major project report 7th sem09eeg17

8/12/2019 Major Project Report 7th Sem09EEG17

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OPTIMIZATION OF DELAY AND MAXIMIZATION OF AVERAGE

REVENUE SUBJECTED TO MINIMUM BANDWIDTH CONSTRAINT

IN WIRELESS COMMUNICATION MESH NETWORKS

Major Project-I Report

Submitted in partial fulfilment of the requirements for the award of the degree

BACHELOR OF TECHNOLOGY

IN

ELECTRICAL AND ELECTRONICS ENGINEERING

BY

ABHISHEK VERMA (09EE03)

CHIRAG MAHAPATRA (09EE30)

JITESH AGARWAL (09EE42)

MANTHAN PANCHOLI (09EE65)

ROHAN GUPTA (09EE79)

Under the guidance of

Dr. ASHVINI CHATURVEDI

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA, SURATHKAL

SRINIVASNAGAR-575025, KARNATAKA, INDIADECEMBER, 2012


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DECLARATION

We hereby declare that the project work report entitled Optimization of Delay and

Maximization of Average Revenue Subjected to Minimum Bandwidth Constraint inWireless Communication Mesh Networks which is being submitted to the National

Institute of Technology Karnataka, Surathkalfor the award of the Degree of Bachelor of

Technology in Electrical and Electronics Engineering is a bonafide report of the work

carried out by us. The material contained in this report has not been submitted to any

university or institution for the award of any degree.

SI. NO. NAME ROLL NO. Signature

1 AbhishekVerma 09EE03

2 Chirag Mahapatra 09EE30

3 Jitesh Agarwal 09EE42

4 Manthan Pancholi 09EE65

5 Rohan Gupta 09EE79

Department of Electrical and Electronics Engineering

PLACE : NITK, SURATHKAL

DATE : 4th

December, 2012


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CERTIFICATE

This is to certify that the B-tech project work report entitled Optimization of Delay and

Maximization of Average Revenue subjected to minimum bandwidth constraint inWireless Communication Mesh Networks submitted by:

SI. NO. NAME ROLL NO.

1 Abhishek Verma 09EE03

2 Chirag Mahapatra 09EE30

3 Jitesh Agarwal 09EE42

4 Manthan Pancholi 09EE65

5 Rohan Gupta 09EE79

As the record of the work carried out by them, is accepted as the B-Tech. Project Work

Report Submission, in partial fulfilment of the requirements for the award of Degree of

Bachelor of Technology in Electrical and Electronics Engineering.

Dr. ASHVINI CHATURVEDI

Project Guide,

Department of Electrical and Electronics Engineering,

National Institute of Technology Karnataka, Surathkal

Dr. K.P VITTAL

Head of the Department,

Department of Electrical and Electronics Engineering,

National Institute of Technology Karnataka, Surathkal


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ACKNOWLEDGEMENT

The extensive endeavour, bliss and euphoria to accomplish the task certainly would not have

been realized without the expression and gratitude of people who made it possible. We takethis opportunity to acknowledge all those whose support and encouragement has helped us in

tuning this project.

We are grateful to our guide, Dr. Ashvini Chaturvedi, department of Electrical and

Electronics Engineering for not only providing us opportunity to showcase but also all

facilities and experience in the completion of this project. He bestowed his guidance at

appropriate times without which it would have been very difficult for us to complete the

project. An assemblage of this nature could never have been attempted without the support of

our guide.Our thanks are also due to Prof. K.P. Vittal, the head of the Electrical and Electronics

department who has allowed us use of the facilities at the department.

Abhishek Verma (09EE03)

Chirag Mahapatra (09EE30)

Jitesh Agarwal (09EE42)

Manthan Pancholi (09EE65)

Rohan Gupta (09EE79)


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INDEX

Serial No Topic Page No.

1. Abstract 1

2. Introduction 1

3. Motivation 2

4. Literature Survey 2

Paper 1: WiFi access point pricing as a dynamic game.by J. Musacchio andJ. Walrand.

Paper 2: Market Models and Pricing Mechanisms in a Multihop Wireless

Hotspot Network. by Kai Chen, Zhenyu Yang, Christian Wagener, Klara

Nahrstedt

Paper 3: Efficient multicast routing with delay constraints., by G. Fengand

T.S.P. Yum, International Journal of Communication Systems

Paper 4: A Delay-Constrained Shortest Path Algorithm for Multicast Routingin Multimedia Applications. by M.F. Mokbel, W.A. El-Haweet, M.N. El-

Derini

5. Part A 8

6. Part B 15

7. Appendix I 22

8. Appendix II 31

9. Reference 37


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ABSTRACT

The development of wireless LAN technologies offers a novel platform for internet service

resale via wireless community mesh networks that provide high network coverage and lower

infrastructure cost. In a wireless community mesh network, access point functions as both theInternet service provider and Internet access provider to the mesh network neighbours (end-

users) since the upstream Internet service providers of the access point is not able to monitor

and bill for the resold traffic within the community mesh network. In this Internet service

resale business, the access provider sets their pricing policy as an Internet reseller to

maximize its revenue, while the end-users who are price sensitive, respond to this pricing

policy by controlling their Internet usage. Using a queuing theory model, we propose an

optimal pricing model to achieve revenue maximization for a mesh network access provider.

