Post on 22-Dec-2015
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