Mobile Ad hoc Networks COE 549

Delay and Capacity Tradeoffs II

Tarek SheltamiKFUPMCCSECOE

www.ccse.kfupm.edu.sa/~tarek

04/19/23 1

Outline

Multi-user in Mobile Network Static vs. Mobile Ad Hoc Networks Direct Contact vs. Simple Replication Why multi-hop relaying in static networks? Tradeoff between delay and capacity

Typical Scenario

n nodes communicate in random S-D pairs All nodes are mobile, no fixed base station Applications are delay tolerant

Email Database Synchronization Control message to Explorer on Mars

Topology may change during packet delivery

Multi-user in Mobile Network Direct contact:

The source holds the packet until it comes in contact with the destination

Minimal resource, but long delay

This idea is very simple, but does not perform very well. In fact, any scheme that does not use relaying can not do better than:

Where is the minimum simultaneously successful transmissions

Scheduling Policy We slot time, and index slots by t. In each slot, each node transmits with probability Each transmitter transmits to its closest neighbor There will be a lot of collisions: The expected number of successful receptions Nt is on

the order of n:

With n nodes, it is possible to have around successful

transmissions, with S/N requirements

Multi-user in Mobile Network Simple replication:

S sends a replicate to as many different nodes as possible. These relays hand the packet off to D when it gets close

Each packet goes through at most one relay node Higher throughput, relatively shorter delay

Methodology Using the previous scheduling policy as a building block.

Nodes only transmit to their nearest neighbors.

In odd slots, each node transmits to its nearest neighbor a packet for its destination.

The neighbor will act as a relay. In even slots, each node will relay to its nearest neighbor

a packet destined for that node (if it has such a packet).

Each of the n − 2 intermediate queues has arrival and departure rate equal to

packets/slot The link directly from the source to the

destination has rate packets/slot. The aggregate throughput per node is packets/slot

Multi-user in Mobile Network..

The Book Analogy Imagine a large number of people moving around in a

city Each one carries a stack of books for a friend of his. The

stack is very high Whenever I bump on any other person on the street:

I either give him a book for him to give to my buddy, or I give him a book that his buddy gave to me some

time in the past Chances that I bump on my own buddy are negligible Question: What is the average number of people that

their destinations are also nearest neighbors? This is related to the famous hat problem!

Model Assumptions Session

Each of the n nodes is an S node for one session and a D node for another session

Each S node i has an infinite stream of packets to send to its D, d(i)

The S-D association does not change with time Each node has an infinite buffer to store

relayed packets Central Scheduler

At any time t, the scheduler chooses which nodes will transmit which packet, and its power level

Transmission Model

Random Topology

Static vs. Mobile Ad Hoc Networks When # of users per unit area n increases

Static: The throughput per S-D pair decreases approximately like Long-range direct communication limited due to

interference. Most comm. has to occur between nearest neighbors

Distances of order Hops to D of order Actual useful traffic per pair is small

Best performance achievable with optimal scheduling, routing Traffic rate per S-D pair can actually go to zero

Mobile:The avg. long-term throughput per S-D pair can be kept constant

Direct Contact vs. Simple Replication Mobile Nodes w/ direct contact

Transmission are long range interference prevents more concurrent transactions

For sufficient large N, throughput goes to 0

Mobile Nodes w/ relaying (simple replication) Overcame interference and distance limitation Possible to schedule O(n) concurrent successful

transmissions per time slot w/ local communication Achieved a throughput per S-D pair of O(1)

Numerical Results

Receiver Centric Results

What is capacity here?

Not traditional information-theoretic notion

Notion of network capacity under interference Modulation and coding scheme is fixed

In this notion of capacity, space is resource

d

S

D

dIN

No other transmission in this area of 2d

Capacity of static ad hoc networks

Gupta and Kumar [IEEE Trans. IT, 2000] Uniform distribution of n nodes within a disk of unit area Randomly chosen sender-destination pairs Same power level for all transmissions Per-node throughput as with multi-hop

relaying

Agarwal and Kumar [ACM CCR, 04] Per-node capacity of with power control

nn log

1

n/1

Why multi-hop relaying in static networks?