The users sensitivity to the price is modelled in order to discover the optimal price. The

effects of the price on the traffic load and the maximum number of users at the access point

are explored since price is viewed as an additional strategy to encourage a better usage of the

limited bandwidth resource. Monte Carlo simulation results are presented to verify the

analytically optimal price based on the proposed pricing model.

Another key aspect of wireless mesh networks is the scope of multicast routing. This is when

there is a single source and multiple receivers. This is advantageous when multimedia

applications like videoconferencing and remote collaboration is used. Solving an optimal

multicast tree is an NP problem i.e. it cannot be done in polynomial time. Hence, we can try

to get an approximate solution using heuristics. There are two key ways of optimizing one:

via minimizing the cost, two: via minimizing the delay. Both these methods are not optimal

since there is an upper threshold to the delay incurred in the network and the cost cannot be

prohibitively high. Here, we propose an optimal solution in O(n

2

) time.

INTRODUCTION

The low-cost wireless mesh network (WMN) technology induces the expanding of wireless

community mesh networks or WMNs. It is viewed as an opportunity to expand markets for

telecommunication services to empower local communities and to expand economic capacity

and commerce in rural areas. Internet access is one of the most common applications of

WMNs. A WMN interconnects stationary and / or mobile users and provides internet access

as well as communications within the network. The nodes connected to the Internet are called

access points (APs). In the WMN, the objectives of most end-users would be to access the

Internet at a reasonable cost. In this sense, APs are Internet access providers who also resellInternet services to end-users within the WMN. The upstream Internet service providers

(ISPs) will not be able to monitor resold traffic within the WMN in order to bill the end-

users. The APs set the pricing policy to generate revenue to cover their costs and maximize

their profit. For the end-users as buyers of resold Internet services, each end-user derives

some value from accessing and using the Internet, based on the APs pricing policy. Each

end-users willingness to pay for the Internet service is dependent on their perceived need for

the access. Hence, it is important to analyze the end-usersbehaviour when a pricing strategy

is investigated to maximize revenue for an AP provider Quality of service (QoS) is another

aspect that affects the end-users usage behaviour. As the WMN expands, the AP whose

uplink has a limited data capacity will inevitably result in the end-users having to face traffic

congestion at the AP node. In general, congestion control is especially important for best-effort services, since there is no congestion avoidance mechanisms implemented in the


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network. Pricing is widely viewed as a mechanism to give users incentives to use the network

efficiently or a means for network usage control. Using price, the network could send signals

to the users, providing them with incentives that influence their usage behaviour and

decisions. By these means, APs can provide a better and more stable service to end-users.

MOTIVATION

In this project, we will investigate how price impacts the end-users traffic and the system

utilization at the AP node. We model a typical mesh network in which there is a single AP

providing Internet connectivity and services to the end-user nodes, as an M/M/1/S queue

system. The M/M/1/S is a special type of Markovian system, where customers arrive

according to a Poisson process and are served by a single server with an exponential service-

time distribution. The system can accommodate only S maximum customers simultaneously.

In this model, as long as the end-user accepts the price charged by the AP and there is room

in the queuing system, the end-user is served and the AP earns the revenue based on the end-

users usage. The end-users demand is modelled as a function of the service price. The

utility function is an important concept which is widely used in literature to give a measure of

the users sensitivity to the price and their perceived QoS level. For the general case of

Internet provision, when ISPs offers a service at a particular price to the users, these users

will respond to this price by changing their usage to maximize their utility. From an

economic point of view, the utility function is strictly related to the users demand curve,

which is associated to the users willingness-to-pay and their perceived QoS level. Since it is

difficult to find direct knowledge of users utility function, we will model these dependences

in our analytical pricing model instead of using a utility function to represent the end- users

demand. If the price charged by the AP is out of the range of the end-users willingness to

pay, the end-user is likely to decrease their Internet usage. It is evident that there is a trade-off

between the price and the amount of end-users Internet usage. A lower price attracts moreend-users with large demands but yields less revenue per end-user, while a higher price yields

more revenue per end-user but might discourage more end-users from using the service. In

this project, an optimal pricing model to maximize the APs revenue based on the end -users

behaviour model is presented. In this pricing model, the traffic intensity, the end-users

willingness to pay and the QoS metric are taken into account to develop the optimal pricing

algorithm. The proposed pricing scheme can determine an optimal price in order to maximize

the revenue, while maintaining the traffic intensity and the maximum of end-users, S, at the

AP to a reasonable level. Further, we focus on usage-based pricing. Usage-based pricing is

incentive compatible since it encourages customers to use network resources more efficiently.

Customers are willing to pay an additional per-usage charge in order to improve the network

performance (QoS charge) and to avoid the performance degradation due to the networkcongestion. However, our objective is to investigate the effects of the end-users willingness-

to-pay on the optimal price that maximizes the APs revenue for a finite capacity system.

LITERATURE SURVEY

Paper 1: WiFi access point pricing as a dynamic game.by J. Musacchio and J.

Walrand.

Abstract


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This paper studies the economic interest of a wireless access point owner and his paying

client, and models their interaction as a dynamic game. The key feature of this game is that

the players have asymmetric informationthe client knows more than the access provider.

