Achieving optimal transmission throughput in data networks in a multi-hop wireless networks is fundamental but hard problem. The situation is aggravated when nodes are mobile. Further, multi-rate system make the analysis of throughput more complicated. In mobile scenario, link may break or be created as nodes are moving within communication range. Route Discovery' which is to find the optimal route and transmission schedule is an important issue. Route discovery entails some cost; so one would not like to initiate discovery too often. On the other hand, not discovering reasonably often entails the risk of being stuck with a suboptimal route and or schedule, which hurts end-to-end throughput. The implementation of the routing decision problem in one dimensional mobile ad hoc network as Markov decision process problem is already is discussed in the paper [1]. A heuristic based on threshold policy is discussed in the same paper without giving a way to find the threshold. In this paper, we suggested a rule for setting the threshold, given the parameters of the system. We also point out that our results remain valid in a slightly different mobility model; this model is a first step towards an open' network in which existing relay nodes can leave and or new relay nodes can join the network.
In paper @cite_5 , the authors discussed the route discovery initiation to reduce the frequency of flooding request by elongating the link duration of the selected paths. In @cite_11 , the authors suggested extension in storing multiple paths as route rather than unipath as route .
@cite_5 @cite_11
2170526908 2568950526 2045494719 1985418124
Flooding-based approaches are incorporated in reactive routing protocols as the fundamental strategy for route discovery. They overtly affect traffic as the frequency of route discovery increases along with the mobility of users in a mobile ad hoc network (MANET). This paper presents a scheme for reducing overall traffic and end-to-end delay in highly MANET networks. Firstly a new routing algorithm is proposed to reduce the frequency of flood requests by elongating the link duration of the selected paths. In order to increase the path duration, non-disjoint paths are also considered. This concept is a novel approach in route discovery as previous reactive routing protocols seek only disjoint paths. Secondly another novel approach is presented to estimate the link expiration time without the need for global positioning system (GPS) devices. To prevent broadcast storms that may be intrigued during the path discovery operation, another scheme is also introduced. The basic concept behind the proposed scheme is to broadcast only specific and well-defined packets, referred to as "best packets" in the paper. The new protocol is simulated with regard to traffic overhead. Although our main aim in this paper is to reduce the net control traffic in a MANET network, there are other benefits arising from the proposed schemes, namely the increase in link duration, reduction in the end-to-end communication delay, less disruption in data flow, and fewer path setups. We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 An edge-Markovian process with birth-rate p and death-rate q generates sequences of graphs (G0,G1,G2,…) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e ∉ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e ∉ E(Gt) with probability q. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time--flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t∦ > t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we also show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is k-active if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the k-active flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show that it is even constant whenever the ratio p (p + q) exceeds log n n. Moreover, we also show that being active for a number of steps equal to the reachability threshold (up to a multiplicative constant) allows the flooding protocol to complete in optimal time, i.e., in asymptotically the same number of steps as when being perpetually active. These results demonstrate that flooding can be implemented in a practical and efficient manner in dynamic graphs. The main ingredient in the proofs of our results is a reduction lemma enabling to overcome the time dependencies in edge-Markovian dynamic graphs. We consider the application of route planning in large public-transportation networks (buses, trains, subways, etc). Many connections in such networks are operated at periodic time intervals. When a set of connections has sufficient periodicity, it becomes more efficient to store the time range and frequency (e.g., every 15 minutes from 8:00am-6:00pm) instead of storing each of the time events separately. Identifying an optimal frequency-compression is NP-hard, so we present a time- and space-efficient heuristic. We show how we can use this compression to not only save space but also query time. We particularly consider profile queries, which ask for all optimal routes with departure times in a given interval (e.g., a whole day). In particular, we design a new version of Dijkstra's algorithm that works with frequency-based labels and is suitable for profile queries. We evaluate the savings of our approach on two metropolitan and three country-wide public-transportation networks. On our largest network, we simultaneously achieve a better space consumption than all previous methods as well as profile query times that are about 5 times faster than the best previous method. We also improve Transfer Patterns, a state-of-the-art technique for fully realistic route planning in large public-transportation networks. In particular, we accelerate the expensive preprocessing by a factor of 60 compared to the original publication.