1
A Joint Congestion Control, Routing, and
Scheduling Algorithm in Multihop Wireless
Networks with Heterogeneous Flows
Phuong Luu Vo, Nguyen H. Tran, Choong Seon Hong, *KiJoon Chae
Kyung Hee University, *Ewha Womans University, Korea
{phuongvo, nguyenth, cshong}@khu.ac.kr, *kjchae@ewha.ac.kr
Abstract—We consider the network with two kinds of traffic:
inelastic and elastic traffic. The inelastic traffic requires fixed
throughput, high priority while the elastic traffic has controllable
rate and low priority. Giving the fixed rate of inelastic traffic,
how to inject the elastic traffic into the network to achieve the
maximum utility of elastic traffic is solved in this paper.
The Lagrangian Duality method is applied to solve the op-
timization problem. We decompose the Lagrangian into sub-
problems, and each sub-problem associates with each layer.
The convexity of the primal problem guarantees the duality
gap between primal and dual solutions is zero. The Lagrange
multipliers, which are indeed the queue length on nodes for
every destinations, implicitly update according to subgradient
algorithm. The joint algorithm for rate control, routing, and
scheduling is proposed. However, the scheduling is Max-weight
scheduling and centralized algorithm actually. The Greedy dis-
tributed scheduling is introduced to implement scheduling in a
distributed sense.
I. I NTRODUCTION
Network optimization and control is an active research
area [1]–[4]. There are two main kinds of network formu-
lations: node-centric and link-centric [3]. The node-centric
formulation maximizes the utility such that all queues are
stable: total transmitting rate and incoming flow of a queue
must less than the outgoing flow. On the other hand, the link-
centric formulation uses the capacity constraint: total of load
of all flows on a link must be less than the capacity of the link.
Whereas link-centric formulation need a routing matrix in the
formulation, the node-centric does not; therefore, the dynamic
routing is also solved in the node-centric formulation.
Recent papers apply the frameworks for networks with
heterogeneous flows: elastic and inelastic flows [5]–[8]. By
using the link-centric formulation, giving the inelastic rate, the
authors in [6] maximize the utility of elastic traffic while load-
balancing the inelastic traffic on some predefine routes. Also
using the link-centric formulation, the optimization problem
is solved in [7] with the additional constraint: the probability
of missing the deadline packets less than a threshold. All
these papers use link-centric formulation, therefore, the routing
matrix must be a priori.
This work was supported by the IT R&D program of MKE/KEIT
[10035245: Study on Architecture of Future Internet to Support Mobile
Environments and Network Diversity].
Dr. CS Hong is the corresponding author.
Our paper applies the node-centric formulation to solve the
problem, so the dynamic routing is integrated naturally. We
don’t cover the end-to-end delay constraint in the scope, but
the priority of inelastic traffic in using the links in wireless
environment is considered. The rate of inelastic traffic is fixed
(the source demand). We want to inject the elastic traffic such
that maximizing the utility of elastic traffic while all the queues
in the network keep stable. Our contributions in this paper are:
1) Applying the node-centric formulation in the cross-
layer design for the multihop wireless network with the
requirement of fixed the inelastic rate (source demand)
and optimal utility of elastic traffic.
2) Proposing the rate control for elastic traffic, the dis-
tributed routing and scheduling for both kinds of traffic.
3) Providing the simulation of the impact of higher priority
of inelastic rate demand on the lower priority elastic
traffic.
II. PROBLEM FORMULATION
The network is modeled by a directed graph =( , ℒ),
where is the set of nodes, and ℒ is the set of links. The
network has two kinds of flows: inelastic flows and elastic
flows.
Define ℱ
as the set of inelastic flows. Each inelastic flow
maps a pair of two nodes: source node and destination
node. Let
and
be the sets of inelastic source nodes and
destination nodes respectively. We have
⊂ and
⊂ .
Set
is the rate of flow
.
just depends on the demand of
multimedia service, and it is a constant. We assume that the
inelastic rate is always admissible by the network.
Define ℱ
is the set of elastic flows. Each elastic flow
maps a pair of two nodes: source node and destination
node. Define
and
as the sets of elastic source nodes
and destination nodes respectively. We also have
⊂ ,
⊂ . In this paper, we assume that the sets of of
destination nodes of inelastic and elastic flows are disjoint.
Each elastic flow is associated with a utility function (.),
which is concave, twice-differentiable, and non-decreasing.
For example, log() where is the rate of the flow is a utility
function.
is the rate of flow
, and x
()
is the rate vector
of all elastic flows. Here we want to control the rate
to
archive the maximum total of utility.
Link-Rate Region
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