From the paper it can be inferred that if a client has a web browser utility function (a

temporal utility function that grows linearly), it is a Nash equilibrium for the provider tocharge the client a constant price per unit time. On the other hand, if the client has a file

transferor utility function (a utility function that is a step function), the client would be

unwilling to pay until the final time slot of the file transfer. It also studies an expanded game

where an access point sells to a reseller, which in turn sells to a mobile client and show that if

the client has a web browser utility function, that constant price is a Nash equilibrium of the

three player game. Finally, it states a two player game in which the access point does not

know whether he faces a web browser or file transfer or type client, and show conditions for

which it is not a Nash equilibrium for the access point to maintain a constant price.

Introduction

Today there is a large and growing number of wireless access points deployed by homes and

businesses for private LANs. Many of these access points could potentially be used to

provide Internet access to users from the general public that lie or are passing within

communication range of the access point. However, owners of private WiFi networks often

choose to encrypt their networks to prevent outsiders from accessing them. Without a

mechanism for a potential client to compensate the owner of the network, the network owner

has no reason to accept the increased network traffic and security risk that would come from

allowing the public to access his network. If it were possible to provide incentives to owners

of existing private wireless access points to open their networks to the public, as well as

provide incentives to people and institutions to deploy access points where there are gaps in

coverage, the result might be nearly ubiquitous WiFi coverage. In contrast to cellular phone

networks deployed by a few large providers, this ubiquitous access network would be

deployed by thousands, perhaps millions, of autonomous self-interested agents.

Conclusion

We have seen that if the client is a web browser, with a utility function that grows linearly

with connection duration, it is a PBE for the access point to charge a constant price in each

time slot. Though the value of the price charged depends on U (utility per slot), the fact that

constant price is a PBE is true for any distributions of type variables Uand (the intended

session length) so long as Uand are finite-mean and independent. The result even extendsto a multi-hop case where an access point sells to a reseller which in turn sells to a client.

These results suggest that if a client has a web browsing utility function, that we could expect

an access point to charge constant price without third party supervision, and without the need

for contracts. An architecture based on micropayments would likely lead to a functioning

market. However, if the client has a file transferor utility, where utility has a step with respect

to time, then the access point price is not constant in PBE. Furthermore, when the file length

has a bounded distribution, clients are pessimistic, and the PBE can be very inefficient in

terms of social welfare. The access point prices are not constant even when there is only a

small probability of the client being a file transferor, as we saw in the Bayesian Model. When

the Bayesian Model is modified for clients that have an unbounded intended session length, it

remains true that prices are not constant, and furthermore it is not a PBE for the access pointto charge reasonable prices in every slot. Where a reasonableprice is one in which there


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is a nonzero probability of the clientsone slot utility exceeding it. Despite the disappointing

properties of the equilibria in the file transferor cases, the direct charging model is viable, if

the granularity of the slots is chosen judiciously. For one reason, the web browsing model is a

more realistic representation of a typical clients utility. Most mobile users are probably

interested in browsing the web, using e-mail, or perhaps downloading small files. As long as

the e-mail spool or small files can be downloaded in less than one slot, then the stepdiscontinuities in client utility disappear when looked at using the discrete time scale of the

game. However, the slot size should not be made too large, because the client might not feel

comfortable paying in advance for a large block of time. From a game theory perspective, an

access point with marginal cost per slot would be tempted to take a slot payment and then not

serve the client. With any choice of time slot length, users will on occasion download files

that take longer than one time slot to complete. To address this issue the file transfer software

that already exists today that allow clients to resume an interrupted file transfer at some later

time must be used. A client using such software does get partial utility for partial files, and

thus her utility function would look more like that of our web-browser model than of our file

transferor model.

Paper 2: Market Models and Pricing Mechanisms in a Multihop Wireless Hotspot

Network. by Kai Chen, Zhenyu Yang, Christian Wagener, Klara Nahrstedt.

Abstract

Multihop wireless hotspot network has been recently proposed to extend the coverage area of

a base station. However, with selfish node in the network, multihop packet forwarding cannot

take place without an incentive mechanism. In this paper, we adopt the pay for service

incentive model. i.e., clients pay the relaying nodes for their packet forwarding service. Ourfocus in this paper is to determine a fair pricing for packet forwarding. To this end, we

model the system as a market where the pricing for packet forwarding is determined by

demand and supply. Depending on the network communication scenario, the market models

are different. We classify the network into four different scenarios and propose different

pricing mechanisms for them. Our simulation results show that the pricing mechanisms are

able to guide the market into an equilibrium state quickly. We also show that maintaining

communication among the relaying nodes is important to achieve a stable market pricing.

Introduction

We consider a multihop hotspot network. In this architecture, a mobile client may not be ableto reach the base station (BS) via single hop direct communication. Instead, the client must

rely on another node which is closer to the BS to forward its packets. Such nodes are called

the relaying nodes (RN). This is the multihop wireless hotspot network. Compared to the

traditional single-hop hotspot network where every node communicates directly to the BS, a

multihop hotspot network offers a few advantages. First, it extends the coverage of the BS to

a larger area, which is helpful especially when installing additional BS is not possible due to

real property restrictions. Second, it may increase the throughput of a client who receives

very bad signal from the BS, while a nearby relaying node has much better wireless signal

quality. This situation is possible considering the irregular signal propagation property in a

physical environment with partitions and obstacles. Finally, by multihop forwarding, a client

does not need to have subscription to the BS to use its service. This is helpful when a clientroams outside its own hotspot ISPs service area. In this paper, the authors focus on providing


