Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...
Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...
Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...
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A Uniform Cont<strong>in</strong>uum Model for Scal<strong>in</strong>g of Ad Hoc Networks 97exact positions or movements, or their exact l<strong>in</strong>ks with other nodes. Thus, our modelfocuses on a cont<strong>in</strong>uum approximation rather than a graph-theoretic view of thenetwork.In order to simplify the analysis, we assume that all nodes see similar trafficconditions. In other words, we ignore the edge effects result<strong>in</strong>g from nodes near theextremity of a network hav<strong>in</strong>g fewer neighbors than centrally located nodes. In thissense our model is uniform.Our goal is to model the traffic <strong>in</strong> an ad-hoc network us<strong>in</strong>g simple and optimisticassumptions. Our simple assumptions lead to a mathematically tractable model,which <strong>in</strong> turn reveals several dimensionless parameters that characterize the operationof an ad-hoc network; these may be helpful <strong>in</strong> bridg<strong>in</strong>g the gaps between theparameters of various simulations. Our optimistic assumptions lead to upper boundson the performance of real networks. We avoid an exclusively asymptotic analysisfor a large number of nodes [11] <strong>in</strong> order to deal with practical f<strong>in</strong>ite cases; thereforeour results are derived <strong>in</strong> cf rather than Q(f) format, although the values of constantsare approximate at best.In Sections 2 and 3 we def<strong>in</strong>e the parameters to describe two-dimensional networkgeometry and node behavior, respectively. An expression for the traffic due to userapplications is derived <strong>in</strong> Section 4. In Section 5 we f<strong>in</strong>d how much traffic resultsfrom mobility to support rout<strong>in</strong>g. The user data traffic and rout<strong>in</strong>g traffic arecomb<strong>in</strong>ed <strong>in</strong> Section 6 to f<strong>in</strong>d the total traffic and the power requirement. The twodimensionalresults are extended to m dimensions <strong>in</strong> Section 7, and conclusions aredrawn <strong>in</strong> Section 8.2 Network Geometry <strong>in</strong> Two DimensionsWe consider an ad-hoc network whose nodes lie <strong>in</strong> a plane. With each node we canassociate a Voronoi cell, which is the set of po<strong>in</strong>ts closer to that node than any other.We approximate cells <strong>by</strong> circles with radii r 1 on average, giv<strong>in</strong>g an average distanced 1 =2r 1 between neighbor<strong>in</strong>g nodes, and we suppose that the cell area is approximatelypr 2 1 . (See [6], who <strong>in</strong>vestigate feasible Voronoi tessellations <strong>in</strong> detail.) Thusthe node density (the number of nodes per unit area) is approximately 4/pd 2 1 .We assume that the network consists of N nodes occupy<strong>in</strong>g a circular region ofdiameter D+d 1 , and that the maximum distance between any pair of nodes is D. Thenode density must be approximately 4N/(p(D+d 1 ) 2 ), so that Nd 21 =(D+d 1 ) 2 ,orD=d 1 (÷N-1).3 Node ModelThe essential features of nodes are that (a) they generate user data, (b) they forwardpackets, (c) they move, (d) they have a f<strong>in</strong>ite radio transmission range, and (e) theyhave a f<strong>in</strong>ite transmission bandwidth.(a) We assume that each node is a random source of user data, be<strong>in</strong>g characterized<strong>by</strong> a rate p T , the number of new data packets created and transmitted <strong>by</strong> a node perunit time to a randomly chosen dest<strong>in</strong>ation node. (The subscript T is meant to suggestan application transmitt<strong>in</strong>g, or talk<strong>in</strong>g.).(b) Packet forward<strong>in</strong>g is discussed <strong>in</strong> Section 4.