Direct transmission is bad Transmission over distance d costs Short transmission is better than long transmission

Multi-hop relay (via nearest neighbor) is best Best possible is to transmit only to neighbors

2d

hops n

1VS n/1 For each hop

Required area = Required area = n/1 1

Network capacity = nO Network capacity = 1OPer-node capacity = Per-node capacity = nOnnO /1/ nO /1

S

D

S

D

Capacity of mobile ad hoc networks

Grossglauser and Tse [IEEE INFOCOM, 01] Similar model as Gupta and Kumar, but with mobile nodes

Per-node capacity of is achievable with two-hop relay

Why two-hop relay in mobile networks? Direct transmission cannot exploit mobility More than two-hop decreases capacity

1

Capacity scaling of ad hoc networks

Number of nodes

Per-node Capacity

Gupta, Kumar-Static nodes-Common power level

Francheschetti, Dousse - Static nodes - Power control allowed

Grossglausser, Tse - Mobile nodes

What is ‘price’ for capacity?

Two ways to send a packet to D Wireless transmission Node mobility (=relay movement)

For given distance d between S and D d = (sum of distances by transmission) + (sum of distances by relay movement) To minimize first term is to maximize second term

Time taken for node mobility: Delay Sum of distances by mobility results in time delay

Why tradeoff between delay and capacity?

Tradeoff between delay and capacity d = (sum of distances by transmission) +

(sum of distances by relay movement) For capacity, reduce distances by transmission For delay, reduce distances by relay movement

For given value of d Can not reduce both distances! tradeoff

Illustration of tradeoff between delay and capacity

Assume appropriate scheduling One transmission = distance of

n

c

S

D

R1

R1

R2R2

S

D

d

n

cd 3Total movement of relays =

Delay

Capacity

# of transmissions = 3

Critical Delay and 2-Hop Delay

Critical Delay: Minimum delay that must be tolerated under a given mobility model to achieve a per-node throughput of

2-Hop Delay: Delay incurred by the 2-hop relaying scheme

The delay-capacity tradeoff exists for values of delay between critical delay and 2-hop delay

n/1

Hybrid Random Walk Models The network is divided into n2β

cells for β between 0 and ½ Each cell is divided into n1-2 β

sub-cells Each node jumps from its

current sub-cell to a random sub-cell in one of the adjacent cells

β=1/2 random walk model

Random Direction Models Parameterized by β between 0

and ½ Each node moves a distance of

n-β with a speed of n-1/2 in a random direction

Can pause for some time between steps

Lower Bound for Critical Delay

Main idea If average delay is smaller than a certain value,

packets travel average distance of to reach destination

Then show that this result in throughput of

HRW: Critical delay scales as RD: Critical delay scales as

nnO log/2

nnO log/2/1

04/26/06 29

Calculating Critical Delay using Exit Time Study exit time for a disk of radius r=1/8

centered at nodes initial position

Derive a lower bound on exit time that holds with high probability

r = 1/8

Details of lower bound: Exit time

Let ςhrw and ςrd denote exit times for a disk of radius 1/8 in case of HRW and RD model with parameter β

Lemma (Lower Bound on Exit Time for HRW models):

Lemma (Lower Bound on Exit Time for RD models):

2

2 4

log1024 nn

nP hrw

2

2/1 4

log768 nn

CnP rd

C = slot duration

04/26/06 31

From Exit Time to Critical Delay?

1

1/4

s

d

r

Upper Bound for Critical Delay

Need to develop a scheme that achieves a throughput of

Delay can be upper bounded by first hitting time

for HRW models and

for RD models nnO log2/1

nnO log2

n/1

Summary of Main results 2-Hop delay is roughly for all models Critical delay scales as roughly for HRW models Critical delay scales as roughly for RD models

2n

n

2/1 n

Conclusions

Node mobility has strong impact on delay-capacity tradeoff

There exists minimum value of delay (critical delay) which makes capacity better than that of static ad hoc networks

Nodes change directions over shorter distances exhibit higher critical delay values

Nodes moving in same direction over longer distances shows a wider delay-capacity tradeoff