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International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)
Volume 2, Issue 7, July 2013
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Improving End-to-End Delay Distribution in Wireless
Sensor Networks.
R.J Lawande1
, A.H. Ansari2
1
PDVVPCOE, Ahmednagar, Maharashtra,India
2
P.R.E.C, Loni, Ahmednagar, Maharashtra,India.
Abstract— In today’s world emerging applications of
wireless sensor networks (WSNs) require real-time Qos.
average delay and end to end delay distribution is
important in WSNS. In a typical delay monitoring WSNS,
multiple reports are generated by several nodes when a
physical event occurs, and are then forwarded through
multi-hop communication to a sink that detects the event.
To improve the delay detection reliability, usually timely
delivery of a certain number of packets is required. The
previous delay analysis papers fail to give the single hop
delay distribution, also the busty traffic is not considered
so in this paper, a comprehensive cross-layer analysis
framework is used. The simulations on Network Simulator
2 show the average and end to end delay for both
deterministic and random deployments. Our model gives
closed form expressions for obtaining the average delay
and End to End delay characteristics and models each
node as a discrete time queue. Moreover, the simulation
and experiments show the Throughput and the packet loss
in WSNs. In this paper, the comparison of the CSMA/CA
Mac protocol and cross layer protocol for average delay
and End to end dealy,Throuhput and Packet loss is done
for WSNs.
Index Terms— Average Delay distribution, End to end
delay, real time systems, Throughput, wireless sensor
networks.
I. INTRODUCTION
Real time quality of service is necessary and
important for wireless sensor networks. The wireless sensor
networks are extensively used in the connectivity
infrastructure and distributed data network.Timing and
reliability are the two important factors for the quality of
service gurantees.To characterize average delay and end to
end delay distribution is fundamental for the real time
Ravindra J . lawande1
, Department of Electronics and Telecommunication
PDVVPCOE, Ahmednagar, Maharashtra, India
Abdul H. Ansari2
, Department of Electronics and Telecommunication, PREC
Loni, Maharashtra, India
communication applications with the probabilistic QoS
guarantees. Also to calculate the Throughput and the packet
loss is important for the real time wireless sensor networks
applications.[3] First, a accurate and reliable cross layer
framework is developed to characterize the average delay and
end to end delay distribution in both deterministic and random
deployments of nodes.[1] Second, Throughput and the Packet
loss of the CSMA/CA Mac protocol and Cross layer protocol
is calculated by the graphical analysis.
In existing system, CSMA/CA Mac protocol is
conducted to illustrate how developed framework can
analytically predict the distribution of the end-to-end
delay.[1][2] It does not give the guarantee of quality of
service. In proposed system, present comprehensive cross-
layer analysis framework, which employs a stochastic queuing
model in realistic channel environments, is developed for
average delay and end to end delay in WSNs .The cumulative
distribution function (cdf) of the delay can be used as a metric
to calculate delay. The end-to-end delay distribution depends
on the deterministic deployment and random deployment. For
both deployments, focus on the steady-state behavior of the
routing protocol.
This paper is organized as follows. Section I gives
the introduction. Section II reviews some previous work of
end-to-end delay. Section III introduces the software system
used for delay analysis. Section IV gives results of proposed
system. Section V concludes this paper.
II. Literature Survey
Yunbo Wang Mehmet C. Vuran Steve Goddard [1] have
proposed To improve the event detection reliability, usually
timely delivery of a certain number of packets is required.
Traditional timing analysis of WSNs are, however, either
focused on individual packets or traffic flows from individual
nodes a spatio-temporal fluid model is developed to capture
the delay characteristics of event detection in large-scale
WSNs. Mean delay and soft delay bounds are analyzed for
different network parameters. The resulting framework can be
utilized to analyze the effects of network and protocol
parameters on event detection delay to realize real-time
operation in WSNs. but fail to give single hop delay
distribution.

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Yunbo Wang, Mehmet C. Vuran and Steve Goddard
have proposed that Limited energy resources in
increasingly sophisticated wireless sensor
networks(WSNs) call for a comprehensive crosslayer
analysis of energy consumption in a multi-hop network.
reliability analysis in such networks, the statistical
information about energy consumption and lifetime is
required Traditional energy analysis approaches only
focus on the average energy consumed. a stochastic
analysis of the energy consumption in a random network
environment. the distribution of energy consumption for
nodes in WSNs during a given time period is found. Fail
to analyze the energy consumption for more MAC
protocols, such as BMAC , XMAC , using our model.
