Self-adjusting routing schemes for time-varying traffic in scale-free networks
Ming Tang,
1
Zonghua Liu,
1,
*
Xiaoming Liang,
1
and P. M. Hui
2
1
Department of Physics and Institute of Theoretical Physics, East China Normal University,
Shanghai 200062, People’s Republic of China
2
Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Received 1 January 2009; revised manuscript received 22 April 2009; published 13 August 2009
We consider the effects of time-varying packet generation rates in the performance of communication
networks. The time variations could be a result of the patterns in human activities. As a model, we study the
effects of a degree-dependent packet generation rate that includes a sinusoidal term. Applying a modified traffic
awareness protocol TAP previously proposed for static packet generation rates to the present situation leads
to an altered value of the optimization parameter, when compared to that obtained in the static case. To enhance
the performance and to cope with the time-varying effects better, we propose a class of self-adjusting traffic
awareness protocols that makes use of instantaneous traffic information beyond that included in the modified
TAP. Two special cases that make use of global and local information, respectively, are studied. Comparing
results of our proposal schemes with the modified TAP, it is shown that the present self-adjusting schemes
perform more effectively.
DOI: 10.1103/PhysRevE.80.026114 PACS numbers: 89.75.Fb, 89.20.Hh, 05.70.Jk
I. INTRODUCTION
The study of transport processes on networks is funda-
mental to a large part of the physical, biological, social, eco-
nomic, and engineering sciences and has recently received a
great attention, such as the traffic of information packets,
synchronization, epidemic spreading, particle condensation,
etc. 1,2. It is found that the optimal performance of trans-
ports depends strongly on both the structural characteristics
of the underlying network and routing algorithm of traffic.
For example, the clustering, disassortativity, and modularity
of scale-free network may influence significantly the statisti-
cal properties of traffic 3,4. Based on the fact that most of
the realistic networks are of scale-free architecture, we here
focus on the communication networks with scale-free topol-
ogy such as the famous Barabasi-Albert BA network with
exponent of degree distribution =3 5. The motivation to
choose BA network is to show a general consideration but
not only limit to some specific networks, and also hope the
results can help us to understand the traffic in the Internet
with exponent of degree distribution = 2.2 0.1 6,7.
There are two general ways to enhance the performance
of a network: To increase the capacity of each node and to
improve the routing protocol. The former is less practical as
there is usually no central management to plan and organize
the network, such as the Internet. Thus, much effort has been
focused on improving the routing protocol 8–29. The sim-
plest routing algorithm is to follow the geometrical shortest
path where packets are sent via the path with the minimum
number of intermediate nodes from the source to the desti-
nation. For networks with a power-law degree distribution,
there exist nodes with large betweenness 8. When the traf-
fic is heavy, many packets will have to pass through these
hubs on their way to the destination and lead to a traffic jam
when the packets queue up at the hubs due to the finite ca-
pacity of the hubs in handling packets. One obvious way to
enhance the performance is to focus on reducing the jam at
the hubs. For example, congestions can be largely suppressed
by selectively improving the capacity of only 3% of nodes of
heavy links in a network 21.
To avoid congestions, many variations in the shortest path
routing protocol have been proposed. Typically, they take the
time of queuing at the nodes into consideration. In a com-
munication network, the nodes serve as both hosts and rout-
ers, and the links are pathways through which packets are
delivered. In early models of traffic in communication net-
works, every node is assumed to have the same packet de-
livery rate of handling one packet per time step and R new
packets are generated randomly among the nodes in the sys-
tem 8–20. The purpose of these models is to enhance the
congestion threshold R
c
in scale-free networks. For example,
Yan et al. presented an approach to include the link weight
9. Wang et al. proposed a routing strategy with a tunable
parameter based on the local structural information 10.
Sreenivasan et al. derived an estimate to the upper bound of
the congestion threshold for scale-free networks and intro-
duce a hub avoidance protocol for large packet insertion rate
11. Danila et al. gave a heuristic algorithm that balances
traffic on a network by minimizing the maximum node be-
tweenness 14,15. Also Kujawski et al. introduced some al-
gorithms based on dynamical information, which can handle
a larger load than the random-walk algorithm 16.
The traffic awareness protocol TAP proposed by Ech-
enique et al. 18,19 forms the basis of some variations 20.
In TAP, a node i decides to forward a packet to a neighboring
node with the shortest effective distance hd
, j
+ 1- hn
toward the destination j , where d
, j
is the length of the short-
est path from node to j , n
is the number of accumulated
packets at node and it is in general time-dependent, and h
is a traffic awareness parameter. It was found that h 0.8
gives the best performance 18,19. TAP thus considers a
balance between routing via the geometrical shortest path
first term and the waiting time at the nearest-neighboring
nodes of i second term. In the free-flow phase of traffic
where packets travel freely without delays, the shortest path
algorithm will be adopted under TAP. In the heavily con-
*
zhliu@phy.ecnu.edu.cn
PHYSICAL REVIEW E 80, 026114 2009
1539-3755/2009/802/0261148 ©2009 The American Physical Society 026114-1