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incentive for packet forwarding in a two-hop hotspot network. Since packet forwarding

consumes a RNs resources such as bandwidth and energy, aselfish RN would not be willing

to forward others packets without an incentive mechanism. In this paper, they adopt the pay

for service incentive model, i.e., clients pay the RNs to forward their packets. In human

society, monetary rewards are often given for providing service. Here, packet forwarding can

be considered as RNs service to the clients, considering the fact that the RNs are ownedand controlled by human users. This paper focuses on determining a fair pricing for the

packet forwarding service in this network. The system is modelled as a market where the

pricing for packet forwarding is determined by demand and supply. The RNs compete for

clients traffic; clients can choose a RN who can offer a better price, similar to 2 in a

multiple-buyer multiple-seller market. Its difference with the conventional market is that the

communication scenarios in this network can be very complex, leading to different market

structures. The market structure in this network depends on the number of RNs, the

communication among the RNs, and the reachability of the clients to the RNs. For example,

if there is only one single RN in the network, the RN becomes a monopolist who has unique

pricing power. Therefore, the RN can probe the client(s) with different prices to maximize its

profit. However, if there are multiple RNs, such pricing power is rather limited. Instead, theRNs have to compete with each other by undercutting each others price. The authors classify

the network into four different scenarios and propose different pricing mechanisms for them.

They have introduced a hill-climbing algorithm for a monopoly market (i.e. single RN in the

network), and a second lowest marginal cost pricing mechanism for a market with multiple

RNs and perfect reachability. We further extend these basic network scenarios to cover a

situation where a client can only reach a subset of the relaying nodes, and another situation

where the relaying nodes do not have communication among them.

Conclusion

In this paper, the focus is on the packet forwarding incentive problem in a two-hop wireless

hotspot network. The authors adopt the credit (or micro-payment) based incentive approach,

i.e., the clients pay the relaying nodes for their packet forwarding service. The system is

modelled as a market where the pricing for packet forwarding is determined by demand and

supply. The network is classified into four different scenarios, and different pricing solutions

are proposed for each of them. In particular, hill-climbing algorithms is designed for a

monopoly market, and introduce a VCG-like second lowest marginal cost pricing mechanism

for a market with multiple relaying nodes which guarantees truthful reporting of marginal

costs. The work is further extended the network scenarios to cover the situation where a client

can only reach a subset of the relaying nodes, and another situation where the relaying nodes

do not have communication among them. The simulation results show that the pricingmechanisms are able to guide the market into an equilibrium state quickly. The analysis in

this paper underscores the importance of keeping communication among the relaying nodes,

therefore, the base station should be encouraged to act as intermediate to reliably relay

pricing messages among them.

Paper 3: G. Fengand T.S.P. Yum, Efficient multicast routing with delay constraints.,

International Journal of Communication Systems

Abstract

To support real-time multimedia applications in BISDN networks, QoS guaranteed multicastrouting is essential. Traditional multicast routing algorithms used for solving the Steiner tree


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problem cannot be used in this scenario, because QoS constraints on links are not considered.

In this paper, we present two efficient source-based multicast routing algorithms in directed

networks. The objective of the routing algorithms is to minimize the multicast tree cost while

maintaining a bound on delay. Simulation results show that these two heuristics can greatly

improve the multicast tree cost measure in comparison with the shortest path routing

schemes. Their performance is close to that of the known CST algorithm proposed byKompell et al., but requiring a much shorter computation time.

Introduction

Multimedia applications such as videoconferencing and remote collaboration rely on the

ability of the network to provide multicasting communication. Multimedia traffic consists of

audio and video that consume large bandwidth and require a certain quality-of-service (QoS)

when transferred through networks. Hence efficient multicast routing algorithms which are

capable of constructing low-cost multicast trees that satisfy the constraints imposed by the

QoS requirements are essential for real-time multimedia services. Current multicast routing

protocols, such as PIM,2 DVMRP,3 are based on simple algorithms: shortest pathmulticasting and reverse path multicasting. These multicast algorithms usually assume simply

additive cost metric.

Algorithms for constructing multicast trees have been developed with two optimization goals.

The "rst is the minimum average path delay, which is the average of the minimum path delay

from the source to each of the destinations in the multicast group. This can be done in O(n2)

time using Dijkstra's shortest path algorithm,4 where n is the number of nodes in the graph.

The second goal is to minimize the cost of the multicast tree, which is the sum of the cost on

the edges in the multicast tree. The least cost tree is called a Steiner tree, and the problem of

finding a Steiner tree is known to be NP-complete.4 Many heuristics for low-cost multicast

routes take O(n3) to O(n4) time5,6 and can produce solutions that are within twice the cost of

the optimal solution.

Conclusion

The planning and running of multimedia applications in BISDN require an efficient multicast

protocol. We have presented two efficient multicast routing algorithms that can produce good

solutions and scale to large size networks. Algorithm A is very simple and is suitable for

static multicast connection requests, while Algorithm B allows the tuning of the tree cost by

the run time and can support multicasting dynamics. These two properties are important for

multiparty conferencing applications where the setup speed of multicast connection is critical

and the multicast group is dynamic. The performance of Algorithm B is found to be veryclose to that of CST but at a much lower time complexity.

