Transcript Document

Geographical Delay Tolerant
Routing: Background, Motivation,
and Cost/Delay Tradeoffs
Christos Tsiaras, Argyrios Tasiopoulos,
Stavros Toumpis
1
Organization of this talk
PART A:
Introduction to Wireless Networks
PART B:
Geographic Routing
PART C:
Delay Tolerant Networks
PART D:
The minimum cost path problem in DTNs
PART E:
Geographic Delay Tolerant Routing
2
PART A: Introduction to
Wireless Networks
3
Cellular Wireless Networks
Β
Α
PSTN,
Internet,
etc.
• Mobile terminals communicate with others
exclusively through base stations.
• Mobile terminals have very little responsibility.
• A wireless access network.
Truly Wireless Networks
Β
Α
PSTN,
Internet,
etc.
• Mobile Terminals communicate through their
neighbors.
• Mobile Terminals have many responsibilities.
– For example, they must forward other terminals’ data.
• Much more challenging.
Prehistory
• Research started in the 70’s
– ARPA Project
– Some military communications systems came out
of it (ΕΡΜΗΣ!)
• Interest cooled off in the 80’s
• Renewed interest in the 90’s
– Wireless communications very popular
– Technology became more powerful and could
support algorithms.
• Currently, interest is still going strong.
6
Preprehistory : Naval
Communications at
the Turn of the
(Previous) Century
• Problem: Stop the German High Seas
Fleet going in/out of Denmark Strait
• Setting:
– You are in 1914, most of your ships have no wireless. Must
depend on visual communication.
– Fog, i.e., fading
• Solution: A Hierarchical, Mobile, Visual Sensor
Network.
• Many other examples in history, even in antiquity
7
Many names for the same thing
1. Packet Radio Networks (70’s)
2. Multihop Wireless Networks (80’s)
3. Wireless ad hoc networks (90’s)
– Mostly EE people
4. Mobile Ad Hoc Networks - MANETs (90’s)
– Mostly CS people
5. Wireless Networks (future?)
Question: What do you think is the reason for
this constant change of names?
8
Special Types of Wireless Networks
1.
2.
3.
4.
5.
Wireless Sensor Networks
Vehicular Ad Hoc Networks
Next Generation Cellular Networks
Delay Tolerant Networks
Wireless Mesh Networks
• Others will come up sure enough
• Commercial products exist for most of them
9
Wireless Network Routing
• A data source must find a path to a (typically
distant) destination
• Path is comprised of intermediate nodes lying
in between the source and the destination
• Routing is much more challenging in wireless
networks than in wired networks:
– Bandwidth is much scarcer, and there is
interference
– Topology is changing much faster
– Network diameter is much larger
10
Common approach to routing
• The source asks all its neighbors for a route to
the destination
• These neighbors ask their neighbors
• Process is repeated, until destination is
contacted.
• Essentially same idea as in wired networks
• Adopted by DSR, AODV, TORA, DSDV, OLSR,
and practically all other well known routing
protocols (all these proposed in 1995-2000)
11
Various Engineering Decisions
•
•
•
•
•
Source routing vs Path vector routing
Reactive vs Proactive routing
Hierarchical vs Flat routing
Hop count versus link cost
Etc.
12
PART B: Geographic Routing
13
Basic idea of Geographic Routing
• Suppose we know the location of the
destination D, and the location of all our
neighbors.
• Let’s send the data packets to that of our
neighbors, N, that seems the best suited to be
the next hop (for example, it is the nearest of
our neighbors to the destination)
14
Rules for selecting the next relay N
• N is the node closest to D (Greedy Routing)
• N is the node closest to the SD line (Compass
Routing)
• N has the largest progress (i.e. projection of
SN on SD line is largest) (MFR)
• N is the closest to S that is also towards D
(good when channel is noisy) (NFP)
• N is randomly chosen among those neighbors
closer to D
• N maximizes progress over cost
15
An example
Might be selected
under random selection
Selected by
Greedy Routing
D
Cannot be selected
Selected by
NFP
Selected by
Compass Routing
16
Advantages of Geographic Routing
• Robust with respect to change of topology
– Who handles the packet is unimportant, and can
be decided at the very last moment.
• Very little state is needed
– With traditional routing, nodes need to keep (and
update) routing tables and/or packets need to
carry the routes they will follow
• For these two reasons, it scales very well with
network size.
