International Journal On Engineering Technology and Sciences – IJETS™
ISSN (P): 2349-3968, ISSN (O): 2349-3976
Volume 1 Issue 7, November 2014
183
SYSTEM CONFIGURATION AND
SCHEDULING IN WIRELESS NETWORKS
USING OPTIMIZATION DECOMPOSITION
Ms.KAVITHA.V.KAKADE ASSISTANT PROFESSOR
DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING,
SRI SHAKTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY, COIMBATORE-62
Ms.C.APARNA 2nd YEAR,M.E CSE
DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING,
SRI SHAKTHI INSTITUTE OF ENGINEERING AND TECHNOLOGY, COIMBATORE-62
MAIL ID: [email protected] Abstract—In this work we considered the case of elastic flows and provided a decentralized congestion control algorithm that works in parallel with the randomized algorithm. We showed that the resulting cross-layer algorithm achieves fair allocation of the resources despite the imperfect nature of the switching delay algorithm. Finally, we developed specific distributed algorithms for the two-hop interference model. For this model, existing throughput-optimal strategies require that an NP-hard problem be solved by a centralized controller at every time instant. In this work, we showed that this is not necessary, and full utilization of the network can be achieved with distributed algorithms having only polynomial communication and computational complexity. The proposed work is done with the switching delay algorithm and decomposition is implemented to prove the specified problem.
Index Terms—Scheduling, Congestion, Wireless Networks, Transmission.
I. INTRODUCTION
We provide simple randomized
scheduling-routing schemes that achieves maximum throughput in
multi-hop wireless networks. The simplicity of our
proposed scheme suggests efficient implementation of
throughput-optimal policies. Second, we propose a
cross-layer mechanism combining our
routing-scheduling algorithm with a decentralized congestion
controller for elastic traffic. The key difference between
elastic and inelastic traffic stems from the fact that in
the former case the mean arrival rates of flows can be
controlled in response to delays and congestion, while
in the latter case, the arrival rates are fixed. We model
elastic traffic using the utility maximization framework
introduced by Kelly and further improved in subsequent
works.
In this context our proposed cross-layer
mechanism not only maximizes throughput but also
asymptotically achieves a fair division of network
resources among flows. Congestion control
mechanisms, such as those in Transmission Control
Protocol (TCP), regulate the allowed source rates so
that the total traffic load on any link does not exceed the
available capacity. At the same time, the attainable data
rates on wireless links depend on the interference
levels, which in turn depend on the power control
policy. This paper proposes and analyzes a distributed
algorithm for jointly optimal end-to-end congestion
control and per-link power control. The algorithm
utilizes the coupling between the transport and physical
layers to increase end-to-end throughput and energy
efficiency in a wireless multihop network.
Congestion avoidance mechanisms in TCP
variants have recently been shown to approximate
distributed algorithms that implicitly solve network
utility maximization problems. Traditionally, this class
of optimization problems is linearly constrained by link
capacities that are assumed to be fixed quantities.
However, network resources can sometimes be
allocated to change link capacities, therefore change
TCP dynamics, and the optimum solution to network
utility maximization. For example, in Time-Division
Multiple-Access (TDMA) wireless networks, transmit
powers can be controlled to induce different
Signal-to-Interference Ratios (SIRs) on the links, changing the
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nodes and an established logical topology, where somenodes are sources of transmission and some nodes act
as “voluntary” relay nodes. A sequence of connected
links forms a route originating from
source . Let xs be the transmission rate of source s, and
c1 be the “capacity,” in terms of the attainable data rate
rather than the information-theoretic multiterminal
channel capacity, on logical link . Note that each
physical link may be regarded as multiple logical links.
Source nodes are indexed by s and logical links by I .
Revisiting the network utility maximization formulation
(1), for which TCP congestion control solves, we
observe that in an interference-limited wireless
network, data rates attainable on wireless links are not
fixed numbers, and instead can be written, for a large
family of modulation, as a global and nonlinear
function of the transmit power vector P and channel
conditions
This wireless channel model has several
limitations. It assumes fixed target decoding error
probabilities and coding modulation schemes.
Transmission power is the only resource that is being
adapted. Second, the assumption that is much larger
than 1 is not always true. With this assumption, it will
be shown that while is a nonlinear non concave function
of P, it can be converted into a nonlinear concave
function through a log transformation, leading to a
critical convexity property that establishes the global
optimality of the proposed algorithm. Last but not least,
simple decoding is not the only option for a wireless
channel. Either multiuser decoding that does not treat
all interferences as noise or simple
“amplify-and-III. RELATED WORKS
In this paper, we present distributed algorithms
for link scheduling in wireless networks. Since
interfering links in a wireless network cannot transmit
at the same time, a scheduling policy is required to
resolve the contention between various links attempting
transmission. The well-known maxweight and
back-pressure scheduling algorithms introduced are
throughput-optimal, i.e., they can stabilize the system
under the largest set of offered load vectors. However,
they are centralized algorithms and have high
computational complexity. Using the max-weight or
back-pressure algorithms for scheduling, a number of
recent papers have studied the problem of joint
congestion control, routing, and scheduling in multihop
wireless networks. The focus of this paper is on
designing distributed scheduling algorithms with low
complexity and low implementation overhead.
We consider two simple collision models in
this paper: one where each link is associated with an
interference set such that the link cannot be scheduled if
any other link in its interference set is scheduled. The
other model, called the node-exclusive interference
model, is a special case of the first model where the
interference set of a link consists of all links that share a
common node with the first link. The first model covers
a wide range of collision models that arise in practical
wireless networks while the second model is applicable
to Bluetooth or STDMA type networks.