Paper 4: A Delay-Constrained Shortest Path Algorithm for Multicast Routing in

Multimedia Applications. by M.F. Mokbel, W.A. El-Haweet, M.N. El-Derini

Abstract

A new heuristic algorithm is proposed for constructing multicast tree for multimedia

and real-time applications. The tree is used to concurrently transmit packets from

source to multiple destinations such that exactly one copy of any packet traverses the

links of the multicast tree. Since multimedia applications require some Quality ofService, QoS, a multicast tree is needed to satisfy two main goals, the minimum path


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cost from source to each destination (Shortest Path Tree) and a certain end-to-end delay

constraint from source to each destination. This problem is known to be NP-Complete.

The proposed heuristic algorithm solves this problem in polynomial time and gives near

optimal tree. We first mention some related work in this area then we formalize the

problem and introduce the new algorithm with its pseudo code and the proof of its

complexity and its correctness by showing that it always finds a feasible tree if one exists.Other heuristic algorithms are examined and compared with the proposed algorithm via

simulation.

Introduction

Handling group communication is a key requirement for numerous applications that have

one source sends the same information concurrently to multiple destinations. Multicast

routing refers to the construction of a tree rooted at the source and spanning all

destinations. Generally, there are two types of such a tree, the Steiner tree and the shortest

path tree. Steiner tree or group-shared tree tends to minimize the total cost of the

resulting tree, this is anNP-Complete problem, number of heuristics to this problem can be found in Shortest

path tree or source-based trees tends to minimize the cost of each path from source to any

destination, this can be achieved in polynomial time by using one of the two famous

algorithms of Bellman and Dijkstra and pruning the undesired links. Recently, with the

rapid evolution of multimedia and real-time applications like audio/video conferencing,

interactive distributed games and real-time remote control system, certain QoS need to be

guaranteed in the resulted tree. One such QoS, and the most important one, is the end-to-

end delay between source and each destination, where the information must be sent

within a certain delay constraint D. By adding this constraint to the original problem of

multicast routing, the problem is reformulated and the multicast tree should be either delay

constrained Steiner tree, or delay-constrained shortest path tree. Delay constrained Steiner

tree is an NP-Complete problem, several heuristics are introduced for this problem each

trying to get near optimal tree cost, without regarding to the cost of each individual path for

each destination. Delay-constrained shortest path tree is also an NP-Complete problem.

An optimal algorithm for this problem is presented, but its execution time is

exponential and used only for comparison with other algorithms. Heuristic for this

problem is presented, which tries to get a near optimal tree from the point of view of

each destination without regarding the total cost of the tree. An exhaustive comparison

between the previous heuristics for the two problems can be found. In this paper we

investigate the problem of delay constrained shortest path tree since it is appropriate in

some applications like Video on Demand (VoD), where the multicast group has afrequent change, and every user wants to get his information in the lowest possible

cost for him without regarding the total cost of the routing tree. Also shortest path tree

always gives average cost per destination less than Steiner tree.

Conclusion

In this paper we propose a polynomial time heuristic algorithm that computes the

shortest path tree with delay constraint. The algorithm has a running time O(K2N2)

whereK is a variable adjusted from 1 to N and N is the number of nodes in the

network. Simulation experiments have been done to compare the efficiency of the new

algorithm with other previous algorithms and with the optimal results. Empirical resultsshow that our algorithm is always dominating previous algorithms and gives optimal


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results with certain value of K. Simulations are also done to determine the appropriate

value of K that gives the optimal result. It is clear that a small value ofK could be enough

which makes the running time of the algorithm near O(N2). The work in this algorithm

can be extended in three ways. Firstly, a distributed version of this algorithm could be

introduced by limiting the data kept in each node. Secondly, the dynamic change of

group members should be considered to be embedded on the algorithm and not to start thealgorithm from the beginning. Finally, this algorithm should be incorporated in an

appropriate protocol to be used in real networks.

PART APROPOSED APPROACH

In reported work, an Optimal Pricing Model for Wireless Community Mesh Networks is

implemented. Firstly, the network comprising of a single access provider and multiple users

is designed using M/M/1 queuing theory and then using probability theory the blocking

probability is defined. The blocking probability is used as an indicator minimum bandwidthto determine the limitation for the value of blocking probability. The average revenue of theaccess provider is maximized subject to certain constraints controlled by QoS and the optimal

price is found. The analytical results are compared with the results obtained from Monte

Carlo simulations.

Formulation of Objective Function

When end-users connect to an AP to access the Internet, the AP has a total bandwidth of B

(Mbits/sec) available for all the end-users. Suppose that end-users arrive at the AP according

to a Poisson process distribution with an arrival rate (users/minute) and each end-user

utilizes (transmits and receives) a certain amount of data during their connection to theInternet before disconnecting. Literature on data analysis of internet traffic describes the sizes

of the files transmitted over the Internet as being heavy tail distributed. The transmission

durations also follows a heavy-tailed distribution due to the heavy-tailed distributed file sizes.