17
Challenges of Geographic Routing
1. Location Service is needed: Source needs to
know location of neighbors (easy) and the
data destination (hard)
2. The Local Maximum Problem: While
forwarding, it is possible that the best node
to receive the packet is the current holder
18
Finding the location of destinations
• Solution 1: Each node broadcasts its location
to the whole network
– The faster a node moves, the more often an
update is needed.
– The further away a node lies, the less accurate the
information has to be.
• Solution 2: One of the nodes is selected to
store the locations of everyone
– Hierarchical versions exist.
• Solution 3: Nodes periodically cast rays in
principal directions
19
Solutions to Local Maximum Problem
• Solution 1: Current holder planarizes the
graph and routes around faces (GPSR, Face-1,
Face-2, Greedy-Face-Greedy Routing)
• Solution 2: Whenever a node is a local
maximum, it broadcasts the packet to all
neighbors and removes itself from the
network as far as packets for that destination
are concerned.
• Solution 3:Current holder pretends it is some
place else.
• Solution 4: Landmarks are used.
20
Greedy-Face-Greedy Routing
Example
S
D
21
PART C: Delay Tolerant Networks
22
(My) Definition
• Delay Tolerant Networks (DTNs) are networks
where the delay in the delivery of a packet is
much larger than the time it takes the
topology to change substantially,
– Either by design,
– Or choice
23
DTN Examples
• The Internet, when you try to transmit
Terabits of Data
– You will need a few days, during which time the
topology essentially changes, due to the diurnal
traffic pattern
– Such volumes of data are routinely created by
data centers and research facilities like CERN
• WSNs with low data rates where nodes often
go to sleep
• Interplanetary networks
• WiFi may be thought off as a kind of DTN
24
Zebranet: the ‘canonical’ example
• Problem setting: we must monitor the
behavior of a large group of zebras
• Traditional solution: put collars on zebras.
Each collar directly communicates with a
satellite or a ground station
• DTN solution: put collars on zebras, and
collars are allowed to exchange information.
As you are not interested in getting the
information quickly, use very low power
transmitters, so that resulting network is
always disconnected.
25
Related Concepts
• Intermittently Connected Networks (ICNs).
– The Internet is a DTN but not an ICN
• Disruption Tolerant Networks (DTNs)
• Data muling
26
Routing on DTNs
• Most common approach: epidemic routing
and its variations
– Instead of trying to find a route for a single packet,
just send out to all your neighbors lots of replicas,
and eventually one of them will get to the
destination.
– An obvious throughput/delay tradeoff: the more
replicas there are, the smaller the throughput, but
the smaller the delivery delay too.
27
PART D: The minimum cost path
problem in DTNs
28
Traditional Routing and Static Graphs
• Traditional routing is studied analytically using
static graphs
– Network nodes → Graph vertices
– Network links → Graph arcs
– Link costs/delays/etc.→ Arc weights
• Finding the minimum cost route from a source
to a destination amounts to finding the
minimum weight path in the respective graph
– Dijkstra’s algorithm, Bellman-Ford’s algorithm, etc.
29
DTN Routing and Dynamic Graphs
• In DTN routing, no single network graph exists
– While a packet is routed, the network is changing!
• Solution: dynamic graphs and dynamic flows
– Time is slotted
– For each node in the network, there is a node
replica at each slot.
– The node replicas are connected with arcs that
take into account both the link delay and the link
cost.
– Observe: a packet journey across time and nodes
can be associated with a single path
30
Dynamic Graphs in OR
• Dynamic Graphs are standard tools in
Operations Research
• A good example is the fastest evacuation
problem:
– We are given a ship (the Titanic is a good example)
with the locations of life boats and the passengers
– Find an evacuation plan so that the ship is
evacuated the fastest
• Standard approach: use a dynamic graph and
calculate a dynamic flow
31
Our Network Model
• Time is divided in epochs
– During epochs, properties of the network remain
fixed. Network evolution happens instantaneously
during epoch transitions.
• Nodes are communicating over links with zero
delay and some cost that reflects energy
dissipation, bandwidth usage, buffer
occupancy.
• There is also a cost associated with storing
data
32
Cost/Delay Evolving Graphs (C/DEGs)
• There is a Replica Graph for each epoch.
– Within each replica, arcs denote existing links
during the corresponding epoch.
• Replica graphs are connected using storage
arcs, that reflect the cost of storing data at a
node for the duration of a single epoch.
• Collectively, the replicas with the storage arcs
form a Cost/Delay Evolving Graph
33
Example C/DEG
• A network of 4
epochs and 4
nodes.
34
An example journey
35
A fundamental Cost/Delay Tradeoff
• C/DEGs capture a fundamental tradeoff of
DTNs: the cost of transporting a packet from
node A to node B with a delay of at most T is a
decreasing function of T.
