Shortest Route Mobility Assisted Packet Delivery With Soft Maximum Delay

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Accepted Manuscript

Shortest Route Mobility Assisted Packet Delivery with Soft Maximum Delay

Guarantees in Mobile Ad Hoc Networks

Spyridon Vassilaras, Gregory S. Yovanof

PII: S1570-8705(11)00212-5

DOI: 10.1016/j.adhoc.2011.11.005

Reference: ADHOC 694

To appear in: Ad Hoc Networks

Received Date: 2 March 2011

Revised Date: 14 October 2011Accepted Date: 14 November 2011

Please cite this article as: S. Vassilaras, G.S. Yovanof, Shortest Route Mobility Assisted Packet Delivery with Soft

Maximum Delay Guarantees in Mobile Ad Hoc Networks, Ad Hoc Networks (2011), doi: 10.1016/j.adhoc.

2011.11.005

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Shortest Route Mobility Assisted Packet Delivery with Soft Maximum Delay

Guarantees in Mobile Ad Hoc Networks

Spyridon Vassilaras and Gregory S. Yovanof

Athens Information TechnologyP.O. Box 68, 19.5 km, Markopoulo Ave.

19002, Peania Attikis, Greece{svas, gyov} @ ait.gr

Abstract In delay tolerant Mobile Ad hoc Networks (MANETs) node mobility can be exploited in order toreduce the source-destination path lengths in the expense of higher packet delivery delays. This paper addresses the

problem of minimizing the average source-destination path length under a maximum delay constraint for packet

delivery which is desirable to certain applications. Imposing packet delivery deadlines results in a certain

percentage of multi-hop packet transmissions and poses the practical problem of selecting the optimum moment for

the transmission. We propose an Optimal Stopping Rule algorithm for solving this problem and show how thisalgorithm can be extended in the case that a source-destination route is not always available by relaxing the hard

delay constraint to a soft (probabilistic) constraint. The performance of this algorithm is compared to the ideal case

of scheduling with perfect knowledge of the future and the trade-off between higher allowable delay and lower

average path length is illustrated through several Matlab and ns-2 simulation results. As an application of path

length minimization we explain how this can lead to energy consumption minimization in a MANET with light

traffic loads (low probability of collisions). Finally, we briefly discuss how this path length minimization algorithm

can guide the development of cross-layer throughput maximization algorithms with soft maximum delay

guarantees.

KeywordsMANET, DTN, QoS, scheduling, energy efficiency, ad hoc network capacity, dynamic programming,optimal stopping rule, cognitive networking.

1. INTRODUCTIONA well established principle in the theory of wireless Mobile Ad hoc Networks (MANETs) with randomly moving

nodes states that mobility increases the capacity of such networks at the expense of increased packet delivery

delays. This is achieved by letting Mobile Nodes (MNs) play the role ofdata carriers. A data carrier physically

transfers data between a source node A and a destination node B by receiving a number of data packets from A

when it is close to A and transmitting them to B at a later time when it moves close to B. Most theoretical work in

the field is focused on establishing asymptotic bounds for the network capacity as the number of nodes in the

network goes to infinity.

More specifically, in their seminal paper [1], P. Gupta and P. R. Kumar derived asymptotic bounds for the

capacity of fixed wireless ad hoc networks as the number of nodes in the network grows to infinity. Nodes in this

network are immobile and randomly placed in a given area. Each node is paired with a random destination node to

which it sends data packets either through single hop or through multi hop paths. Messages are buffered at nodes

while awaiting transmission and sufficiently distant radios transmit concurrently. The main result in [1] shows that

the maximum throughput per source-destination (S-D) pair is O(1 )n where n is the number of nodes in a unit

area, while a proposed scheduling scheme can achieve a throughput of (1 )nlogn . This means that the per S-D

pair throughput tends to zero as n grows to infinity. The reason for this is that as the number of nodes increases,

either the per hop transmission range should decrease (and therefore the number of hops between source and

destination increase) or stay constant in which case the number of nodes in the transmission range of any given

node increases. In both cases, the number of interfering single hop transmissions will increase resulting in an

overall capacity reduction. (Note that the above proposed scheduling scheme assumes that all transmissions are


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conducted at the same power lever and transmission rate; if nodes are allowed to exercise power or rate control

then a slightly better throughput of (1 )n is achievable as shown in [2], [3].)

In a subsequent paper [4], M. Grossglauser and D. Tse proved that mobility can drastically increase the

capacity of ad hoc wireless networks in which Mobile Nodes (MNs) play the role of data carriers. More

specifically, the authors in [4] showed that the average long term throughput per S-D pair can be kept constant as

the number of nodes in a unit area increases. The caveat is that, in order to maintain constant throughput, nodesbuffering capacity and packet delivery delay will increase unboundedly with the number of nodes. This significant

increase in capacity is achieved by limiting the number of hops in each S-D path by using randomly moving MNs

as physical data carriers. Fewer hops result in reduced interference with other transmitting MNs thus potentially

achieving capacity increase.

In addition to increasing the overall network capacity, using MNs as data carriers offers a considerable

reduction to the energy consumption for end-to-end data transmission. Assuming a generic radio propagation

model, for a fixed transmit power Pt , the average received power Pris given by:

a

tr

d

PGP (1)

where G is a constant depending on the transmitter and receiver antenna gains and the wavelength of thetransmitted signal, dis the distance between the transmitter and the receiver and 2 a 5 is a parameter dependingon the propagation environment. As a result of the power law in the distance, using a larger number of shorter

transmissions and lower transmit power (in a multi-hop path) saves energy with respect to fewer transmissions with

longer distances between subsequent nodes in the path. Reducing the number of hops in the path and at the same

time keeping the transmission distances short (which can be achieved through taking advantage of MNs mobility)can obviously have a significant energy saving effect.