Mehmet C. Vuran, Member, IEEE, and Ian F. Akyildiz,
Fellow, proposed that[3] Severe energy constraints of
battery-powered sensor nodes necessitate energy-
efficient communication in Wireless Sensor Networks
(WSNs). the vast majority of the existing solutions are
based on the classical layered protocol approach, which
leads to significant overhead a cross-layer protocol
(XLP) is introduced, which achieves congestion control
routing, and medium access control in a cross-layer
fashion.
The design principle of XLP is based on the
cross-layer concept of initiative determination, which
enables receiver-based contention, initiative-based
forwarding, local congestion control, and distributed
duty cycle operation to realize efficient and reliable
communication in WSN .Fail to investigate of various
networking functionalities such as adaptive modulation
,error control, and topology control in a cross-layer
fashion to develop a unified cross-layer communication
module Omesh Tickoo and Biplab Sikdar[2] proposed
that Traditional system fail to evaluating the queueing
delays and channel access times at nodes in wireless
networks paper presents an analytic model for evaluating
the queueing delays and channel access times at nodes in
wireless networks using the IEEE 802.11 Distributed
Coordination Function (DCF) as the MAC protocol. The
model can account for arbitrary arrival patterns, packet
size distributions and Number of nodes. Fail to give end
to end delay analysis for deterministic and random
deployment of nodes in WSN.
III. System Overview
Wireless sensor networks (WSNs) have been utilized in
many applications as both a connectivity infrastructure
and a distributed data generation network due to their
ubiquitous and flexible nature . Increasingly, a large
number of WSN application requires real-time quality-
of-service (QoS) guarantees. Such QoS requirements
usually depend on two common parameters: timing and
reliability. The resource constraints of WSNs, however,
limit the extent to which these requirements can be
guaranteed. Furthermore, the random effects of the
wireless channel prohibits the development of
deterministic QoS guarantees in these multihop
networks. Consequently, a probabilistic analysis of QoS
metrics is essential to address both timing and reliability
requirements.
In our analysis, we consider a network
composed of sensor nodes that are distributed in a 2-D
field.Sensor nodes report their readings to a sink through
a multihop route in the network.Two different types of
network deployments are investigated.Figure.1shows
the architectural diagram of our cross layer framework
Network deployment is divided into two types
1.Determnistic deployment:-The deterministic
deployment has the position of sensor nodes is fixed
with deterministic locations which is useful to calculate
the single hop delay distribution with queuing model.
2.Random Deployment:-Random deployment uses
Poisson point process with log normal fading channel.
queuing model deals with inter arrival distribution and
discrete time Markov Process. Locally generated packets
gives the local packet information. End to end delay is
calculated by the sum of incoming relay traffic rate at
each of the next hop.[1] Figure.2 shows the activity
diagram for developing the cross layer framework.
Figure.3 shows the structure of Markov chain showing
successful transmission of the packets with 3 attempts.
As shown in figure successfully transmitted traffic rate
from one node should be equal to the sum of the
incoming relay traffic rate at each of the next-hop
neighbors of the node.The topology of the queueing
network depends on the routing protocol used which is
also elaborated in activity diagram also. The discrete
time Markov chain is made up of M+1 layers , where
each layer m(0<m<M) represents the state there are m
packets in the queue and M is the queue capacity. The
detailed knowledge of Discrete chain Markov Process is
essential while developing a cross layer. Before each
transmission , the packet in the queue is transferred from
the microcontroller to transreceiver. The time needed for
such transfer differs for various transreceivers, but it is
not negligible. Our Experiments with Network Simulator
2 suggest that the durations of loading time and after
radio transmission are constant and approximately 1.7
and 2.0 ms, respectively.