It is generally assumed that the service time is strongly correlated to the file size. In this

context, the service time is taken to be equal to the transmission time of a file, which is

proportional to the size of the file. For simplification, we suppose that file sizes are

exponentially distributed with meanF (Mbits). When there areN1 users in the system at the

same time, each user is allocated an instantaneous bandwidth ofB/N. This system is shown in

the following figure and is equivalent to an M/M/1/S PS (Processor Sharing) queue with

arrival rate and exponentially distributed service rate (minute). The figure shows that

the system moves from one state to the other based on arrival rate and service rate .


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Therefore, the traffic intensity is denoted as = / . In practice, it is suggested that a shared

resource should be designed in such a way that its utilization is less than two-third of its full

capacity (=1).In an M/M/1/S queue system, when there are S customers in the system or the

system is saturated, theblocking probabilityPSis:

(1)

Since the maximum value of end-users that can be accommodated (S) is determined by the

blocking probability given a certain traffic intensity , the minimum bandwidth allocation for

a certainPSisB/S given a certain traffic intensity . Therefore, we can also say a minimum

bandwidth allocated to the end-users can be determined by a givenPS. From the viewpoint of

the AP providers, the lower blocking probability (PS) implies that more end-users can obtain

services and more revenue can be generated. However, according to Eq.1 the lower blocking\

probability also means that the maximum of end-users (S) in the system is higher. Hence,

from the end-user point of view, even while their requests can be accommodated with higherprobability due to the lower blocking probability, the minimum bandwidth that can be

allocated to them might be lower. In this pricing model, we use the blocking probability as an

indicator of the minimum bandwidth to determine the limitation for the value ofPS, we will

use the blocking probability to model the end-users reaction to the minimum bandwidth.

According to queue theory, the average number of customers at the services facilityNSis:

(2)However, the arriving end-users are price sensitive. Their responses to the price charged by

the AP depend on a number of factors. A probabilistic model for end-users willingness-to-

pay the quoted price using a Pareto distribution of customer capacity to pay is used. Everyend-user has the capacity to pay based on a Pareto distribution with scale b and shape ,

where all customers have capacities at least as large as b and determines how the capacities

are distributed. Thus and b are the Pareto distribution parameters for the end-user capacity

to pay function. It is reasonable to assume that end users willingness-to-pay is associated

with their capacities to pay. Therefore, the expectation of acceptance given price p is:

(3)Where is the equivalent to the economic elasticity of demand of the end-users. The higher

the value of , the more willing the end-users is to pay. Thus, the arrival rate of our model

is different from that of the conventional M/M/1/S queuing system as mentioned above by a

factor of E: E. In other words, the arrival rate is denoted as a function of the price.

Correspondingly, the traffic intensity of the system model that we mentioned above is

denoted as (p)= E(p) / . Figure (a) shows that the traffic intensity decreases when the

quoted price increases, since a higher price leads to a smaller end-user arrival rate.

Substituting (p) for in (1) and (2), we get the following:


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(4)&(5)

Therefore, the long-term average revenue per unit time isexpressed as:

(6)wherep is the price per Mbit of data transferred.

Now we can formulate the optimization problem to determine the optimal price:

(7)where is a constraint of blocking probability S P . The solution of this optimization problem

is characterized by:

Therefore, the long-term average revenue per unit time is maximized whenpoptis equal to:

Analytical Simulation Results

Figure (a): Traffic intensity versus quoted price


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The objective function in Eq.7 is shown numerically in Figure (b) with =2, b=4, =6,

=0.01. Figure (b) characterizes the relationships between the revenue, the price and the end-

usersresponse to the price by adjusting the amount of usage of the Internet service. As the

price increases, numbers of end-users decreases while the revenue per end-user increases.

The total revenue is maximized when the price reaches the optimal price popt.

popt = 3.68

Figure (b): Average revenue v/s quoted price

Figure (c)-Figure (e) shows how the parameters of the function of willingness-to-pay affect

the value of the optimal price. It is shown that the parameters and have little impact on the

value of the optimal price while parameter b plays an important role in determining the

optimal price.


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Figure (c): Average revenue v/s quoted price for different a

Figure (d): Average revenue v/s quoted price for different b


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Figure (e): Average revenue v/s quoted price for different delta

Monte Carlo Simulation Results

popt = 3.65

Figure(f): Comparison of Analytical result and Monte Carlo result


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Conclusion

In this work, an optimal pricing model for Internet service resale via WMN is presented. We

model end-users traffic as a function of the service price. Based on a queuing system model,

an optimal price algorithm is developed to maximize the AP providers revenue. The

performance of the proposed pricing scheme is investigated and the analytically optimal priceis compared to the results of the session level Monte-Carlo simulations. It is shown that the

proposed optimal pricing scheme can provide maximized revenue to the AP provider, a better

quality of service in terms of the minimum bandwidth allocation to the end-users and an

efficient control of the traffic load at the AP node to avoid congestion. The optimal price

found in both the analytical method and Monte Carlo method is almost same.


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PART BPROPOSED APPROACH

Our goal is to find a multicast tree which minimizes the cost function along with having an

optimal level of delay. This is very important in multimedia applications like videoconferencing and remote collaboration which rely on the ability of the network to give

multicast communication.

Goal

The QoS parameters we have taken into consideration in this project is

Bandwidth (modelled as cost)

Delay in the link

The goal is to:

Minimize Average path delay

Minimize total tree cost

Network model

Figure (a): Network model


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Minimum cost tree

We find this using the Prims algorithm.

