5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The mobile CTR (3) Mobility: 6/10 [SantiBlough02]: it is shown through simulation that a relatively modest increase (about 21%) of the transmitting range with respect to the critical value is sufficient to ensure full connectivity in case of RWP mobility Simulation results also show that the transmitting range can be considerably reduced (in the order of 35 - 40%) if the requirement for connectivity is only on 90% of the network operational time (giant component) An analytical result [Santi04]: if we denote with r p the CTR with RWP mobile networks when the pause time is p>0 and v min = v max = v, we have w.h.p. If p = 0, then r 0 >> Sqrt (ln n / n) w.h.p. n n p v p r p ! ln 521405.0 + = 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica The mobile CTR (4) Mobility: 7/10 CTR in case of stationary and RWP mobile networks (from [Santi04]) Remark: note the “threshold phenomenon”: for n ≤ 50, r p when p = 0 is smaller than the CTR for the stationary case, while when n > 50 the situation is reversed 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Non-homogeneous TC Mobility: 8/10 In case of non-homogeneous TC: more relevant effect of mobility is the message overhead needed to maintain the desired topology Overhead depends on the frequency with which the reconfiguration procedure is executed, which in turn depends on: – The mobility pattern – The properties of the topology generated by the protocol Example: MST-based vs. k-neighbor based TC – The message overhead needed to build the MST is much larger than that needed to build the k-neighbors graph – Given the same mobility pattern, the MST should be reconfigured much more frequently than the k-neighbors graph k-neighbor based TC is more resilient to mobility than MST-based TC 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Mobile TC protocols Mobility: 9/10 In order to be resilient to mobility, a TC protocol should be based on local information only Many protocols presented in the literature enjoy this property, but only some of them have been adapted to explicitly deal with node mobility – [Li et al.01a]: a reconfiguration protocol for CBTC that deals with mobility is presented – [RodopluMeng99]: the authors discuss how their protocol can be adapted to the mobile scenario – MobileGrid [LiuLi02] and LINT [RamanathanRosales-Hain00] k-neighbors based protocols are explicitly designed to deal with mobility 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Mobility: a final observation Mobility: 10/10 More subtle effect of mobility on k-neighbors based TC protocols: – Non-uniform node distribution in case of RWP mobility This fact should be carefully considered in setting the “optimal value” of k In general, we might expect that the “optimal value” of k in presence of RWP mobility is larger than in the stationary case (similar to the CTR case) How much larger? Open issue 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Open issues Open issues: 1/11 Considerable body of research devoted to TC in ad hoc networks, but several aspects have not been carefully investigated yet We can classify these “open fields” for research into three areas: – More realistic (network and energy) models – More accurate analysis of mobile networks – Considering the effect of multi-hop data traffic 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica More realistic network models Open issues: 2/11 Ad hoc network model used in this presentation is widely accepted, but it is a very idealized model of a real wireless network Main limitation of this model: assumption that the radio coverage area is a perfect circle In realistic scenarios: radio coverage area influenced by many factors (obstacles, buildings, existing infrastructure, weather conditions, etc.), and it is hardly regular Including too many details in the network model would make it extremely complicated and scenario dependent On the other hand, current network model is maybe too simplistic, at least to derive quantitative results 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica A more realistic network model Open issues: 3/11 An example of a more realistic wireless channel model could be the following: – The occurrence of wireless links between units is probabilistic: o For instance, we might have a link with probability 1 if δ(u,v) < c, for some value of c, and with probability p(δ(u,v)) < 1 otherwise – We might assume that the link probability is a non-increasing function of the distance – With this model, the radio coverage area in general is not regular A similar model has been proposed in [Farago02] Open issue: characterize network connectivity under this network model 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Impact of interferences Open issues: 4/11 Another possibility for more realistic models is considering interferences between nodes Preliminary step in this direction: [Dousse et al.03] – A bi-directional link between u and v exists if the signal to noise ratio at the receiver is larger than some threshold – The noise is the sum of the interferences of other nodes and background noise – The authors analyze the impact of this wireless link model on network connectivity Further investigation in this direction is needed 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica More realistic node distributions Open issues: 5/11 Most of the analytical results presented in the literature assume a uniform node distribution This assumption seems reasonable in some settings, but it is unrealistic in many scenarios (e.g., RWP mobility) Open issues: define “realistic” node distributions, and analyze network connectivity (and other network properties) using these distributions . issue 5 th ACM MobiHoc – Tokyo, May 24, 2004 Istituto di Informatica e Telem atica Open issues Open issues: 1/11 Considerable body of research devoted to TC in ad hoc networks, but several. very idealized model of a real wireless network Main limitation of this model: assumption that the radio coverage area is a perfect circle In realistic scenarios: radio coverage area influenced by many. influenced by many factors (obstacles, buildings, existing infrastructure, weather conditions, etc.), and it is hardly regular Including too many details in the network model would make it extremely complicated