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Figure 1: Architecture Diagram
Figure 2: Activity Diagram
End-to-End Delay Distribution:-
Figure 3: Structures of Markov chains are shown in (a) for
{xn} and (b) for {Yn}. The common structure of blocks{zn }
and{In} are shown in (c) and (d), respectively.[1]
With each hop modeled as a Geom/PH/1/M queue, the entire
network is considered as a queuing network. Nodes are
interrelated according to the traffic constraints. More
specifically, the successfully transmitted traffic rate from one
node should be equal to the sum of the incoming relay traffic
rate at each of the next-hop neighbors of the node. The
topology of the queuing network depends on the routing
protocol used. In this paper, we focus on the class of routing
protocols with which each node maintains a probabilistic
routing table for its neighbors, e.g., geographic routing
protocols [4].Nodes relay their packets to each of their
neighbors according to a probability in their routing tables. By
first calculating the relaying traffic and the single hop delay
distribution for each pair of nodes, the end-to-end delay is
obtained using an iterative procedure.[1]
A. Constructing Markov Chain{Xn }
The discrete time Markov chain
{Xn} is made up of M+1 layers , where each layer m(0<m<M)
represents the state there are m packets in the queue and M is
the queue capacity. idle layer {In}and the communication
layers{Cn}m ,each of which consists of one or more states
each of which consists of one or more states. The states and

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the transitions among the states in each layer are determined
by the protocols used by each node and represent the
operations conducted by the nodes according to the protocols.
The idle layer{In}(m=0),represents the idle process, during
which the node does not have any packet to send and waits for
new packets. The communication layers {Cn}m, (m>0)
represent the communication process in which packets are
transmitted
According to the MAC protocol
employed, and are respectively parameterized by the
following notations:
•PI and PC : the transition probability matrix among the states
in {In }and {Cn} ;
•αI and αC : the initial probability vector for {In}and
{Cn};
• tI
S
and tc
s
: the probability vector from each state in{In} and
{Cn} to complete the idle process and the transmission process
successfully;
•tc
f
: the probability vector from each state in to complete the
transmission process unsuccessfully;
•‫ג‬ 1 and ‫ג‬ 2: the packet arrival probability vector for each state
in{In}and {Cn} . Each element in the vector is the probability
of a new packet arrival in a time unit when the process is in
the corresponding state.
Each communication layer {Cn }consists of Markov chain
blocks for each transmission attempt {Zn} , which is further
characterized by the transition probability matrix Pz , the
initial probability vector αz, the success probability vector tz
s
,
the failure probability vector tz
f
, and packet arrival probability
vector ‫ג‬z.
Accordingly, the transition probability matrix among the
states in a single layer {Cn} in {Xn} can be organized as rows
and columns of blocks
where the number of PZ blocks in PC is equal to x , i.e., the
maximum number of attempts for each packet transmission.
Similarly, the initial probability vector αc and the probability
vectors tc
s
and tc
f
to complete a layer in success and failure are
respectively organized as
αC = [ αZ 0 ……. 0 ] (1)
tc
s
= [tz
s
tz
s ………
tz
s
]T
(2)
tc
f
= [0 0 ……tz
f
]T
(3)
Note that since the idle layer does not have multiple attempts
like the communication layer does, there is no similar
organized internal pattern in the corresponding matrices and
vectors for {In}. The states and the transitions related to {In}
and {Zn} depend on the MAC protocol employed. The
transition probability matrix Qx of the entire Markov chain
{Xn} can then be found according to transitions between
different states at each layer as explained next.[1]
For layer m ,1<m<M-1 , the queue is not full.
Whenever a packet arrives, the process transits to a higher
layer since the queue length increases. The probabilities of
such transitions are governed by the probability matrix
Au=(1 ‫ג‬c )T
* Pc (4)
where is a properly dimensioned matrix containing all 1’s, and
* is the entrywise product operator.‫ג‬c and Pc are parameterized
according to the MAC protocol. Note that element (v,v’) in Au
represents the transition probability from the v th state in
previous layer to the v’ th state in the upper layer, and other
transition probability matrices in the following are defined the
similar way. The transition probability matrix at the same
level m ,1<m<M-1, is
As=(1‫ג‬c)T
*(tcαc) + (1-1‫ג‬c)T
*Pc (5)
Where tc = tc
s
+ tc
f
is the probability vector from each layer to
complete the current communication process regardless of
success or failure. The first term in (5) captures the case where
a locally generated packet arrives at the same time unit in
which a packet service is completed. The second term in (5) is
for the case where neither service completion nor new packet
arrival occurs during the time unit.
At layer m=M, the queue is full. Hence,
new arriving packets are directly dropped. Therefore, the
transition probability matrix in this layer is Au + As .When
there is no packet arrival and the current packet service is
completed, the Markov chain transits to one layer below.The
transition probability matrix from level m+1 to level m
,1<m<M-1 is
Ad = (1-1‫ג‬c)T *
tcαc (6)
The transition probabilities are similar when the idle layer is
involved as follows:
Au0= ‫ג‬I
T
* αC ( 7)
Ad0=( 1-1‫ג‬c)T
*tcαI (8)
As0 = ( 1-1‫ג‬I)T
* (PI + tI
S
αI (9)
When a new packet arrives while there
is no packet in the system, the chain transits from the idle
layer to layer 1 according TO Au0 to in (8). When the service
is completed for the only packet in the system and no new
packet arrives, the chain transits from layer 1 to the idle layer
according to Ad0 in(8).
