4
Some authors devoted themselves to QoS routing algorithms
under the many-to-many multicast scenario. In [40], the
many-to-many multicast QoS routing problem was formulated
as a concave quadratic program and binary Integer Linear
Program (ILP), and a Difference of Convex functions
Algorithm (DCA) and proximal decomposition technique are
proposed to solve it. The delay and delay jitter constrained
many-to-many multicast tree problems were formulated in [41].
A Source-Based Scheme (SBS) is devised, which at first finds a
feasible multicast tree for each source node in the multicast
group and then a minimum cover of these multicast trees so that
there exists at least one feasible multicast tree in the minimum
cover for each source node. A necessary and sufficient
condition is also derived for a core-based multicast tree to be
feasible, and a Core-Based Scheme (CBS) based on the derived
condition is provided. However, in all the aforementioned
literature, only the rigid QoS was taken into account when
routing, while the power consumption factor was ignored.
Some literature embedded power consumption metrics in
their routing decisions. In [42], a new heuristic algorithm based
on the ILP formulation (H
ILP
-GreenRE) was introduced to solve
the energy-aware routing problem. A new energy-aware routing
model with the support of data redundancy elimination (RE)
was proposed. It was enabled within routers and it could
virtually increase capacities of network links. In [43], a novel
energy-efficient routing approach called Safe and Practical
Energy Efficient Detour Routing (SPEED) was proposed to
maximize the number of the aggregated links and then
aggregate traffic for power savings in IP networks without any
changes to the traditional IP packets forwarding diagram and
routing protocols. In [44], a power model that can quantify the
relationship between traffic volume and power consumption
was presented, and three Hop-By-Hop Green Routing
Algorithms (HBHGRA) which guaranteed loop-free routing
and substantially reduced energy footprint in the Internet were
progressively developed. Energy conservation and path stretch
were jointly considered. However, QoS guarantee was not
provided to the user when routing and the multicast scenario
was neglected in [42–44].
Only a few works took both power consumption and QoS
requirements into account in the routing algorithms. For
instance, two routing algorithms subject to routing cost and
rigid QoS constraints were proposed in [45], that is, a
constrained Unicast-Max-Flow-Min-Cost algorithm (UMFMC)
for routing unicast traffic flows and a constrained
Multicast-Max-Flow-Min-Cost algorithm (MMFMC) to
maximize the throughput of a one-to-many multicast tree while
simultaneously minimizing energy costs. However, the flexible
QoS constraints were not considered and the many-to-many
multicast scenario was ignored in [45].
3. Modeling and problem formulation
3.1. Model description
3.1.1. Network model
The network model in this paper is denoted as a connected
graph G = (V, E), as shown in Fig. 1, where V represents a set of
vertices (namely network nodes) and E represents a set of edges
(namely network links).
Fig. 1 Network model
3.1.2. Node model
A node model is proposed and its structure is illustrated in
Fig. 2. It consists of multiple chassis, line cards, a master engine
(ME), a switching fabric, multiple forwarding engines (FEs),
multiple replication engines (REs), and so on. Among them, the
ME is responsible for routing packets and updating routing
table; the switching fabric connects input and output ports
inside the router; the FE is in charge of routing table lookup; the
RE is used for multicast replication. Note that all the engines
are equipped with the buffer of certain size [46]. Power
consumption of network node i can be formulated by Eq. (1).
Data bus
Fig. 2 The proposed node structure
1
1
1
(1 ( ) )
i
chass
k
lc
lc
port
i k
chass i
i i lc
N
ford repl k
i i
N
node ctrl
N
k
i p
lc
port p lc
p
P ChaSt
P P LkdSt
P P
P trf PortSt
(1)
,
and
represent the power consumption of
the ME, a FE and a RE in node
respectively.
i
and
represent the power consumption of a
chassis and a port in node
respectively.
i
N
represents the number of chassis in node
,
represents the number of line cards in chassis
and
represents the number of ports in line card
.
represents the traffic passing port
in node
.