– If we are willing to wait for more time, the
topology might become more favorable.
– In the C/DEG setting, the smallest-cost journey of
delay at most T is found considering all C/DEG
paths of delay at most T. Increasing T implies
more paths are considered.
36
Optimal Cost/Delay Curves (OC/DCs)
• Let the Optimal Cost/Delay Curve (OC/DC)
Cij(t) be the minimum cost of transporting a
packet from node i at epoch 1 to node j at
epoch t the latest.
• Based on previous discussion, OC/DCs are
non-increasing functions of t.
• OC/DCs are useful because they allow us to
compare the performance of practical
protocols with the theoretical optimum (as we
will see later on).
37
Efficient Calculation of OC/DCs
• In principle, we could calculate the value of
the OC/DC Cij(t) by finding the minimum cost
path from node i at epoch 1 to node j at
epoch t for all t=1,…,T
• However, due to the special structure of the
C/DEG, the calculation can take place faster.
38
Sketch of Algorithm
1. Find the minimum cost paths of the first
replica.
2. For t=2 to T,
– Find all minimum cost paths involving replica t,
using the previous step
• Gains are modest. Complexity is proportional
to T, instead of T logT
39
40
Example (1/6)
41
Example (2/6)
42
Example (3/6)
43
Example (4/6)
44
Example (5/6)
45
Example (6/6)
46
Example: The resulting journeys
47
A more realistic setting (1/2)
• N=1001 nodes communicating over a
common wireless channel
• Node 1 is immobile and acting as a base
station.
• Nodes move in a square region of side L=10
km.
• There are T=500 epochs, each with a duration
of d=10 sec.
• Nodes move according to a random waypoint
model with constant speed v=36 km/sec.
48
A more realistic setting (2/2)
• Maximum communication range R=600 m
• Communication cost C(d)=d2
– Long transmissions are penalized
– Reasonable choice when cost is bandwidth usage
– Reasonable choice also when cost is energy
dissipation.
• Each node 2,…,1001 wants to send a packet to
the Base Station, node 1.
49
10 sample
OC/DCs
and the
average of
the 1000
OC/DCs
50
PART E: Cost/Delay Tradeoffs of
Geographical Delay Tolerant Routing
51
Basic Idea: Greedy and Lazy routing
• Setting: Wireless network where sources
know the locations of their destinations.
• Greedy and Lazy routing
– Packets are routed taking into account the
locations and velocity vectors of the current
holder, its neighbors, and the destination (the
greedy part)
– When a local maximum is encountered, just wait
for the topology to change! (the lazy part)
52
Various choices exist:
• AeroRP: The next relay is the node
approaching the destination the fastest.
• MOVE: The next relay is the node pointing
most closely toward the destination
• GeOpps: The next relay is the node expected
to arrive at the destination the fastest.
• Our contributions:
– Minimum Cost per Progress Rule (MCpPR)
– Balanced Ratio Rule (BRR)
– Composite Rule (CR)
53
Minimum Cost per Progress Rule (MCpPR)
C AB
r ' AB 
AD  BD
• Let node A have a packet.
• Among all its neighbors within distance R’, A selects
that neighbor B that has forward progress and for
which the ratio above is minimum.
• If no such neighbor exists, node A simply waits for
the topology to change.
54
Balanced Ratio Rule (BRR)
C AB  adBZ
r ' ' AB 
AD  DZ
• Let node A have a packet.
• Among all its neighbors within distance R’, A selects
that neighbor B that has forward progress and for
which the ratio above is minimum.
• If no such neighbor exists, node A simply waits for
the topology to change.
55
Composite Rule (CR)
cAB  minr ' AB , r ' ' AB 
• Let node A have a packet.
• Among all its neighbors within distance R’, A selects
that neighbor B that has forward progress and for
which the quantity above is minimum.
• If no such neighbor exists, node A simply waits for
the topology to change.
56
Achievable Cost/Delay Curves
(AC/DCs)
• Let the Achievable Cost/Delay Curve (AC/DC)
CijX(t) give the minimum aggregate transport
cost that protocol X can achieve with a delay
of at most t epochs.
• AC/DCs capture how well a protocol performs
in terms of the cost/delay tradeoff
57
10 sample
AC/DCs
and the
average of
the 1000
AC/DCs
58
Some results on the realistic
setting
59
60
61
62
63
Future Work
• How small can the gap between the optimal
and the practical performance be?
• Can we analyze the performance of the
protocols theoretically? With what tools?
64