Finally, the transition probabilities with
which the node stays in the idle layer are given in As0 in (9).
Using (4)–(9), the transition probability matrix Qxfor
the entire recurrent Markov chain {Xn} can be constructed as
follows:
Qx
Event Scheduler
To drive the execution of the simulation, to
process and schedule simulation events, NS makes use of
the concept of discrete event schedulers . In NS, network
components that simulate packet-handling delay or that
need timers use event schedulers. Figure 4 shows two
network objects, each of it using an event scheduler. If an

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network object issues an event, it has also to handle the
event later at scheduled time.
In NS, there are two different types of event schedulers –
real-time and non-real-time schedulers. There are three
implementations (List, Heap and Calendar) for non-real-
time schedulers; the default is Calendar.
Figure.4 The discrete event scheduler.[11]
Hardware Emulation
The real time scheduler (one of the two types of NS event
schedulers) is used for emulation. Emulation allow the
simulator to interact with a real live network NS is an OTcl
script interpreter with network simulation object libraries. But
NS in not only written in OTcl but also in C++. For efficiency
reasons, NS exploits a split-programming model. This is
because the developers of NS have found that separating the
data path implementation from the control path
implementation will reduce packet and event processing time.
Task such as low-level event processing and packet
forwarding requires high performance and are modified
infrequently, therefore the event scheduler and the basic
network component objects in the data path are implemented
in a compiled language that is C++. [11]
NS2 provides users with an
executable command ns which takes on input argument, the
name of a Tcl simulation scripting file. Users are feeding the
name of a Tcl simulation script (which sets up a simulation) as
an input argument of an NS2 executable command ns. In most
cases, a simulation trace file is created, and is used to plot
graph and/or to create animation.NS2 consists of two key
languages: C++ and Object-oriented Tool Command
Language (OTcl). While the C++ defines the internal
mechanism (i.e.,a backend) of the simulation objects, the OTcl
sets up simulation by assembling and configuring the objects
as well as scheduling discrete events (i.e., a frontend). The
C++ and the OTcl are linked together using TclCL. Mapped to
a C++ object, variables in the OTcl domains are sometimes
referred to as handles.
Conceptually, a handle (e.g., n as a
Node handle) is just a string (e.g.,_o10) in the OTcl domain,
and does not contain any functionality. Instead, the
functionality (e.g., receiving a packet) is defined in the
mapped C++ object (e.g., of class Connector). In the OTcl
domain, a handle acts as a frontend which interacts with users
and other OTcl objects. It may defines its own procedures and
variables to facilitate the interaction. Note that the member
procedures and variables in the OTcl domain are called
instance procedures instprocs) and instance variables
(instvars), respectively. Before proceeding further, the readers
are encouraged to learn C++ and OTcl languages. We refer the
readers to for the detail of C++, while a brief tutorial of Tcl
and OTcl tutorial are given in Appendices A.1 and A.2,
respectively. NS2 provides a large number of built-in C++
objects. It is advisable to use these C++ objects to set up a
simulation using a Tcl simulation script. However, advance
users may find these objects insufficient. They need to
develop their own C++ objects, and use a OTcl configuration
interface to put together these objects. After simulation, NS2
outputs either text-based or animation-based simulation
results. To interpret these results graphically and interactively,
tools such as NAM (Network AniMator) and XGraph are
used. To analyze a particular behavior of the network, users
can extract a relevant subset of text-based data and transform
it to a more conceivable presentation.[11]
Installation
NS2 is a free simulation tool, which can be
obtained from . It runs on various platforms including UNIX
(or Linux), Windows, and Mac systems.Being developed in
the Unix environment, with no surprise, NS2 has the
smoothest ride there, and so does its installation. Unless
otherwise specified,the discussion in this book is based on a
Cygwin (UNIX emulator) activated Windows system. NS2
source codes are distributed in two forms: the all-in-one suite
and the component-wise. With the all-in-one package, users
get all the required components along with some optional
components. [11]
The current all-in-one suite consists of the following main
components:
• NS release 2.30,
• Tcl/Tk release 8.4.13,
• OTcl release 1.12, and
• TclCL release 1.18.
and the following are the optional components:
• NAM release 1.12: NAM is an animation tool for viewing
network simulation traces and packet traces.