Although unbounded delays and packet buffer sizes are considered impractical in real life networks,

increasing these parameters to a large but realistic value can increase a MANETs capacity and/or reduce energyconsumption. Researchers have coined the term Delay Tolerant Networks (DTNs) to characterize a subclass of

mobile wireless networks that can tolerate large and unpredictable delays (beyond the conventional forwarding

delays) depending on the supported applications. Several applications of DTNs (such as urban monitoring using a

vehicular sensor network[5], [6]) have been proposed in the literature. Intuitively, the ability of taking advantageof the nodes mobility in order to reduce the end-to-end path lengths in such networks depends on the degree of

topology change that can be achieved in the time scale of the maximum tolerable delay. If the speed of mobile

nodes or the maximum delay is so low that the positions of the nodes barely change until the packet delivery

deadline is reached, one can only hope to achieve the path length distribution of a fixed ad hoc network. It should

also be expected that in real life DTNs, where data carriers are used to move packets from source to destination, the

single or multi-hop communication delay (including queuing, transmission and propagation delay) is negligible

compared to the physical data transfer delay.

In many DTNs, delay tolerance is not just a useful property of certain applications that can be exploited to

achieve greater network throughput, but a network requirement imposed by the intermittent connectivity of

network nodes. In terms of their connectivity, we can classify Delay Tolerant MANETs into four connectivity

classes:

Class I: The MANET remains connected at all times so that there exists always a route between any S-Dpair.

Class II: There are times where a route between a given S-D pair does not exist but the probability that no

path exists at all times up to the packet delivery deadline is small.

Class III: End-to-end S-D paths are commonly not available. In this case, routing is a challenging task and

buffering of packets in intermediate relay nodes until a connection becomes available is an integral part of most if

not all end-to-end communication. This type of MANETs is also referred to as Intermittent Connectivity Networks

(ICNs) [7]-[8]. However, many researchers use the term Delay Tolerant Networks as synonymous to Intermittent

Connectivity Networks (see for example [9]-[15]).

Class IV: The connectivity is so sparse that even by using broadcasting and buffering at intermediate nodes,

the probability of reaching the destination prior to the deadline is small. Obviously, this is not a useful network, at

least with the given delay requirements.


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Note that the connectivity class of a MANET depends on the node number and density, transmission range,

mobility model and maximum tolerable delay. If all other variables are kept constant, varying the transmission

range alters the network connectivity graph at each moment in time, directly affecting the connectivity class of a

MANET as illustrated in Figure 1.

In prior work[16] we have considered Delay Tolerant MANETs of Class I, with randomly moving MNs in

which packets need to be delivered to their destination prior to a deadline determined by a given maximum

allowable delay. Motivated by the fact that mobility can increase the overall capacity of and economize in the

energy consumption in such networks, we developed a cross-layer transmission scheduling / routing policy that

aimed at minimizing the average end-to-end path lengths while guaranteeing a maximum delay on packet delivery

(and consequently a maximum queue size) under certain simplifying assumptions. The developed policy was

essentially an Optimal Stopping Rule (OSR) [17] that instructs the node to transmit a packet as soon as the current

hop count to the destination is less than or equal to the expected average hop count of the minimum path until the

packet delivery deadline. This expected value is computed by assuming a stationary Markovian behaviour of the

shortest path length between source and destination nodes. The minimum path length is assumed to be known to

the source nodes at all times; this can be achieved by using a proactive MANET routing protocol such as DSDV

[18].

In this paper we extend our algorithm to cover DTNs of Classes I & II. Obviously, if the probability that at

any given moment a S-D path is not available is greater than zero, the probability that such a path is not available atany moment till the packet delivery deadline is also greater than zero (although it can be many orders of magnitude

smaller) which means that the packet delivery prior to the deadline cannot be guaranteed with probability 1. One

possible way of dealing with this issue is to apply the timely delivery constraint in a soft, i.e., probabilistic sense. In

other words the optimization problem now is to find a transmission scheduling policy that minimizes the average

end-to-end path length subject to not exceeding the maximum allowable delay with a probability greater than Pv

(which we will call the deadline violation probability or deadline violation tolerance). Alternatively, an upper

bound to the mean delay might be a preferable QoS guarantee, depending on the application. In this paper, only the

soft maximum delay guarantee approach is considered.

Taking this approach, we formulate the constrained optimization problem that produces an optimum

scheduling policy under a soft maximum delay constraint. We then propose an efficient solving algorithm for this

problem by transforming it into an equivalent unconstrained optimization problem. The unconstrained optimization

problem can be easily solved by the optimal stopping rule algorithm presented in [16]. The extended algorithm hasbeen implemented in Matlab and ns-2 and evaluated under a random waypoint mobility model [19] for the MNs. In

this context, we are also investigating transmission range optimization for minimizing the total energy consumption

in the network.

It should be noted that capacity optimization is not a straightforward result of average path length

minimization. This is evident by the fact that a relatively high number of long connections might not be interfering

with each other (apart from the interference between neighboring links in the same connection) whereas just two

one-hop connections can be interfering. Thus, the full-fledged optimum scheduling problem cannot be decoupled in

a minimum path part and a subsequent optimal scheduling of minimum path transmissions. However, the full-

fledged problem is prohibitively hard and a two part heuristic approach is worth investigating.

The rest of the paper is organized as follows: In Section 2, we review related work and point out the

contributions and novelty of our work. In Section 3, a more detailed description of the problem is provided together

with a discussion of the assumptions used. The optimal stopping rule algorithm adapted to this particular problem isthen explained in Section 4. Simulation results are presented and analyzed in Section 5 while transmission range

optimization with regards to energy efficiency is explored in Section 6. Some practical issues in applying the

proposed approach in more realistic scenarios are addressed in Section 7. Finally, conclusions and directions for

future work are discussed in Section 8.

2. RELATED WORKApart from the two fundamental papers [1] and [4] discussed in the previous Section, the problem of

determining the capacity of a generic fixed or mobile ad hoc network and proposing protocols that achieve

maximum throughput has attracted a lot of attention from the research community. While, as pointed out in [20],


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most current capacity results rely on the allowance of unbounded delay and reliability, many researchers haveconsidered the delay aspect of such schemes. However, in the majority of papers where delay is also taken into

account, authors consider the asymptotic n regime and calculate the average delay under a proposed schedulingand relaying algorithm or investigate the trade-off between the experienced average delay and the achievable

capacity. Examples of average delay for n results under a variety of network settings, mobility models andrelaying algorithms can be found in [21]-[30].

