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GPSR: Greedy Perimeter Stateless Routing for Wireless Networks. Brad Karp; Harvard University H. T. Kung; Harvard University. Hierarchy is the most widely deployed approach to scale routing as the number of network destinations increases.
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GPSR: Greedy Perimeter Stateless Routing for WirelessNetworks Brad Karp; Harvard UniversityH. T. Kung; Harvard University
Hierarchy is the most widely deployed approach to scale routing as the number of network destinations increases. • An Autonomous System runs an intra-domain routing protocol inside its borders, and appears as a single entity in the backbone inter-domain routing protocol by BGP. • This hierarchy is based on well-defined and rarely changing administrative and topological boundaries. • It is therefore not easily applicable to freely moving ad-hoc wireless networks, where topology has no well-defined Autonomous System boundaries, and routers may have no common administrative authority.
Caching has come to prominence as a strategy for scaling ad-hoc routing protocols • Dynamic Source Routing (DSR) , Ad-Hoc On-Demand Distance Vector Routing (AODV) , and the Zone Routing Protocol (ZRP) all eschew constantly pushing currenttopology information network-wide. • Instead, routers running these protocols request topological information in an on-demand fashion as required by their packet forwarding load, and cache it aggressively.
On-Demand Protocols we have looked • Ad-hoc On-demand Distance Vector (AODV) • Zone Routing Protocol (ZRP) • Location-aided routing (LAR) ….
Greedy Perimeter Stateless Routing • New wireless routing protocol Greedy Perimeter Stateless Routing (GPSR) proposes an aggressive use of geography to achieve scalability. • The protocol aims for scalability with increase in number of nodes in the network, and increasing mobility.
Greedy Perimeter Stateless… • Measures of scalability are: • Routing protocol message cost: How many routing protocol packets does a routing algorithm send? • Application packet delivery success rate: What fraction of applications’ packets are delivered successfully by a routing algorithm? • Per-node state: How much storage does a routing algorithm require at each node?
Greedy Perimeter Stateless… • Networks that push on mobility, number of nodes, or both include: • Ad-hoc networks: Perhaps the most investigated category, these mobile networks have no fixed infrastructure, and support applications for military users, post-disaster rescuers • Sensor networks: Comprised of small sensors, these mobile networks can be deployed with very large numbers of nodes, and have very impoverished per-node resources. Minimization of state per node in a network of tens of thousands of memory-poor sensors is crucial.
Working of the Algorithm • The algorithm consists of two methods for forwarding packets: greedy forwarding, which is used wherever possible, and perimeter forwarding, which is used in the regions greedy forwarding cannot be.
Greedy Forwarding • Under GPSR, packets are marked by their originator with their destination’s location. • As a result, a forwarding node can make a locally optimal, greedy choice in choosing a packet’s next hop. • Specifically, if a node knows its neighbors’ positions, the locally optimal choice of next hop is the neighbor geographically closest to the packet’s destination. • Forwarding in this regime follows successively closer geographic hops, until the destination is reached.
Greedy Forwarding • Greedy forwarding’s great advantage is its reliance only on knowledge of the forwarding node’s immediate neighbors. The state required is negligible, and dependent on the density of nodes in the wireless network, not the total number of destinations in the network. • The power of greedy forwarding to route using only neighbor nodes’ positions comes with one attendant drawback: there are topologies in which the only route to a destination requires a packet move temporarily farther in geometric distance from the destination.
Benefits of Greedy Forwarding • A node only needs to remember the location info of one-hop neighbors • Routing decisions can be dynamically made
Problem • In the figure, there are two routes from x to D, namely, x-w-v-D and x-y-z-D. But x will not choose w or y under greedy forwarding.
The Right-Hand Rule:Perimeters • Right hand rule for traversing a graph: When arriving at node x from node y, the next edge traversed is the next node that is sequentially counterclockwise about x from the edge (x,y). • Fact: This rule traverses the interior of a polygon in clockwise order.