Pseudocode

Minimum-Spanning-Tree-by-Prim(G, weight-function, source)1 for each vertex u in graph G

2 set key of u to_

3 set parent of u to nil

4 set key of source vertex to zero

5 enqueue to minimum-heap Q all vertices in graph G.

6 while Q is not empty

7 extract vertex u from Q// u is the vertex with the lowest key that is in Q

8 for each adjacent vertex v of u do

9 if (v is still in Q) and (weight-function(u, v) < key of v)

then10 set u to be parent of v // in minimum-spanning-tree

11 update v's key to equal weight-function(u, v)

Output

Figure (b): Minimum cost tree

Shortest Delay Tree


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We find this using Djikstras Algorithm.

Pseudocode

1 functionDijkstra(Graph, source):

2for each

vertexvin

Graph:

//Initializations3 dist[v] := infinity ; // Unknown distance function

from4 // source to v5 previous[v] := undefined ; // Previous node in optimal

path6 end for // from source

7

8 dist[source] := 0 ; // Distance from source to

source9 Q:= the set of all nodes in Graph; // All nodes in the graph are10 // unoptimized - thus are in Q11 whileQis notempty: // The main loop

12 u:= vertex in Qwith smallest distance in dist[] ; // Startnode in first case13 remove ufrom Q;14 ifdist[u] = infinity:15 break; // all remaining vertices are16 end if // inaccessible from source

1718 for eachneighbor vof u: // where v has not yet been

19 // removed from Q.20 alt:= dist[u] + dist_between(u, v) ;21 ifalt< dist[v]: // Relax (u,v,a)

22 dist[v] := alt;23 previous[v] := u;

24 decrease-key vin Q; // Reorder v in the Queue25 end if

26 end for27 end while28 returndist;

Output


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Figure (c): Shortest delay tree

Our proposed algorithm

Step 1: Compute minimum cost tree

Step 2: Set a delay constraint Delta

Step 3: Remove all the nodes from MCT recursively which do not satisfy Delta

Step 4: Identify the paths from the network which have minimum delay from source. Step 5: Remove loops if any

Step 6: Add these paths to the tree

Operating details

Input:

A graph G=(V,E)

A delay matrix of dimensions nxn where n is the number of nodes

A cost matrix of dimensions nxn where n is the number of nodes

Delay constraint Delta=9Output:


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An optimized tree spanning from source to all nodes

Output

Figure (d): Our algorithm with delta=9


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Calculations

Minimum cost tree Shortest delay tree Our tree

Node Cost Delay Cost Delay Cost Delay

A 5 9 11 7 5 9

B 2 7 8 5 2 7

C 3 2 3 2 3 2

D 12 16 14 8 14 8

E 11 8 11 8 11 8

F

G 5 7 13 5 5 7

H 5 4 5 4 5 4

I 9 11 12 5 12 5

Sum 52 64 77 44 57 50

Results

MCT:

Cost of tree: 35

Average cost per path: 6.5

Average delay per path: 8

SDT:

Cost of tree: 48


Average delay per path: 5.5

Our solution:Cost of tree: 42


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Average delay per path: 6.25

We are able to provide an algorithm which provides an intermediate value of delay and cost.

This is very important because for applications like videoconferencing and remote

collaboration there is a need to have delay within specific constraints. Otherwise theapplication is rendered useless. As future work we wish to focus on including other QoS

parameters such as jitter into the framework. This will make the algorithm more

comprehensive.


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APPENDIX I

MATLAB CODES

clear all

lambda=3/60;mu=1/19;

a=2;

b=4;

delta=6;

p=[0:.001:20];

i=1;

forp=0:.001:20

ifp


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end

j=1;

s=15;

F=10;

forp=0:.001:20

AvgR(j)=(rho(j).*(1-(((1-rho(j)).*(rho(j).^s)))./((1-(rho(j).^(s+1)))))).*(p)*10;

X(j)=(((1-rho(j)).*(rho(j).^s)))./((1-(rho(j).^(s+1))));

j=j+1;

end

p=[0:.001:20];

plot(p,AvgR);

grid on

xlabel('quoted price');ylabel('average revenue');

title('figure-b:AVERAGE REVENUE V/S QUOTED PRICE');

clear all

lambda=3/60;

mu=1/19;

a=2;

b=4;

delta=6;

p=[0:.001:20];

%for p=0:.1:20

i=1;

forp=0:.001:20

ifp


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else

rho1(i)=(lambda/mu).*((delta/(a+delta)).*((b./p).^delta));

i=i+1;

end

enda=6;

i=1;

forp=0:.001:20

ifp


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j=j+1;

end

p=[0:.001:20];

plot(p,AvgR,p,AvgR1,p,AvgR2);

xlabel('quotted price')

ylabel('average revenue')

title('figure(c): AVERAGE REVENUE V/S QUOTED PRICE FOR DIFFERENT VALUES

OF a');

grid on

legend('blue:a=2,green:a=4,red:a=6');

clear all

lambda=3/60;

mu=1/19;

a=2;

b=4;

delta=6;

p=[0:.001:20];

%for p=0:.1:20

i=1;

forp=0:.001:20

ifp


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b=12;

i=1;

forp=0:.001:20

ifp


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title('figure(d): AVERAGE REVENUE V/S QUOTED PRICE FOR DIFFERENT VALUES