Although average delay results are useful, for some applications the average experienced delay is not as

important as the maximum delay and therefore the applicable QoS requirement is a maximum delay guarantee. The

asymptotic capacity of ad hoc networks under a maximum delay constraint has been investigated in [31]. However,

the assumption in [31] is that the maximum allowable delay is large enough to ensure that, with a very high

probability, the relay node will become a 1-hop neighbor of the destination before the maximum delay. Under this

approach the network mobility rather than the application requirements defines a lower bound to the allowable

delay that can be guaranteed to an application. The ad hoc network capacity is then calculated as a function of the

allowable maximum delay. If an application requires a maximum delay that is below this lower bound, there is no

mechanism to achieve this delay other than achieving it only for a fraction of the packets sent. A similar approach

is taken in [32] where network coding is shown to improve the optimal delay-throughput trade-off in MANETs

under a particular mobility model. More specifically, if the required maximum allowable delay D is both3

( )n and (n) then a per S-D pair throughput ( )D / n=O can be achieved. The work in [33] is significantlydifferent from all the above since it is not providing asymptotic results for n and the network nodes are bothfixed and mobile. The similarity with [31] and [32] is that the proposed protocol can provide guarantees on the

maximum allowable delay provided that this is greater than a lower bound (which is a function of the network and

mobility parameters). In particular, the protocol presented in [33] guarantees a maximum delay of2d

v, where dis

the diameter of the network and v is the speed of mobile nodes. In addition, the scenario examined in [33] assumes

static sources and destinations and several mobile nodes which act as relays and are aware of the locations of all

static nodes. Also, the mobile nodes should be able to determine their own location and the approximate direction

in which they are moving, either using a Global Positioning System (GPS) device or by observing the sequence of

static nodes which they encounter during their movement.

In this paper, we are investigating a more realistic scenario where the maximum tolerable delay isdetermined by the application and might be relatively small with respect to the time needed by a source or relay

node to come into range with the destination node. In such cases, using a multi-hop source-destination path is

sometimes necessary to meet the maximum allowable delay constraint. We are also interested in networks with a

bounded number of nodes, instead of the asymptotic regime where n.The control of opportunistic forwarding mechanisms in Class III Delay Tolerant networks (according to the

classification in the previous Section) has also received a lot of attention recently. In this type of mobile networks,

single nodes are isolated (i.e., no other nodes are within their communication range) most of the time. Forwarding

protocols in this case are based on some variation ofepidemic routing where copies of a message are disseminated

through the network until one copy reaches its intended destination. Proposed algorithms can be categorized in

zero-knowledge algorithms, where no information on the past and future encounter patterns of nodes is used in

making forwarding decisions (see for example [11]-[14]), and knowledge-based algorithms which make use of

such information (see [15] and references within). The goal in the above algorithms is to minimize the number ofgenerated copies (or equivalently the number of one-hop transmissions) while keeping the average delay (or the

probability that the delay does not exceed a given threshold) below a certain limit. Alternatively, the optimization

objective can be to maximize the delivery probability prior to a given allowable delay subject to a constraint to the

number of generated copies. Note that although the above optimization objectives are similar to the ones assumed

in this paper, the forwarding problems in Class II and Class III networks are fundamentally different. For this

reason, it wouldnt be fair to compare the performances of our proposed algorithm and any algorithm designed fora Class III network when used in a Class II network.

The optimization algorithm proposed in this paper for the selection of the optimal transmission time is based

on the well known Optimal Stopping Rule in Dynamic Programming [17]. The use of an OSR in scheduling for

wireless transmissions is also employed in previous work on opportunistic spectrum access: The Multi-channel

Opportunistic Auto-Rate (MOAR) protocol [35] deals with the decision to skip frequency channels in search for

better quality channels. To balance the tradeoff between the time and resource cost of channel measurement /


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channel skipping and the throughput gain available via transmitting over a better channel, an OSR algorithm is

proposed in order to maximize the expected throughput. HC-MAC [36] is a MAC layer for Cognitive Radio where

the secondary users decision of whether to continue sensing for available (not used by primary users) channels orstart transmitting in the already discovered idle channels is formulated and solved as an OSR problem. Although

our work is not related to Cognitive Radio (with its traditional definition involving primary and secondary users of

radio spectrum), it can be viewed as a case of Cognitive Networking since nodes intelligently decide when to

transmit and which route to use aiming at improving the overall network performance. Moreover, the transmission

scheduling policy is dynamically adapted based on the maximum allowable delay demanded by the application and

the networks stochastic behavior (due to mobility) which the nodes learn by observing the evolution of shortest

paths in time. A different version of the optimal stopping problem (commonly known as the secretary problem) is

used in [15] in order to decide to which nodes to forward a message in a Class III delay tolerant network.

Finally, a number of energy efficient protocols for MANETs have been proposed in the literature. These

protocols rely on a variety of energy efficiency mechanisms such as transmit power control, minimum power

routing, node sleeping to conserve energy as well as remaining node energy aware routing and load-balancing

algorithms. Taking advantage of node mobility to minimize energy consumption in a MANET under maximum

delay constraints has been investigated in [37], [38]. However, the cross-layer (scheduling, routing and power

control) algorithms developed in [37], [38] are based on a significantly different problem formulation than ours:

power control is allowed (which ensures the existence of at least one end-to-end path at all times) and the futurenetwork topology (exact location of nodes at all times) is assumed known in advance (deterministic future

mobility).

3. PROBLEM DEFINITION AND SIMPLIFYING ASSUMPTIONSConsider a Mobile Ad Hoc Network which comprises of n nodes moving in a rectangular area according to a

stationary mobility model with identical and independent stochastic mobility behavior for all nodes (e.g., the

Random Waypoint mobility model [19]). There are n(n-1) statistically identical traffic flows in this network, one

for each ordered pair of nodes. Packets generated by these traffic flows at the source node need to be delivered to

their destination within a maximum delivery delay D. All nodes transmit at a fixed power which translates into a

fixed transmission range R. The transmission range R of all nodes is smaller than the smallest dimension of therectangular area. The selection of an optimum transmission range for energy consumption minimization is

investigated in Section 6. Multi-hop transmissions of packets from source to destination through relay nodes are

allowed. Node movement can occasionally create disconnected nodes and therefore a S-D route between any two

nodes in the network is not available at all times. However such end-to-end connections are assumed available for

at least a sufficient amount of time to send the packet end-to-end with high probability (Class II MANET according

to the classification of Section 1). The objective is to minimize the average hop count of source to destination

transmissions while guaranteeing that all packets are delivered to their destination prior to their delivery deadline

with probability higher than 1-Pv. To this end, each node can take advantage of the allowable delivery delay and

deadline violation probability to wait for a shorter path to the destination prior to transmitting the packet.