The dark area is void area. Right hand rule amounts to navigating around the pictured void, specifically to nodes closer to destination than x.
Remove Crossing Edge • Make the graph planar • Remove(w,z)from the graph • Right-hand rule results in the tour x-u-z-d-x
Make a Graph Planar .Convert a connected graph to a planar graph by removing “bad” edges • Ensure the original graph will not be disconnected • Two types of planar graphs: • Relative Neighborhood Graph (RNG) • Gabriel Graph (GG)
Concepts related to Graph Theory Planarized Graphs • While the no-crossing heuristic empirically finds the vast majority of routes in randomly generated networks, it is unacceptable for a routing algorithm persistently to fail to find a route to a reachable node in a static, unchanging network topology.
Planarized Graphs • The Relative Neighborhood Graph (RNG) and Gabriel Graph (GG) are two planar graphs long-known in varied disciplines. • Removing edges from the graph to reduce it to the RNG or GG must not disconnect the graph; this would amount to partitioning the network.
Planarized GraphsRelative Neighborhood Graph (RNG) • Given a collection of vertices with known positions, the RNG isdefined as follows: • An edge (u,v) exists between vertices u and v if the distance between them, d(u,v), is less than or equal to the distance between every other vertex w, and whichever of u and v is farther from w. In equational form:
Planarized GraphsGabriel Graph (GG) • The GG is defined as follows: • An edge (u,v) exists between vertices u and v if no other vertex w is present within the circle whose diameter is (u,v). In equational form:
Combining Greedy and Planar Perimeters • Upon receiving a greedy-mode packet for forwarding, a node searches its neighbor table for the neighbor geographically closest to the packet’s destination. If this neighbor is closer to the destination, the node forwards the packet to that neighbor. When no neighbor is closer to the destination, the node marks the packet into perimeter mode.
Combining Greedy and Planar Perimeters • The packet header fields GPSR uses in perimeter-mode forwarding are (destination location, location packet entered the perimeter mode, packet mode-greedy or perimeter, etc).
Combining Greedy and Planar Perimeters • All data packets are marked initially at their originators as greedymode. • Packet sources also include the geographic location of the destination in packets. Only a packet’s source sets the destination location field; it is left unchanged as the packet is forwarded through the network.
Combining Greedy and Planar Perimeters • A full graph and the corresponding GG and RNG subgraphs.
Combining Greedy and Planar Perimeters • When a packet enters perimeter mode at x, GPSR forwards it along the face intersected by the line xD. x forwards the packet along the first edge counterclockwise about x from the line xD. • Once a packet reaches a location closer than where greedy forwarding previously failed for that packet, the packet can make greedy progress without danger of returning to the prior local maximum.
Protocol Implementation • Graph planarization RNG & GG planarization depend on having the current location info of a node’s neighbors Mobility may cause problems Re-planarize when a node enters or leaves the radio range • What if a node only moves in the radio range? • To avoid this problem, the graph should be re-planarize for every beacon msg Also, assumes a circular radio transmission model
Protocol Implementation • Simulation in ns-2 • Protocol compared with: DSR (Dynamic Source Routing • Random waypoint model A node chooses a destination uniformly at random Choose velocity uniformly at random in the configurable range – simulated max velocity 20m/s A node pauses after arriving at a waypoint – 300, 600 & 900 pause times
Protocol Implementation • Promiscuous use of the network interface: • Also as used in DSR, GPSR disables MAC address filtering to receive copies of all packets for all stations within its radio range. All packets carry their local sender’s position, to reduce the rate at which beacon packets must be sent, and to keep 50, 112 & 200 nodes 30 CBR flows generated by 22 sending nodes About 20 neighbors for each node – very dense Each CBR flow sends 2Kbps, and uses 64byte packets • Nominal radio range: 250m (802.11 WaveLan radio) • Each simulation lasts 900 seconds • Take an average of the six different randomly generated motion patterns.
