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Space-Time Routing in Ad Hoc Networks 3number of hops) or physical (e.g., euclidean distance, energy cost). The bindingS-T metric is used to compare two route entries to a destination of differentdistance and age and to decide which is closest in the joint spatio-temporalspace.The rest of the paper is organized as follows. In Section 2, we give a generalformulation of STR and discuss some properties. In Section 3, we give examplesof two specific STR algorithms: FRESH, GREP, and outline a third algorithmusing physical notions of space and time. In Section 4, we discuss some propertiesof STR, including loop-freedom. Section 5 concludes the paper.2 Space-Time Routing2.1 Notation and AssumptionsWe note V = {1 ...n} the set of nodes in the network, and E the set of edges(i, j) ∈ E for i, j ∈ V . Associated with the set of edges is a distance function 2△ : E → R. For example if distance is counted as the number of hops, wewould have △(i, j) = 1. We assume that any node can obtain the distance toits neighbors (trivially in the case of hop-count distance, or for example using asignal-strength based estimation in the case of euclidean distances). Each nodemaintains its own clock, which is used to stamp every packet with the clock timeof the node which originates it. Simple examples of a node clock are a physical(oscillator-based) clock giving a continuous reading, for example in seconds, ora logical clock providing a discrete ordering of routing events relative to thatsource. Whichever temporal representation is used, STR does not require anyform of inter-node clock synchronization.Then STR requires a binding spatio-temporal metric, which is a functionf : R 2 → R, taking as input a (spatial) distance value and a (temporal) clockvalue and returning a scalar representing the “norm” of this pair in the spatiotemporalspace. The binding S-T metric must satisfy the following conditions:argminf(s, t) =(0, 0) (1)For fixed d, f is an increasing function of tsgn(f(d, t 1 ) − f(d, t 2 )) = sgn(t 1 − t 2 ) (2)For fixed t, f is an increasing function of dsgn(f(d 1 ,t) − f(d 2 ,t)) = sgn(d 1 − d 2 ) (3)Routing Table Entries. Each node maintains a distance-vector routing tablecontaining one entry for each destination node. In addition to the next hop anddistance fields which are used in spatial routing algorithms, STR routing entriesalso include the age of the entry.2 Note that given node mobility, E and △ vary over time. For simplicity of notationwe drop the time index since we only refer to the values of E and △ “at the presenttime”.
4 H. Dubois-Ferrière, M. Grossglauser, and M. VetterliTable 1. Routing table entries.n N D Next hop to node D in N’s routing table.d N D Distance to node D in N’s routing table.Source Time of the routing entry to D in N’s routing table.t N DTable 1 summarizes the notation used to describe routing state at each node.We drop the superscript and use the notation n D ,d D ,t D when the context allowsdoing this unambguously. We use the convention that when a node has no entryfor D, n D = null, d D = ∞, and t D = ∞.Packet Types. Beside regular data packets, STR uses route request (RREQ)and route reply (RREP) packets. A node sends a RREQ packet when it has noroute to the destination, or if the next hop along the route is broken. It sends aRREP packet in reply to a route request when it has a route fresh enough andshort enough to satisfy that request. Note that STR does not use any route errorpackets: since link breaks are always repaired locally, there is no need to informthe source and upstream nodes when this occurs.Apart from the usual source and destination addresses of a packet, we introducethe following STR-specific fields: The source time ofapacket(p.st) isthe clock time at the packet’s source node when it originated the packet. Eachpacket is stamped with the clock time of the source that originates it. This fieldis present in all packets.The source distance ofapacket(p.sd) is the distance this packet has traversedsince leaving the source. It is updated at each hop to reflect the new distancefrom the source. This field is present in all packets.The destination distance (p.dd) and destination time (p.dt) ofapacketarepresent only in RREQ and RREP packets. In the case of a RREQ packet, theycome from the routing entry that the source of the RREQ has to the requesteddestination. In the case of a RREP packet, they represent the distance to therequested destination from the replying node.2.2 STR AlgorithmDATA Processing. We first describe originating and forwarding of data packets.A node S originating a data packet initializes the source distance field to 0and initializes the source time field to the present value of its clock. A node Nreceiving from neighbor M a packet originated by node S first increments thesource distance field of the packet to reflect the distance that the packet has nowtraversed: p.sd ← p.sd + △(N,M).Then, if the packet has come over a shorter (in the spatio-temporal metricspace) route than the route it currently has, N updates its routing entry to S.Formally, if f(p.sd, p.st)
Page 2 and 3: Lecture Notes in Computer Science 2
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3BerlinHeidelbergNew YorkHong KongL
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Series EditorsGerhard Goos, Karlsru
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Organizing CommitteeConference Co-c
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Table of ContentsSpace-Time Routing
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Author IndexAlonso, G. 104Bachir, A
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