Note that most related work assumes n traffic flows (that is each node in the network sends packets to a

single destination node). This creates an additional limitation to a one-hop transmission policy at close distances:

the fraction of time the source and destination nodes of each flow are nearest neighbors is too small thus limiting

the achievable capacity in a different way than interference or the need of multi-hop transmissions. To overcome

this limitation a two-hop (single relay) policy was first suggested in [4] and adopted in many subsequent papers. By

assuming n(n-1) traffic flows, we achieve the same availability of traffic destined for each nodes nearest neighboras in the case ofn traffic flows with relays and thus we dont need to spread the traffic to random relays.

In this paper we study the problem of minimizing the average hop count under a probabilistic maximum

delay constraint with the following additional assumptions:

A1. The current number of hops of the shortest source-destination path is assumed to be known at the sourceat all times. If an end-to-end path is not available the number of hops is assumed equal to infinity. To

obtain such information in practice, a distributed proactive MANET routing protocol, such as DSDV,

can be used.


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A2. The total delay experienced by a packet consists of the transmission scheduling delay at the source andthe end-to-end communication delay (which is the standard sum of queuing, transmission, propagation

and processing delays over all hops including retransmissions of unsuccessfully received packets). In

other words intermediate nodes forward packets to the next hop as soon as possible without trying to

schedule them for transmission at a later more appropriate time.

A3. The communication delay (including all necessary retransmissions until the packet is received correctlyby its intended destination) is negligible with respect to the maximum allowable delay. Consequently,

the packet delivery time is assumed equal to the packet source scheduling delay. In the same token, the

network topology remains virtually unchanged during the end-to-end transmission (and possible

retransmissions) and therefore the path identified at the source is successfully followed to the

destination.

A4. Each node has enough buffer space to avoid buffer overflows of generated or relayed packets. Since thepacket scheduling time is upper bounded, the required buffer space at each node is also bounded

provided that the packet arrival processes are appropriately dimensioned (or the generated traffic is

appropriately shaped).

A5. Each node has been in the network long enough to acquire an accurate statistical knowledge of theconnectivity dynamics. In particular, it is able to calculate a stationary conditional probability

distribution of the optimum path length to each destination in future times given the optimum path

length to the same destination at past and present times.

Although the proposed algorithm is developed and tested under the above assumptions through Matlab

simulation experiments, we have also investigated the effect of relaxing some of these assumptions using more

realistic simulation setups in ns-2. Simulation results are presented in Section 5. Certain practical considerations

regarding assumption A5 are discussed in Section 7.

4. THE SOURCE TRANSMISSION SCHEDULING ALGORITHMIn [16] we solved the scheduling problem described in Section 3 with the additional assumption of a completely

connected network at all times. In this case (where it is feasible to demand that P v = 0), the optimal scheduling

policy can be derived by applying an Optimal Stopping Rule algorithm which is a well studied algorithm in the

theory of Dynamic Programming (DP) [17]. Time is discretized into time slots and it is assumed that the path

length for a given S-D pair at a given time slot depends on the path length in the previous time slots in a Markovian

way described by a transition probabilities matrix P. In other words, the transition probabilities p ij from an i -hops

path to a j -hops path in the next time slot are constant over time and equal for all S-D pairs (where i,j= 1,2,,n-

1,).

These transition probabilities are estimated by observing the nodes moving around for a large enough periodof time prior to the network communication operation so that estimation errors are negligible. The time slot

duration should be adjusted according to the velocity range of the mobile nodes: for too small a slot duration all

diagonal elements of the transition probabilities matrix will be close to 1 and all non diagonal close to zero for

too large a slot duration the next state (number of hops) will be independent of the current state. Note that the

Markovian assumption is an approximation of the true stochastic nature of the path length evolution as the next

state is not entirely independent of previous states given the current state. However, a more accurate stochastic

model would significantly complicate the solution of the optimization problem for a small gain in performance. In

the next Section we illustrate the error caused by the Markovian approximation for a specific example case.

In Class I MANETs where the probability of a disconnected S-D state ( path length) is equal to zero, theoptimum transmission scheduling policy which guarantees that all packets are delivered to their destination prior to

their delivery deadline is calculated by executing the following DP algorithm [16]:

Define:


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the cost to transmit immediately when at state i (minimum path length = i), ( )c i i the optimum cost-to-go vector

kJ whose i-th element ( )kJ i represents the expected path length at

time kgiven that the current path length is i and that the optimum decisions are going to be taken at

each step up to the sending of the packet. The optimum cost vector is initialized with:

( ) ( ) 1 2 3 1D

J i c i i, i , , ,...,n

the cost-to-go vector kw if the decision is not to send at time k. a decision vector

ku whose i-th element is 1 if the decision at time kand with current cost i is to send

and 0 otherwise. Obviously, (1,1,1,...,1)D

u

Then, work backwards in time k= D-1, D-2, , 1 to determinek

w ,kJ and ku according to the iterative

formulas:1

1

1

( ) ( )n

k ij k

j

w i p J j

1 2 1i , j , ,...,n

( ) ( ( ) ( )) 1 1k k J i min w i ,c i , k ,...,D

And finally for the decision vectors:

0 if ( ) ( )( ) 1 1

1 if ( ) ( )

k k

k

k

, J i w i ,u i k ,...,D

, J i c i ,

Now, if we apply the same algorithm to the Class II MANETs where the disconnected state occurs with

positive probability and assume infinite cost for the disconnected state ( ( )c ) then all ( )kw i will become

infinite (and all ( )k

u i equal to 1) at least for any 1k D n . Furthermore, even if we adopt a policy of sending

immediately as soon as we get to a connected state of any path length, the probability of being in the disconnected

state for the whole time up to the deadline is non zero. For these reasons, as already mentioned, we modify theproblem from:

Problem A: min ( )k

k J i , i,k u

with ( )c

to

Problem B: min ( )k

k,

J i , i,k

u

with ( ) 1c n (where is a positive number)

s.t. Pr{transmit while in infinite state} < Pv

Note that in Problem B we set the cost of transmitting while at state equal to a finite number (so that wecan afford this happening with a non-zero probability) but higher than the cost of transmitting at any other state (so

that we never transmit at this state, unless k=D). Therefore the probability of transmitting while in the infinite state(which we will denote by P) is equivalent to the probability of reaching the deadline and being in the infinite state.