OF b');

grid onlegend('blue:b=4,green:b=8,red:b=12');

clear all

lambda=3/60;

mu=1/19;

a=2;

b=4;

delta=6;p=[0:.001:20];

%for p=0:.1:20

i=1;

forp=0:.001:20

ifp


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i=i+1;

else

rho2(i)=(lambda/mu).*((delta/(a+delta)).*((b./p).^delta));

i=i+1;

end

end

j=1;

s=15;

F=10;

forp=0:.001:20


j=j+1;

end

j=1;

s=15;

F=10;

forp=0:.001:20

AvgR1(j)=(rho1(j).*(1-(((1-rho1(j)).*(rho1(j).^s)))./((1-(rho1(j).^(s+1)))))).*(p)*10;

j=j+1;

end

j=1;

s=15;

F=10;

forp=0:.001:20

AvgR2(j)=(rho2(j).*(1-(((1-rho2(j)).*(rho2(j).^s)))./((1-(rho2(j).^(s+1)))))).*(p)*10;

j=j+1;

end

p=[0:.001:20];




title('figure(e): AVERAGE REVENUE V/S QUOTED PRICE FOR DIFFERENT VALUESOF delta');


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grid on

legend('blue:delta=6,green:delta=8,red:delta=10');

clear all

lambda=3/60;mu=1/19;

a=2;

b=4;

delta=6;

N=1000;

p=20*rand(N,1);

j=1;k=1;

fori=1:1000

ifp(i)


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end

j=1;

s=15;

F=10;forp=0:.001:20


X(j)=(((1-rho(j)).*(rho(j).^s)))./((1-(rho(j).^(s+1))));

j=j+1;

end

p=[0:.001:20];

plot(p,AvgR,'r');

grid onxlabel('quoted price');

ylabel('average revenue');

title('figure-b:AVERAGE REVENUE V/S QUOTED PRICE for both');

legend('red:analytical,blue:monte carlo');


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APPENDIX II

C++ code#include

#include

int cost[9][9]={{0, 3, 9999, 9999, 12, 9999, 9999, 9999, 9999},

{3, 0, 5, 9999, 9999, 2, 9999, 9999, 7},

{9999, 5, 0, 9999, 9999, 3, 9999, 2, 9999},

{9999,9999, 9999, 0, 11, 9999, 7, 9, 9999},

{12, 9999, 9999, 11, 0, 9999, 9999, 6, 9999},

{9999, 2, 3, 9999, 9999, 0, 5, 9999, 12},

{9999,9999, 9999, 7, 9999, 5, 0, 8, 9999},

{9999,9999, 2, 9, 6, 9999, 8, 0, 9999},

{9999, 7, 9999, 9999, 9999, 12, 9999, 9999, 0}};

int delay[9][9]={{ 0, 2,9999,9999, 5,9999,9999,9999,9999},

{ 2, 0, 3,9999,9999, 7,9999,9999, 4},

{9999, 3, 0,9999,9999, 2,9999, 2,9999},

{9999,9999,9999, 0, 4,9999, 9, 4,9999},

{ 5,9999,9999, 4, 0,9999,9999, 4,9999},

{9999, 7, 2,9999,9999, 0, 7,9999, 5},

{9999,9999,9999, 9,9999, 7, 0, 1,9999},

{9999,9999, 2, 4, 4,9999, 1, 0,9999},

{9999, 4,9999,9999,9999, 5,9999,9999, 0}};

int t[10][2];//holds the minimum spanning treeint f[10][2];//holds the final tree

int k=0,d[10],p[10];

void prims(int n,int source)

{

int i,j,u,v,min;

int sum; //holds the cost of the minimum spanning tree

int k; //index for storing the edges w.r.t minimum spanning tree

int p[10]; //holds the vertices selected

int d[10]; //holds the weights for the selected edges

int s[10]; //has the information of nodes visited and nodes not visited

//int source; //contains the vertex from where least edge starts

min=9999;

//source=5;

/*for (i=0;i


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min=cost[i][j];

source=i;

}

}

}*/

//initialization

for (i=0;i


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if (s[v]==0 && cost[u][v]=9999)

printf("Spanning tree does not exist\n");

else

{

printf("Minimum cost tree\n");

for (i=0;i


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void dijkstra(int n, int source, int dest)

{

int i,j,u,v,min;

int s[10];

for (i=0;i


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}

}

}

void add_path(int source, int destination)

{int i;

i=destination;

while(i!=source)

{

printf("%d


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for (int i=0;i


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REFERENCES

1.

J. Musacchio and J. Walrand, WiFi access point pricing as a dynamic game inIEEE/ACM Trans. Networking,Vol. 14(2), pp. 289-301, Apr. 2006.

2. K. Chen, Z. Yang, C. Wagener, and K. Nahrstedt, Market model and pricingmechanisms in a multihop wireless hotspot network in Proceeding of ACM

MobiQuitous Conference, July 2005.

3. M.L. Mokbel, W.A. El-Haweet and M.L. El-Derini, A Delay-Constrained Shortest Path

Algorithm f or M ulti cast Routing in M ultimedia Appli cations

4. R. Bellman, Dynamic Programming. Princeton University Press, 1957.

5. G. Feng, and T.S.P. Yum, Efficient multicast routing with delay constraints

International Journal of Communication Systems, 1999

major project report 7th sem09eeg17

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