000 episodes, our DRL-P can
obtain a blocking probability that is as low as that of QTS-
P-0.8, while its average lightpath reroutings per session is
fewer than that of QTS-P-0.8in Fig. 4(b). In other words, by
utilizing its graph-aware intelligence, our DRL-P can balance
the tradeoff between overall blocking probability and average
lightpath reroutings per session much better than the two
benchmarks that use deterministic strategies.
Moreover, to clearly see how the average value of DRL-
P’s reward correlates with the metrics in Figs. 4(a) and 4(b)
in the training, we plot it in Fig. 4(c). Here, we empirically
set the positive coefficients in (7) as k1= 6.0,k2= 1.0and
k3= 2.0. It can be seen that the average reward generally
increases with the decreases of overall blocking probability
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
(c) Average reward
Fig. 4. Training performance (NSFNET, 25 Erlangs).
TABLE I
AVERAGE RUNNING T IME OF OFFLI NE TRAI NIN G (SECO NDS)
Topology NSFNET USB EUB RT
DRL-P 25167.35 34698.01 34944.14 32342.45
DRL-F 31541.22 40423.58 45508.86 36843.80
and average number of lightpath reroutings per session in Figs.
4(a) and 4(b), respectively. Note that, we also check other
traffic loads in NSFNET and the cases with full rearrangement,
and confirm that our DRL-based approach can always achieve
similar training performance as that in Fig. 4. Hence, the
results are omitted due to the page limit.
Table I lists the running time of the offline training that
makes our DRL model suitable for online operation/training.
We observe that for the EONs with the NSFNET, US Back-
bone (USB), European Backbone (EUB), and random (RT)
topologies, the running time actually increases with the size
of the topology. Meanwhile, the DRL model that is for the
full rearrangement scheme usually takes longer offline training
time than that for the partial rearrangement scheme, regardless
of the topology. These trends are expected, because when
the topology of the EON becomes larger or the multicast
reconfiguration changes from partial rearrangement to full re-
arrangement, the problem of multicast reconfiguration actually
become more complex.

8
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 5. Results of dynamic operations (NSFNET, partial rearrangement).
C. Performance in Dynamic Network Environments
Next, we evaluate the performance of our DRL-based ap-
proach by putting the graph-aware DRL model, which has
passed the offline training in a dynamic network environment
with the NSFNET topology, and compare its performance
with DTS-based and QTS-based algorithms. Figs. 5 and 6
show the simulation results for the cases using partial and
full rearrangements, respectively. Here,“NR” denotes the case
without multicast session reconfiguration. Note that, in Figs.
5(a) and 6(a), when the traffic load is above 35 Erlangs,
the blocking probabilities from the algorithms with multicast
session reconfiguration can actually exceed the practical range
of the blocking probability in a real-world EON. Although the
traffic loads exceed what should be considered in a real-world
EON, we still simulate them to get a complete picture about
how the algorithms will perform at various traffic loads. The
DTS-based algorithm still provides the lowest overall blocking
probability with the largest number of lightpath reroutings
per session. By combining the results in the figures, we
can conclude that to keep the overall blocking probabilities
comparable to those of DTS-based and QTS-based algorithms,
our DRL model always requires the smallest number of light-
path reroutings per session effectively, for all the simulation
scenarios considered in Figs. 5 and 6. Hence, our graph-aware
DRL-based approach can effectively reduce the operational
complexity of dynamic multicast session reconfiguration, with-
out sacrificing much performance on request blocking.
Moreover, we notice that QTS-based algorithm can change
the value of Qlb to balance the tradeoff between blocking prob-
ability and average lightpath reroutings per session. Hence, we
change Qlb to obtain different sets of blocking probability and
average lightpath reroutings per session, and plot the results
in Fig. 7, when the traffic load is set as 40 Erlangs. Here,
we take average lightpath reroutings per session and blocking
probability as the X-axis and Y-axis, respectively, to illustrate
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 6. Results of dynamic operations (NSFNET, full rearrangement).
(a) Partial rearrangement
(b) Full rearrangement
Fig. 7. Tradeoff between blocking probability and average lightpath rerout-
ings per session (NSFNET, 40 Erlangs).
the tradeoff more clearly. It can be seen that no matter partial
or full rearrangement is used, the data point for the results
from the DRL model is always below the curve for the results
from QTS-based algorithm. This verifies that the DRL model
balances the tradeoff better than QTS, regardless of the choice
of Qlb. In addition to 40 Erlangs, the simulations also check
other traffic loads, and similar trends can be obtained.