The DP algorithm of[16] cannot be adapted to solve the constrained Problem B. Consequently, we resort to

the following trick: in order to solve Problem B we solve:

Problem C: min ( )k

k J i , i,k

u

with ( ) Mc

calculate P and ( ) = min ( )*

k k J i J i for the resulting policy and iteratively determine the optimum

M>n-1 for which P < Pv (optimum in the sense that it minimizes all ( )*

kJ i ).

The validity of this approach is proved in the following two lemmas. For convenience we will call Problem

C(M) the subproblem [ denotes equal by definition]:


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Problem C(M): ( ( (M)) ) min ( )k

*

k k J i C J i , i,k

u

with ( ) Mc

Lemma 1: If Problem C is feasible, i.e., there exists at least one M for which the optimizing policy for C(M)

satisfies P < Pv , then an optimizing M exists, i.e.,*

M s.t. the optimizing policy for C(M*) satisfies P < Pv

and ( (M )) ( (M')) and M'* * *k k

J i C J i C i,k , for which the optimizing policy for C(M) satisfies P < Pv .

Proof: For a given value of M, ( (M))*k J i C and the associated policy can be calculated by the OSR

algorithm i,k . If there exists only one M for which the optimizing policy for C(M) satisfies P < Pv , then this is

automatically M*. Otherwise, we need to show that it is never the case that ( )*

kJ i for some values of i and kare

smaller for one value of M whereas ( )*k

J i for some other values of i and kare smaller for another value of M.

Consider two values of M, M1 < M2 and let 1*

and 2*

be the optimal policies for Problem C(M1) and Problem

C(M2) respectively. Assume further that both policies satisfy P < Pv (this holds when applying the policies in both

C(M1) and C(M2) since P does not depend on the costs, only on the policy). Then, since 1*

is the optimal policy

for Problem C(M1), for any i, k:* *

1 1 1 2 1( C(M )) ( ,C(M )) ( ,C(M ))*k k k J i J i J i .

Furthermore, * *2 1 2 2 2( ,C(M )) ( ,C(M )) ( C(M ))*

k k k J i J i J i because when policy

2

* is applied, the

probabilities of all sample paths are independent of the costs and in problem C(M2) the costs of all states are either

equal or strictly higher than the respective costs in C(M1). Thus the average cost is greater or equal in C(M2) than in

C(M1) when applying the same policy. By combining both inequalities above we get

1 2( C(M )) ( C(M ))

* *

k k J i J i which proves that for all i, kthe smaller the value of M the lower the optimum cost-

to-go function ( )*

kJ i and consequently Lemma 1 is proven.

Note that the above proof reveals that the optimizing M for Problem C is the minimum M> n-1 for which the

optimizing policy achieves P < Pv .

Lemma 2: The optimum policy (denoted by *

) derived by solving Problem C is also an optimum policy forProblem B.

Proof: Obviously, *

is a valid policy for Problem B, i.e., a policy that satisfies its constraint. Assume that

there is another valid policy for Problem B, with ( ) ( )*k k J i ' J i for some i, k. But then we have found

a policy for Problem C(M) with M = n-1+ that is better than *

for these particular i, k. As policy satisfies

the constraint P < Pv , it is also a better policy for Problem C than *. But this violates our hypothesis and thus

there is no better policy than *

for Problem B.

Note that in some cases Problem B is not feasible, i.e., for any value of and under all policies the

probability of violating the deadline is greater than Pv. If this is the case, we need to increase the required D or Pv

and, if these parameters are set by the application, we need a denser or higher mobility network in order to satisfy

the constraints. In the other extreme, if Pv is small enough orD large enough then the constraint cannot be violated

by any policy that simply defers from sending a packet while in the infinite state. In this case, maintaining a high

cost for ending up in the infinite state when reaching the deadline is meaningless and therefore the optimum policy

will be achieved by an infinitesimal and typically with P


10/40

1

[ 0] if u ( ) 0for =1,2,..., ()

[0 0 ... 0 1] if u ( ) 1

for = +1 () [0 0 ... 0 1]

( i )

k( i )

k

k

( n )

k

ii n

i

i n

PP

P

The probability vector that at step k the system will be at state i assuming a steady state probability

distribution [ | 0] at step 1 is given by: P1()P2() ... Pk-1(). Thus P can be obtained as the n-th element(corresponding to the infinite state) of the vector P1()P2() ... PD-1().

5. PERFORMANCE EVALUATIONIn this Section, we evaluate the performance of our proposed scheme through simulation experiments in Matlab

and ns-2. Note that in order to avoid well known transient state issues with the Random Waypoint mobility model,

the steady state position and velocity distributions [19] were used in initializing all Matlab and ns-2 simulation

experiments. Simulations run with Matlab were used in order to isolate the effects of the lower layers (packet

collisions, DSDV overhead, route breaks after a packet has been scheduled) and study the performance of the

proposed OSR policy under the assumptions of Section 3. In particular, in these simulations we are only interestedin calculating the delay until a packet is scheduled for transmission and the number of hops that it needs to reach its

destination at the exact time when it is scheduled for transmission. In all these experiments 50 mobile nodes are

moving around in a square 1200m 1200m area according to the Random Waypoint mobility model with [vmin,

vmax] = [1, 3] m/s and with an R=250m transmission range (this transmission range guarantees a relatively high

degree of connectivity at this node density). A Markovian model for the source-destination path lengths is adopted

and the transition probabilities estimated by running the simulation for an adequate amount of time before

generating any packets. The duration of the time slot is set to 10 sec in all experiments. Calculation of the optimum

path lengths for all S-D pairs is performed using the centralized Floyd-Warshall algorithm (both in the transition

probabilities estimation period and in the performance evaluation period). The OSR policy for Pv = 10-3

is then

calculated as described in the previous Section. Recall that this policy is the same for all source nodes (the decision

on whether to send a packet depends only on the current path length and remaining time until the deadline).

