5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The CBTC protocol (2) TC protocols: 8/12 The CBTC protocol produces a connected communication graph if ρ ≤ 2π/3 The obtained communication graph is made symmetric by adding the reverse edge to every unidirectional link A set of optimizations are also proposed, that prune energy-inefficient edges while not impairing connectivity and symmetry Drawback: directional information required Several variants of CBTC have been introduced [Bahramgiri et al.02][Huang et al.02] 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Neighbor-based TC TC protocols: 9/12 Other class of TC protocols based on the k-neighbors graph, i.e. the graph in which every node is connected to its k closest neighbors First neighbor-based TC protocol: the LINT protocol of [RamanathanRosales- Hain00]: – Basic idea: try to keep the number of neighbors of every node within a low and high threshold centered around an “optimal value” – Number of neighbors estimated overhearing control and data messages – Drawbacks: the “optimal value” is not characterized; the estimation of the number of neighbors might be inaccurate (silent neighbors are not detected); connectivity is not guaranteed KNeigh [Blough et al.03a]: – Goal: maintain the number of physical neighbors equal to (or slightly below) k – k is chosen in such a way that the graph generated is connected w.h.p. – The graph produced is symmetric – On the average, it is 20% more energy-efficient than CBTC – Drawback: based on distance estimation; connectivity only w.h.p. 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The optimal value of k TC protocols: 10/12 Optimal value of k for increasing n 0 1 2 3 4 5 6 7 8 9 10 10 100 1000 n k Optimal value Optimal value of k for increasing values of n (from [Blough et al. 03]) Remark: setting k = 9 guarantees connectivity w.h.p. for values of n ranging from 50 to 500 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Sample topologies TC protocols: 11/12 Sample topologies generated in case of CTR topology control (left), and after KNeigh (center) and CBTC (right) execution. The number of nodes is n = 100 (from [Blough et al. 03]) 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The XTC protocol TC protocols: 12/12 XTC is a very recent protocol by the same author of CBTC [WattenhoferZollinger04] Basic idea (similar to KNeigh): – at the beginning, every node orders its neighbors (set of nodes in the maximum transmitting range) according to some criterion (e.g., link quality) – then, every node transmits its order at maximum power – based on its own order, and on the orders of its neighbors, every node determines the set of “logical” links according to a simple rule XTC always produces a connected communication graph (provided the original graph is connected) Drawback: no upper bound on the number of physical neighbors 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Mobile networks Mobility: 1/10 Which is the impact of mobility on TC? – Increased message overhead: contrary to the stationary case, the protocol must be re-executed periodically in response to node mobility the “message efficiency” of the protocol is fundamental: protocols that exchange few messages to maintain the topology are needed – Non-uniform node distribution 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Mobility models Mobility: 2/10 Impact of mobility on TC depends on the mobility pattern Mobility models: – Random waypoint model: most widely used mobility model in the ad hoc networks community. Every node chooses uniformly at random a destination in [0,1] 2 , and moves towards it along a straight line with velocity chosen at random in [v min ,v max ]. When it reaches the destination, it rests for a time t pause , then it starts moving according to the same rule – Random direction model: nodes move with direction chosen uniformly at random in [0,2π [, and velocity chosen at random in [v min ,v max ]. After a randomly chosen time, the node chooses a new direction and velocity – Brownian motion: the node position at the next time step is chosen uniformly at random in a disk centered around the current node position 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica RWP and Random Direction Mobility Mobility: 3/10 RWP mobility (left) and Random Direction mobility (right). In case of RWP mobility, nodes tend to cross the center of the deployment region (border effect) 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The mobile CTR Mobility: 4/10 With homogeneous topology control, message overhead is not an issue, since the nodes’ transmitting range is set at the design stage and cannot be change dynamically However, the node spatial distribution generated by the mobility pattern could be an issue For instance, it is known that the RWP model generates non-uniform node spatial distribution [Bettstetter et al.03] On the other hand, the node distribution generated by random direction and Brownian mobility is very close to uniform [Blough et al.02b] 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The mobile CTR (2) Mobility: 5/10 Node distribution generated by the RWP model with different values of the pause time (from [Blough et al.02b]) Remark: the fact that the node spatial distribution generated by RWP mobility is not uniform should be carefully considered when simulating mobile ad hoc networks . value Optimal value of k for increasing values of n (from [Blough et al. 03]) Remark: setting k = 9 guarantees connectivity w.h.p. for values of n ranging from 50 to 50 0 5 th ACM MobiHoc – Tokyo, May 24,. waypoint model: most widely used mobility model in the ad hoc networks community. Every node chooses uniformly at random a destination in [0,1] 2 , and moves towards it along a straight line with. 2π/3 The obtained communication graph is made symmetric by adding the reverse edge to every unidirectional link A set of optimizations are also proposed, that prune energy-inefficient edges