• Zlib version 1.2.3: This is the required library for NAM.

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IV. Discussion and results
Figure 3(a): CSMA/CA Mac Protocol
Figure 3(b): Average and end to end delay for CSMA/CA
Mac protocol.
Figure 4(a): Graph of Throughput Vs Packetloss
Crosslayer protocol.
Figure 5(a): Comparison graph of Throughput Vs
Packetloss Crosslayer and CSMA/CA Mac
Figure 3(b): Graph of Throughput Vs Packetloss For
CSMA/CA Mac protocol.
Figure 4(a): Crosslayer protocol
Figure 3(b): Average and end to end delay for Crosslayer
protocol.
Figure 5(b): Comparison graph of End to end delay
Crosslayer and CSMA/CA Mac

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The end-to-end delay distribution model has
been evaluated using NS2 to determine the single-hop and
multi hop delay distributions for the CSMA/CA MAC
protocol and the cross layer protocol . The computing
environment is a PC with a INTEL I3 working at 2.66
GHz and 4 GB RAM. Moreover, empirical experiments
and NS2-based simulations have been conducted on our
WSN test bed to validate the results. The simulations are
conducted in the same PC environment. For the empirical
validations, The packet size is B. Each node generates
local traffic to be sent to sink according to a Poisson
distribution with rate . Our experiments with the NS2
suggest that it requires on the average 1.7 ms to transfer
each packet from the sender to the receiver. The
transmission power is set to 15 dBm for all the
experiments unless otherwise stated. In the experiments,
the single-hop delay and end-to-end delay are measured as
follows. When the source node generates a packet, it
simultaneously sends an electric pulse to the destination
node through a pair of wires. The destination node starts a
timer when it receives the pulse and waits for the packet.
When the packet is received by the destination node, the
duration after the reception of the pulse is recorded as the
packet delay. This eliminates the need for synchronization
among all the nodes.
As shown in fig.3(a) a wireless topology
of nodes is implemented with CSMA/CA Mac protocol. A
packet transfer from sender to receiver is shown with the
shortest path possible with the CSMA/CA Mac protocol.
Algorithm finds the nearest node for transmitting the
packet in network. As shown in Fig.3(b) the graph of
throughput vs packetloss is drawn for CSMA/CA protocol.
Graph clearly shows that as packet loss is increased the
throughput is decreased. Fig.3(c) shows the average delay
for sending packet from sender to receiver as shown in the
network topology of module 2. Fig. also shows the average
end to end delay for sending packet from one end of
network to the other end, for CSMA/CA Mac
protocol.Fig.4(a) shows the network topology for Cross
layer protocol Fig. shows the packet transfer from sender
to receiver Sender nodes are shown by green and red color
while receiver nodes are shown by pink color. The average
delay for sending packet from sender to receiver is
calculated for cross layer protocol. Also average end to
end delay for sending packet from one end to other end of
network is calculated for cross layer protocol. As shown
in Fig.4(b) the graph of throughput vs packet loss is drawn
for Cross layer protocol. Graph clearly shows that as
packet loss is increased the throughput is decreased.
Fig.4(c) shows the average delay for sending packet from
sender to receiver as shown in the network topology of
module 2. Fig. also shows the average end to end delay for
sending packet from one end of network to the other end,
for Cross layer Mac protocol.
fig.5(a) shows the comparison of
CSMA and cross layer protocol for throughput vs packet
loss. as the red line indicates cross layer protocol and green
line shows the CSMA/CA Mac protocol. the graph clearly
shows that the packet loss is less in cross layer protocol as
compared to CSMA/CA protocol. due to this throughput
is more for cross layer protocol as compared to CSMA
/CA Mac protocol.
The average delay for the CSMA/CA
protocol is 0.267msec considering transfer of 30 packets.
The End to end delay for CSMA/CA Mac protocol is
0.5112 msec. The average delay for Cross layer protocol
is 0.062 m sec considering transfer of 30 packets. The end
to end delay for Cross layer protocol is 0.11008 msec.
Following Table I shows the analytical results.
Table I
Sr.
No
.