After obtaining the OSR policy and the theoretical average path length under this policy (calculated as J1)we ran simulations to estimate the actual average path length, average delay, and P . To simplify the bookkeeping

of the performance evaluation part of the simulation, a single packet is generated for each traffic flow at time 0.

The OSR policy is then applied to determine the transmission times and associated path lengths of all generated

packets under a random realization of nodes movement up to timeD. At the same time the probability that a packet

reaches the deadline and having no route to its destination, P, is calculated. The same process is repeated many

times and the average path lengths, delays and violating probabilities are calculated over all flows and realizations

(since all nodes and flows in the system are statistically identical). The process is continued until the widths of the

95% confidence intervals of all estimated metrics become less than 10% of their respective metrics. Note that when

the above stopping criterion is achieved for P , the widths of the 95% confidence intervals for the other two

metrics have already dropped to 0.1% - 2% of their respective metrics as will be evident in the following graphs.

For comparison, we also calculate average path lengths and delays under the following extreme transmission

scheduling policies: Immediate transmission of packets when generated at the source. Idealized policy with perfect knowledge of the future, under which packets are transmitted when the

shortest S-D path first attains its minimum value in the whole interval until the transmission deadline.

Figure 2 illustrates the trade-off achieved between the average number of hops in the shortest S-D path and

the maximum allowable transmission scheduling delay. The maximum allowable delay D is varied in the range 20-

500 time slots, that is 200-5000 seconds. The average S-D shortest path length with immediate transmission is

close to 3 hops as shown in Figure 2. As expected, the OSR policy achieves an increasingly smaller average

shortest path length as the maximum allowable delay is progressively relaxed. For a large enoughD an S-D path of

length 1 (direct transmission) will occur prior to the delivery deadline with probability 1. Note the slight

discrepancy between the theoretical average path length and its simulation estimated value, which is due to the

Markovian approximation used to calculate the OSR policy and compute the theoretical value and (to a smaller


11/40

extent) to the small estimation errors in the transition probabilities. Figure 3 shows how increasing the maximum

allowable delay affects the average scheduling delay. As expected the two quantities are positively correlated but

their relationship is not linear: For small values ofD an increase inD is used by the scheduling algorithm to reduce

the average path length and thus the average scheduling delay is increasing. But as D is getting larger (and the

average path length close to 1) increasing the scheduling delay is no longer necessary to achieve minimum path

length and thus the average delay stays more or less constant. It is also interesting to note that for relatively small

values ofD, the average scheduling delay under the OSR policy is smaller than the average delay under the ideal

policy whereas the opposite is true for large values ofD.

Figure 4 presents the probability that a packet reaches its transmission deadline and has no route to its

destination (P) as a function of the maximum allowable delayD. The blue solid line depicts the target deadline

violation probability Pv = 10-3

. This Figure should be examined in conjunction with Figure 5 which reveals the

optimum infinite state cost M*

determined by solving Problem C. As explained in the previous Section, for large

values ofD a large penalty M is not needed in order to avoid ending up in the infinite state when reaching the

deadline. Therefore, M*

is set to its minimum possible value (in this case 49) and the attainable P is much lower

than Pv. On the other hand, for small values ofD a relatively large penalty M needs to be applied in order to avoid

ending up in the infinite state when reaching the deadline. In this regime, P is close to Pv and the OSR algorithm

takes full advantage of the deadline violation tolerance in order to optimize the average number of hops.

As mentioned above, our Matlab simulations aimed at testing the basic idea of the OSR policy under theidealistic assumptions of Section 3 and the additional simplification of centrally calculated S-D path lengths. In

order to evaluate the effects of certain more realistic conditions and overheads to the performance of the OSR

scheduling, ns-2 simulations were carried out. In all ns-2 simulations the BonnMotion [39] utility was used to

generate ns-2 mobility files. However, the BonnMotion code was modified so that the Random Waypoint steady

state probability distributions [19] were used to initialize the positions and velocities of nodes. All wireless nodes

utilized the 802.11 MAC protocol and the DSDV routing protocol. In Figure 6, we compare the results obtained by

Matlab and ns-2 simulations for the exact same simulation setup and the same parameters as above (Figures 2-5).

The goal of this first experiment was to replicate the results obtained using Matlab by ns-2 simulations, i.e., to

come as close as possible to the ideal model built in Matlab, by using ns-2. For this reason, the path lengths are

obtained by the ns-2 GOD object which has a centralized view of the whole network. For the same reason, the path

lengths are calculated at the moment a packet is scheduled for transmission so that subsequent changes to the actual

path length (due to node mobility) are not taken into account. Despite all these, a slight deviation of the obtainedresults can be observed. We believe that this discrepancy is due to the way BonnMotion generates node mobility

files and more specifically to the fact that one needs to define slightly smaller x and y dimensions of the simulation

area if nodes are to remain strictly within boundaries.

Figure 7 provides a comparison of average path lengths as estimated through ns-2 simulations under

increasingly realistic assumptions and the same simulation parameters used as above. The red dashed line depicts

the same results that were shown in Figure 6. The blue dotted line graphs the average path lengths as estimated by

the distributed DSDV protocol at the sender. This introduces a certain error as the view of the path lengths obtained

by the DSDV protocol is not always reflecting all recent changes of the network topology. The black solid line

shows the actual path length as measured at the packet destination. This is also different since the path length can

change during end-to-end transmission. In fact a small percentage (around 7%) of transmitted packets never

reached the destination due to path breaks and this introduced another discrepancy to the 3 average path length

estimates. The fact that the discrepancies between these 3 quantities diminish as the average path length decreasesis also to be expected: for shorter paths the DSDV protocol estimates are more accurate and the probability that a

path breaks during end-to-end transmission is smaller.

6. TRANSMISSION RANGE OPTIMIZATIONSo far, the transmission range of all nodes in the network was assumed to be predetermined. In fact the transmit

power and consequently the transmission range of many commercial transceivers is either fixed or can be only

manually adjusted. It is evident that as the transmission range increases, the average path length decreases at the

expense of increased transmit power and interference to other receivers in the network. This suggests that there

exists an optimum value of the transmission range that maximizes the network capacity and a probably different


12/40

value that minimizes energy consumption. As discussed in the Introduction, our minimum average path achieving

policy is not intended to maximize network capacity although it could be used as a basis to develop sub-optimal yet

simpler capacity maximization scheduling algorithms. Developing such algorithms is outside of the scope of this

paper. On the other hand, average path minimization can achieve energy consumption minimization if combined

with transmission range optimization.