The study of low-complexity scheduling
algorithms has its roots in the high-speed switching
literature where maximal matching has been studied as
an alternative to the maxweight algorithm. These papers
show that low-complexity maximal-matching-type
International Journal On Engineering Technology and Sciences – IJETS™
ISSN (P): 2349-3968, ISSN (O): 2349-3976
Volume 1 Issue 7, November 2014
185
of the maximum possible throughput, where the lowerbound is a function of the local topology of the
network. In particular, it was shown that the lower
bound is 1/2 for the node-exclusive interference model
while show that the lower bound is the inverse of the
maximum number of links that can be simultaneously
scheduled in interference set. The main drawback of the
algorithms is that they focus primarily on computational
complexity but do not consider distributed
implementation.
For example, in the node-exclusive
interference model, each valid schedule is a matching.
A maximal matching can be found as follows: each
node requests a connection to one of its neighbors. A
connection is accepted if the node receiving the request
is not already part of the matching; otherwise, the node
requests again. However, such a process, if not
implemented in a structured fashion, would require
many rounds of requests and incur a huge overhead,
negating the benefits of the simplicity of maximal
matching. We note that this problem is unique to
wireless networks. In contrast, in many high-speed
switches, a matching can be implemented by a central
controller. Even if a central controller is not available,
input and output ports are just one hop from each other
and thus message passing is relatively easy in
high-speed switches. In view of the discussion above, the
goal of this paper is to devise complexity,
low-overhead distributed algorithms for multi-hop wireless
networks. We will present two distributed algorithms
which we summarize below:
(a) The first algorithm, which we call Q-SCHED, uses
queue length information in a local neighborhood of
each link to perform scheduling. Q-SCHED is a
randomized algorithm which works in two phases: in
the first phase, each link tosses a coin to determine if it
will participate in the schedule. In the second phase, the
links that decide to participate use a one step collision
resolution protocol to determine if they will be part of
the schedule or not. Such a two-phase algorithm was
originally proposed but the key contribution in this
paper is to modify the algorithm to achieve dramatically
larger throughput. We will show that the computational
complexity of Q-SCHED is independent of the network
size and throughput, although in order to obtain the
queue-length information in a local neighborhood,
Q-SCHED requires communication overhead that is a
function of the maximum node-degree of the network.
(b) The second algorithm, which we call
BP-SIM(Business Process-Simulation Interchange
Standard), is also a randomized algorithm but does not
require queue-length information. BP-SIM is presented
for the node-exclusive interference model, and is an
adaptation of the algorithm for the case of wireless
networks. The algorithm proceeds by emulating a
bipartite graph: each node randomly decides to be a left
or a right node. Then connection requests are made
from left to right nodes. The key distinction between
wire line networks considered and multi-hop wireless
networks is that the connection requests collide in the
wireless networks and a contention resolution protocol
is required. We design such a protocol and show that
the overall complexity of BP-SIM is a function only of
the maximum node degree and not of the size of the
networks. One of the main reasons that Q-SCHED and
BP-SIM require lower complexity than maximal
scheduling is that they do not attempt to compute a
maximal schedule. Under maximal scheduling, at each
time slot, every backlogged link has the following
property: either the link is scheduled or some other link
in its local neighborhood is scheduled.
OUR WORK
While Q-SCHED can compute a schedule in a
constant number of mini-slots, it requires knowledge of
queue-length information. This may or may not be
difficult to obtain. At moderate loads, queue-lengths
will not be very large; thus, queue-lengths can be
186
However, in practice such queue-length informationexchange has to be performed asynchronously and thus
may reduce the performance of the algorithm. In this
section, we present an alternative algorithm, named
BP-SIM, that requires no queue-length information. As in
the case of Q-SCHED, BP-SIM does not attempt to find
a maximal schedule. Instead, BP-SIM ensures that, for
any backlogged link l, the probability that a link in El is
scheduled is high. This stems from the key observation
that for the stability of maximal schedules can be
adapted easily even when the schedule is not maximal.
We will show with both analytical and numerical results
that the complexity of BP-SIM is low for networks with
even a few hundred nodes. BP-SIM is presented for the
node-exclusive interference model. To be more specific,
we refer to the following STDMA system that adheres
to the node-exclusive interference model. Each node is
assigned a unique orthogonal fast-hopping sequence. At
each time, a node can be either in a sending mode, or in
a receiving mode. If it is in a receiving mode, its
frequency hops according to its own hopping sequence.
If it is in a sending mode, it uses the hopping sequence
of the intended receiver in order to send information to
the receiving node. Clearly, if two or more sending
nodes want to send information to the same receiver at
the same time, their messages will collide. Hence, such
a system can be modeled well using the node-exclusive
interference model. Finally, it is assumed that the
maximum degree of any node in the network is
upper-bounded by for all nodes v.
IV. CONCLUSION
As a step toward “layering as optimization
decomposition,” this paper expands the scope of the
network utility maximization methodology to handle
nonlinear, elastic link capacities. This extension enables
wireless multihop networks. The proposed algorithm is
robust to wireless channel variations and path loss
estimation errors. Suboptimal but much simplified
versions of the algorithm are presented for scalable
architectures. With high probability, Q-SCHED
schedules links in those interference sets where the total
queue-length is large. On the other hand, BP-SIM
ensures that the probability that at least one link is
scheduled in the interference set of each backlogged
link is high. The complexity of both algorithms can be
made to only depend on the maximum node-degree and
an approximation factor, but are otherwise independent
of the size of the network. Recently, there have been a
number of papers addressing complexity and
decentralization questions in multi-hop wireless
networks. We now briefly comment on the contribution
of this paper in the overall context of this line of
research.
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International Journal On Engineering Technology and Sciences – IJETS™
ISSN (P): 2349-3968, ISSN (O): 2349-3976
Volume 1 Issue 7, November 2014
187
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