D. Universality across Different Topologies
We then evaluate the universality of our graph-aware DRL-
based approach across different topologies. The operation
principle of our graph-aware DRL model ensures that the

9
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 8. Results of dynamic operations (USB, partial rearrangement).
DRL model trained in one EON topology can be directly
applied to solve the problem of dynamic multicast session
reconfiguration in others. Specifically, we only need to abstract
the new topology information of the EON and the provisioning
scheme of each multicast session as graph-structured data
G(V, ˜
V , E , ˜
E)and input the data to the trained DRL model,
while the DRL model does not need to be redesigned or
retrained. To verify this, the simulations apply the DRL model
trained in NSFNET to solve the problem of dynamic multicast
session reconfiguration in the other topologies in Fig. 3.
Fig. 8 shows the results for the dynamic operations in USB,
when partial rearrangement is considered. We can see that
the results follow the similar trends as those in Fig. 5. To
further clarify the adaptability of our DRL model, we take the
case of traffic load at 25 Erlangs in USB as an example, and
plot how the performance metrics change over the simulation
time in Fig. 9. As we directly apply the DRL model trained
in NSFNET to the EON with the USB topology, a zero-
shot transfer learning (i.e., applying a trained DRL model
to an unseen environment for the same task [35]) is actually
considered. It can be seen that due to the superior adaptability
of our DRL model, it achieves relatively good performance
on the performance metrics at the beginning of the online
operation/training, and both the overall blocking probability
and average number of lightpath reroutings per session only
changes slightly afterwards.
Figs. 10 and 11 illustrate the results obtained by directly
applying the DRL model trained in NSFNET to the EONs
with EUB and RT topologies, respectively. The results still
follow the similar trends as those in Fig. 5. Note that, when
the EON topology changes, we might need to change the value
of Qlb (i.e., the threshold on Q-value for session selection)
for QTS-based algorithms empirically. This is the reason why
we simulate QTS-P-0.9 in EUB (as shown in Fig. 10). On
the other hand, with its graph-aware intelligence, our DRL
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 9. Performance on zero-shot transfer learning (USB, 25 Erlangs).
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 10. Results of dynamic operations (EUB, partial rearrangement).
model can adapt to different topologies without such manual
adjustments. Although the results in Figs. 8-11 are all about the
cases that use partial rearrangement, we also check those with
full rearrangement and confirm that our DRL-based approach
achieves similar performance in them too. Therefore, we prove
the universality of our DRL model across different topologies.
Table II lists the average running time per multicast session
reconfiguration of the algorithms. Here, for our DRL model,
the running time is only for its online operation/training,
because the offline training should be finished before the DRL
model can be put into operation and its running time has
already been summarized in Table I. The results in Table
II suggest that the running time of all the algorithms is

10
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 11. Results of dynamic operations (RT, partial rearrangement).
TABLE II
AVERAGE RUNNING TIM E PER M ULTICAS T RECONFIGU RATIO N (SEC ONDS)
Topology NSFNET USB EUB RT
DRL-P 0.1943 0.2494 0.2383 0.2908
QTS-P 0.2964 0.3941 0.4040 0.3986
DTS-P 0.0693 0.0900 0.1016 0.0867
DRL-F 0.2104 0.2823 0.3022 0.3110
QTS-F 0.3620 0.4648 0.4927 0.4448
DTS-F 0.1995 0.2723 0.2882 0.2687
comparable and short enough to adapt to dynamic operations.
The running time of our DRL model is less than that of the
QTS-based algorithm in all the simulation scenarios, while
as the DTS-based algorithm only makes decisions according
to the depth of each logical light-tree, it runs the fastest.
Meanwhile, the running time of each algorithm generally
increases with the size of the topology, or from using partial
rearrangement to using full rearrangement.
E. Generalization to Various EON Settings
Finally, we consider more simulation settings to verify that
our proposed graph-aware DRL model can adapt to various
EON settings. First of all, we notice that the assumption
of Poisson traffic model might not hold in today’s Internet.