More specifically, let us assume that all nodes transmit at the same power level Pt and the power attenuation

model described by Equation (1). As in all results reported in this paper, a simplistic on / off capture model is

employed, i.e., we assume that a packet is correctly received if and only if the received power is greater than or

equal to a threshold Pth . This results in a common transmission rangeR for all nodes given by:1a

t

th

PR G

P

Therefore, in order to achieve a transmission rangeR the transmit power should be:

atht

PP R

G

Thus, if the average path length for end-to-end packet transmission is denoted by L, the total energy

consumption for data transmission in this network will be proportional to LRaand hence this is the quantity we

want to minimize by appropriate selection of the transmission rangeR.

In Figure 8 we plot f(R) = LRa

for the network parameters used in the previous Section, a maximum

allowable delay ofD = 100 time slots (= 1000 sec), a = 2 and number of nodes n = 50 (left graph) or n = 100 (right

graph). In order to plot these graphs, for each value ofR we first ran a long simulation of the nodes movement in

order to estimate the transition probability matrix P and then calculated the optimum policy and the theoretical

value of the average path length L under this policy. As expected, the trade-off between lower transmission range

and lower path length results in a convex function f(R) and therefore a unique optimizing transmission range.

However, the estimation errors in P result in estimation errors of the values off(R) which distort the functionsconvexity and make this a stochastic optimization problem. This is more noticeable for denser sampling of the

function, as in the right graph in Figure 8. Note that this graph was based on results obtained by running Matlab

simulations that lasted about 2 days for determining P for each point in the graph. Thus, it is quite obvious that

determining the optimum transmission range with high accuracy is a tedious task. However, a very high accuracy is

not needed in practice since a relatively small error in the value of the optimumR results only in a small penalty in

average energy consumption.

Naturally, as the number of nodes in a given area increases, the optimum transmission range decreases and

due to the power law (with a 2), the average energy consumption decreases as well albeit the increase in averagepath length. It is also interesting to note that not only the number of nodes but also other network parameters (such

as the maximum allowable delay, the deadline violation tolerance Pv , and the nodes mobility model and velocity

distribution) affect the optimum transmission range that achieves energy consumption minimization under soft

maximum delay requirements.

7. PRACTICAL CONSIDERATIONSIn the previous sections we have employed a centralized approach in estimating the transitions probabilities and

determining the optimum policy. This centralized approach can take advantage of the assumed identical stochastic

behavior of all nodes in the simulation by combining the state transitions at all nodes in order to arrive to a good

approximation ofP as quickly as possible. In practice there are several scenarios for estimating P. In an ideal case,

the mobility behavior of all nodes is known a priori so that P can be estimated by centralized simulation. In the

more realistic case that mobility patterns are not known in advance the appropriate estimation method depends on

the network topology:


13/40

In a hierarchical network topology communication takes place over multihop connections, whereas control

messages are exchanged with a central controller over single hop long range links. This hierarchical network

topology has been proposed in the literature (see e.g., [40]) and is justified by the observation that short range links

(e.g., WiFi links) support higher data rates at a smaller energy and monetary cost than long range links (e.g.,

cellular connections). In such a network topology, individual nodes can periodically send a list of their neighboring

nodes to a central controller over long range links and let the central controller calculate path lengths and count

state transitions in order to speed up the estimation process.

In a pure ad hoc network topology, each node has to estimate P based on its own state transition

measurements. State transitions are observed on the shortest paths to all other n-1 nodes (as provided by the

employed proactive routing protocol). Each node will estimate its own transition probabilities and might arrive to a

different optimum policy. The price to pay is slower convergence to the true transition probabilities. In addition, a

distributed estimation of the optimum transmission range would be quite tedious. It would require several iterations

with differentRs in order to converge to a sufficiently good R and at each iteration all nodes should estimate P(R)for the same value ofR. It is a subject of future work to investigate how this distributed optimization can be

performed within a reasonable amount of time for practical applications.

In order to illustrate the convergence properties of the average number of nodes under policies estimated by

individual nodes, the following experiments were performed: First a very good approximation of the theoretical

average path length forD = 20, 100 and 200 time slots was calculated by a centralized policy calculation based on aP estimated out of 106

transitions (time slots) which is denoted by PL. Let us denote these theoretical average path

lengths as20

Lc ,100

Lc and

200

Lc for D = 20, 100 and 200 time slots respectively. Then for 3 different simulation runs

(withD = 20, 100 and 200 time slots respectively) each node kept estimating its own P based on a growing number

u of state transition observations (ranging from 5000 to 50000 with step 100). For each observed P, an optimum

policy was determined and the theoretical average path length (under this policy and the above close approximation

PL of the true P) was computed. Let us denote this theoretical average path length by ( )D

uc i where i is the

estimating node index. Finally the absolute relative error between DLc and ( )

D

uc i is calculated as:

( )( ) =

D D

D u L

u D

L

c i - ce i

c

where |

| denotes absolute value.In Figures 9-11 the decadic logarithm of the maximum, average and minimum (over i) relative errors (forD

= 20, 100 and 200) are plotted as a function of the elapsed estimation time u (measured in number of time slots or

state transition moments). A number of observations can be made from these graphs: First, the convergence of the

relative errors is relatively fast for small values ofu but slows down for larger us. It can be verified that in most

cases the relative errors decrease as O(1 )u . This rule seems to be violated for the20

imax{ ( )}

ue i line. This is due

to the fact that for such small values ofD, small estimation errors in the transition probabilities make the

optimization problem under the soft deadline violation constraint unfeasible, in which case an immediate

transmission policy is assumed resulting to a large error. Second, it is clear that for the same u the relative error

increases with decreasing D. Hence, for small values ofD a longer estimation period is necessary in order to

achieve small relative errors. Third, a quite large deviation is observed between the minimum and maximum

relative errors. While for most practical purposes, a maximum relative error requirement is more appropriate, onehas to keep in mind that many nodes will have achieved orders of magnitude better accuracies when the worst-off

node attains this requirement.

