Geographical Delay Tolerant Routing: Background, Motivation,

and Cost/Delay Tradeoffs

Christos Tsiaras, Argyrios Tasiopoulos, Stavros Toumpis

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Organization of this talk

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PART B:Geographic Routing

PART C:Delay Tolerant Networks

PART E:Geographic Delay Tolerant Routing

PART A:Introduction to Wireless Networks

PART D:The minimum cost path problem in DTNs

PART A: Introduction to Wireless Networks

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Cellular Wireless Networks

• Mobile terminals communicate with others exclusively through base stations.

• Mobile terminals have very little responsibility.• A wireless access network.

PSTN, Internet,

etc.

Α Β

Truly Wireless Networks

• Mobile Terminals communicate through their neighbors.

• Mobile Terminals have many responsibilities.– For example, they must forward other terminals’ data.

• Much more challenging.

PSTN, Internet,

etc.

Α

Β

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.

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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 antiquity7

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 people4. Mobile Ad Hoc Networks - MANETs (90’s)

– Mostly CS people5. Wireless Networks (future?)

Question: What do you think is the reason for this constant change of names?

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Special Types of Wireless Networks

1. Wireless Sensor Networks2. Vehicular Ad Hoc Networks3. Next Generation Cellular Networks4. Delay Tolerant Networks5. Wireless Mesh Networks

• Others will come up sure enough• Commercial products exist for most of them

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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

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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)

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Various Engineering Decisions

• Source routing vs Path vector routing• Reactive vs Proactive routing• Hierarchical vs Flat routing• Hop count versus link cost• Etc.

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PART B: Geographic Routing

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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)

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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

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D

Selected by Compass Routing

Selected by Greedy Routing

Might be selected under random selection

Cannot be selected

Selected by NFP

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.

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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

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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

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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.

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Greedy-Face-Greedy Routing Example

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S D

PART C: Delay Tolerant Networks

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(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

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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

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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.

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Related Concepts

• Intermittently Connected Networks (ICNs).– The Internet is a DTN but not an ICN

• Disruption Tolerant Networks (DTNs)• Data muling

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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.

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PART D: The minimum cost path problem in DTNs

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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.

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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

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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

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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

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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

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Example C/DEG

• A network of 4 epochs and 4 nodes.

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An example journey

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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.

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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).

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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.

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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

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Example (1/6)

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Example (2/6)

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Example (3/6)

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Example (4/6)

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Example (5/6)

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Example (6/6)

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Example: The resulting journeys

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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.

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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.

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10 sample OC/DCs and the

average of the 1000 OC/DCs

PART E: Cost/Delay Tradeoffs of Geographical Delay Tolerant Routing

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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)

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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)

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Minimum Cost per Progress Rule (MCpPR)

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• 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.

Balanced Ratio Rule (BRR)

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• 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.

Composite Rule (CR)

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ABABAB rrc '','min

• 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.

Achievable Cost/Delay Curves (AC/DCs)

• Let the Achievable Cost/Delay Curve (AC/DC) Cij

X(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

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10 sample AC/DCs and the

average of the 1000 AC/DCs

Some results on the realistic setting

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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?

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