Hence, we design a new simulation scenario, in which the mul-
ticast sessions are generated dynamically in a bursty manner,
i.e., they come in according to the realistic ON/OFF pattern
for bursty Internet traffic [36]. Note that, we still quantify the
traffic load of the multicast sessions with Erlangs, i.e., the
production of the average number of new sessions per unit-
time and the average lifetime of each session in time-units. The
results of the simulations with NSFNET are shown in Fig. 12,
and by comparing them with those in Fig. 5, we can see the
similar trends. Meanwhile, as the bursty traffic model is more
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 12. Results of dynamic operations with bursty multicast sessions
(NSFNET, partial rearrangement).
likely to cause session blockings, the blocking probability of
each algorithm in Fig. 12 is higher. Nevertheless, our DRL
model still retains its advantage of significantly reducing the
number of reconfiguration operations without sacrificing the
performance on blocking probability. With the bursty traffic
model, we also simulate other EON topologies and test the
algorithms with full rearrangement, while the results always
follow the similar trends as those in Fig. 12.
Secondly, we increase the number of FS’ on each fiber
link to 200, for simulating the EONs with more spectrum
resources. The results of the simulations with NSFNET are
shown in Fig. 13, and by comparing them with those in Fig.
5, we still see the similar trends. Meanwhile, since there are
more spectrum resources in the EON, we need to increase the
traffic load to see the same blocking probability. Our DRL
model still exhibits the advantages over the heuristics, which
suggests that its performance is not affected by the change
of spectrum resources in the EON. With the new setting of
spectrum resources, we also simulate other EON topologies
and test the algorithms with full rearrangement, and the results
always follow the similar trends as those in Fig. 13.
Finally, considering the fact that in a real-world EON, there
are unicast and anycast lightpaths coexisting with multicast
sessions, we design a realistic simulation scenario that unicast
and anycast lightpaths are used as the background traffic of
multicast sessions. Specifically, to create a stressful scenario
for our DRL model, we make the total bandwidth demands
of unicast, anycast, and multicast account for 25%, 25% and
50% of the overall bandwidth usage in the EON, respectively.
The results of the simulations with NSFNET are shown in Fig.
14, and by comparing them with those in Fig. 5, we can see
that the blocking probability of multicast sessions becomes
lower. This is because for the same traffic load, unicast and
anycast lightpaths generally require less spectrum resources

11
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 13. Results of dynamic operations with 200 FS’ per fiber link (NSFNET,
partial rearrangement).
(a) Overall blocking probability
(b) Average number of lightpath reroutings per session
Fig. 14. Results of dynamic operations with unicast/anycast background
traffic (NSFNET, partial rearrangement).
than multicast sessions, and thus the total spectrum usage
is actually smaller. Meanwhile, for the same reason, the gap
on blocking probability between the multicast reconfiguration
algorithms and the case without multicast reconfiguration (i.e.,
NR) becomes smaller too. Note that, compared with the
QTS-based and DTS-based algorithms, our DRL model still
invokes a smaller number of lightpath reroutings per session
to maintain almost the same blocking probability. This verifies
the effectiveness of our DRL model in the EON environment
that contains mixed types of traffic demands.
VI. CONCLUSION
In this work, we revisited the problem of how to formulate
and reconfigure multicast sessions in an EON, and proposed
a DRL model based on GNNs that can solve the sub-problem
of multicast session selection in a more universal and adap-
tive way. Specifically, we abstracted the state information
of each multicast session as graph-structured data, which
can be directly analyzed by our graph-aware DRL model.
Then, the graph-based reasoning capability of our proposal
made sure that the state information of each multicast session
can be analyzed in depth for dynamic reconfiguration, and
facilitated the universality across different topologies. Hence,
an important takeaway is that our graph-aware design of the
DRL model made its architect and operation independent of
the EON’s topology, and thus avoided the hassle of redesigning
its architecture to adapt to different EON topologies.
Simulation results verified that compared with the exist-
ing deterministic algorithms based on DTS and QTS, our
graph-aware DRL based approach can significantly reduce
the average lightpath reroutings per multicast session while
maintaining the overall blocking probability approximately
at the same level. This suggested that our proposal can
balance the tradeoff between the number of reconfiguration
operations and blocking performance much better than the
existing algorithms. Moreover, our simulations also confirmed
that the DRL model trained in one EON environment can
easily adapt to solve the problem of dynamic multicast session
reconfiguration in EONs with various settings (e.g., different
topologies, spectrum resources, traffic models and request
types). Therefore, the universality of our proposal helped to
effectively save the time and efforts that are needed to adjust
the DRL model according to an EON’s setting, and provided
a more realistic solution for network automation.
ACKNOWLEDGMENTS
This work was supported in part by the National Key
R&D Program of China (2020YFB1806400), NSFC project
61871357, SPR Program of CAS (XDC02070300), and Fun-
damental Funds for Central Universities (WK3500000006).
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