Parameter No.of
Packets
CSMA Crosslayer
1. Average
Delay(msec)
30 0.267 0.5112
2. End-to-End
Delay(msec)
30 0.062 0.11008
3. Average
Delay(msec)
80 0.512 0.9843
4. End-to-End
Delay(msec)
80 0.342 0.29870
V. Conclusion and Future work
In this paper, an end-to-end analysis of the
communication delay is provided. Our model shows
comparatively stronger results for Cross layer protocol
than CSMA/CA Mac protocol as shown in Table I. A
Markov process is used to model the communication
process in network. Average and End to end delay for
CSMA/CA protocol and Cross layer protocol is calculated.
The results show that the developed framework accurately
models the distribution of the end-to-end delay and
captures the heterogeneous effects of multi hop WSNs.
The developed framework can be used to find out the
Throughput and packet loss for the both CSMA/CA Mac
and Cross layer protocol. for WSNs
In some applications, the traffic generated for the
physical event can be bur sty. For tractability, the bur sty

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traffic pattern is not considered in this project. so in future
we can implement a system with bursty traffic. As future
work, we plan to analyze the delay for more MAC
protocols, such as BMAC [21], XMAC [3], using our
model. We also plan to extend the model to capture more
generic network topologies, and traffic types, such as
periodic and bursty traffics. Moreover, other network
lifetime definitions will be investigated. We also plan
extend our model to proposals in IEEE 802.11e to reduce
these delays which allow a node to schedule a burst of
packets once they gainchannel access. Each node in now
modeled as a discrete time queue with interruptions.
VI. References
[1] Yunbo Wang, Member, IEEE, Mehmet C. Vuran,
Member, IEEE, and Steve Goddard, Member, IEEE
“Cross-Layer Analysis of the End-to-End Delay
Distribution in Wireless Sensor Networks.” IEEE/ACM
transactions on networking, vol. 20, no. 1, february 2012
[2] Omesh Tickoo and Biplab Sikdar, Member, IEEE
“Modeling Queueing and Channel Access Delay in
Unsaturated IEEE 802.11 Random Access MAC Based
Wireless Networks.” IEEE/ACM transactions on
networking, vol. 16, no. 4, august 2008
[3] “Stochastic Analysis of Energy Consumption in
Wireless Sensor Networks.” Yunbo Wang, Mehmet C.
Vuran and Steve Goddard Department of Computer
Science and Engineering,University of Nebraska-Lincoln
[4] T. Abdelzaher, S. Prabh, and R. Kiran, “On real-time
capacity limits of multihop wireless sensor networks,” in
Proc. IEEE RTSS, Lisbon, Portugal, Dec. 2004, pp. 359–
370.
[5] K. Akkaya and M. Younis, “A survey on routing
protocols for wirelesssensor networks,” Ad Hoc Netw., vol.
3, no. 3, pp. 325–349, Sep. 2005.
[6] I. F. Akyildiz, T. Melodia, and K. R. Chowdhury, “A
survey on wireless multimedia sensor networks,” Comput.
Netw. J., vol. 51, no. 4, pp. 921–960, Mar. 2007.
[7] I. F. Akyildiz,W. Su, Y. Sankarasubramaniam, and E.
Cayirci, “Wireless sensor networks: A survey,” Comput.
Netw. J., vol. 38, no. 4, pp. 393–422, Mar. 2002.
[8] G. Bianchi, “Performance analysis of the IEEE 802.11
distributed coordination function,” IEEE J. Sel. Areas
Commun., vol. 18, no. 3, pp.535–547, Mar. 2000.
[9] N. Bisnik and A. Abouzeid, “Queuing network models
for delay analysis of multihop wireless ad hoc networks,”
Ad Hoc Netw., vol. 7, no.1, pp. 79–97, Jan. 2009.
[10] A. Burchard, J. Liebeherr, and S. Patek, “A min-plus
calculus for end-to-end statistical service guarantees,”
IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4105–4114,
Sep. 2006.
[11] Teerawat Issariyakul & EkramHossain”Introduction
to Network Simulator 2.”2009 Springer Science,Business
Media,
Ravindra J. Lawande 1
BE in Electronics from
Pune University,
pursuing ME in VLSI
and embedded form
PREC, loni, Pune
University, working as
an assistant professor at
PDVVPCOE,
Ahmednagar,
Maharashtra ,India
His field of interest is
Wireless Comm. and
Microwave.
.
Abdul .H.Ansari 2
BE and ME from
S.S.G.MCE,Shegaon,
Amaravati University
has 16 years of teaching
Experience, presently
working as Associate
professor at PREC,Loni
His field of interest is
Wireless Comm. and
Cognitive Radio.