8. CONCLUSIONSA celebrated principle in MANETs dictates that node mobility can be taken advantage of in order to reduce the

source-destination path lengths in the expense of higher packet delivery delays. This can result to higher network

capacity and lower energy consumed for communication. This paper investigated ways of exploiting this principle

in order to minimize the average source-destination path length for the case when a maximum delay constraint for

packet delivery is required. Imposing packet delivery deadlines results in a certain percentage of multi-hop packet


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transmissions and poses the practical problem of selecting the optimum moment for the transmission. This can be

addressed by an OSR policy first proposed in [16] and extended in this paper for the more complex (and more

realistic in MANETs) case where a source-destination route is not always available. This policy for scheduling

packet transmissions is based on a stochastic model for the evolution of the path lengths which is estimated by

observing the network topology for a long period of time. The trade-off between higher allowable delay and lower

average path length was illustrated through several Matlab and ns-2 simulation experiments.

Achieving minimum average path lengths (for a given maximum allowable delay) is not necessarily leading

to optimum network capacity but can guide the development of promising heuristics that are much simpler than

trying to solve the full-fledged network scheduling, MAC and routing problem for maximizing throughput under

maximum delay constraints. For example, such heuristics could be derived by devising an appropriate packet

transmitting benefit function and schedule packets that can be transmitted simultaneously so that to maximize the

aggregate benefit. This benefit function should be inversely related to current path length and time to deadline.

Developing and evaluating such cross-layer algorithms is outside of the scope of this paper and is left for future

work.

On the other hand, energy consumption minimization is a direct effect of average path length minimization

under light traffic loads (low probability of collisions). To this end, an optimum fixed transmission range for all

nodes can be selected that achieves minimum communication energy consumption. This optimum range depends

not only on the network density but also on node mobility, maximum allowable delay and deadline violationtolerance. It seems that the optimum range is sensitive to mobility model parameters estimation errors but this is

not a serious issue as the associated average energy consumption is not sensitive to optimum range estimation

errors. What is important is to ensure that all nodes use the same transmission range instead of relying on individual

estimations based on their own perception of the network mobility. This requests node coordination through

information exchange which needs to be properly designed so that not to create excessive communication

overhead.

Although the applicability of this papers results is not limited to MANETs in which nodes move accordingto the Random Waypoint mobility model, a stationary and uniform (same for all nodes) mobility pattern is

required. Developing path length minimization algorithms with maximum delay guarantees for MANETs with non-

stationary and / or non-uniform mobility remains an open and challenging issue.

ACKNOWLEDGEMENTS

We would like to thank the anonymous reviewers for their valuable comments which helped improve the content

and presentation of this paper. This work has been partly funded by the CROWN project which acknowledges the

financial support of the Future and Emerging Technologies (FET) Open Scheme within the Seventh Framework

Programme for Research of the European Commission, under FET-Open grant number 233843.


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http://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://cobweb.ecn.purdue.edu/~mazum/adhoc_mobility.pdfhttp://net.cs.uni-bonn.de/wg/cs/applications/bonnmotion/http://net.cs.uni-bonn.de/wg/cs/applications/bonnmotion/http://net.cs.uni-bonn.de/wg/cs/applications/bonnmotion/http://net.cs.uni-bonn.de/wg/cs/applications/bonnmotion/http://cobweb.ecn.purdue.edu/~mazum/adhoc_mobility.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput2.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdfhttp://www.stanford.edu/~balaji/papers/06optimalthroughput1.pdf


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Figure 1. Node connectivity graphs for a random instance of a MANET with 30 nodes moving in a 1200m1200m area

and 3 different transmission ranges: R=250m (left), R=150m (center) and R=75m (right). For relatively low node

mobility (e.g., nodes move by an average of 300m in a time interval equal to the maximum tolerable delay) the 3

connectivity ranges result to a connectivity Class II, Class III and Class IV MANET respectively.


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Figure 2: Average number of hops in S-D paths (and associated confidence intervals) versus maximum

allowable delay. Note that some confidence intervals (especially in the case of immediate transmission) are so

small that look like thick line segments.

Figure 3: Average transmission scheduling delay (and associated confidence intervals) versus maximum

allowable delay


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Figure 4: Average probability (and associated confidence intervals) of not transmitting a packet (P) versus

maximum allowable delay

Figure 5:The optimum value of M as a function of the maximum allowable delay


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Figure 6: Comparison of the average number of hops in S-D paths as estimated by Matlab and ns-2

simulations. Confidence intervals are also shown.

Figure 7: Comparison of the average number of hops in S-D paths as estimated by ns-2 simulations under

increasingly realistic assumptions. Confidence intervals are also plotted.


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Figure 8: Average energy consumption metric LR2

estimates as a function of the transmission range R for

n=50 (left) and n=100 (right)

Figure 9: Evolution of the maximum (over all nodes) absolute relative error in the average path length as the

sample size grows


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Figure 10: Evolution of the mean (over all nodes) absolute relative error in the average path length as the

sample size grows

Figure 11: Evolution of the minimum (over all nodes) absolute relative error in the average path length as

the sample size grows


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Spyridon Vassilaras is an Assistant Professor at the Athens Information TechnologyCenter for Research and Education. He received the Engineering Diploma in Electricaland Computer Engineering from the National Technical University of Athens in 1995 and

both M.S. and Ph.D. degrees in Computer Engineering from Boston University in 1997

and 2001 respectively. His current research interests include Quality of Serviceprovisioning through cross-layer optimisation in fixed and wireless networks, various

aspects of wireless ad hoc and sensor networks such as routing, transmission scheduling,cognitive radio and networking, network and data security (including node cooperationissues), automotive telematics and wired/wireless integration.


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Gregory S. Yovanofis a Professor, Associate Dean and Program Director of the MBIT

program at the Athens Information Technology. He received a Ph.D in Communications

from the University of Southern California in 1988. Before joining AIT in 2002, he

worked as a staff scientist at the Eastman Kodak Research Labs and Hewlett-Packard

Laboratories, engaged in multimedia signal processing for computer peripheral devices.

He has also led the development of several award-winning ICs for the DVD market as a

co-founder and an executive manager at two start-up companies in Silicon Valley. Dr.

Yovanofholds four patents on imaging systems.


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Documents

Shortest Route Mobility Assisted Packet Delivery With Soft Maximum Delay