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The Optimal Allocation problem is to determine what fraction (xi ) of the b code blocks should be sent on the ith path, subject to the path volume constraint, to maximize the overall probability of message delivery. Formally, let Y = n xi Si . Find (x 1 , x2 , . . ., xn ) that maximize Prob(Y i=1 r y1), where n xi = 1 and .i 1. . . n, 0 xi Vi /mr . i=1 By xing the replication factor and treating delay as a constraint, they formulate the problem as an optimal allocation problem and consider two cases of path failure scenarios: Bernoulli (0 1) path failure and partial path failures. In the Bernoulli path failure case, when a path fails, all the messages sent over the path are lost. In the partial path failure case, some messages can be recovered with certain probabilities. They proved that the optimal allocation problem under the Bernoulli path failure case, which is formulated as a mixed integer programming, is NP hard. For the partial path failure case, they rst show that maximizing the successful probability is equivalent to maximizing the Sharpe ratio, which plays an important role in the theory of allocation assets in investment portfolios (see references in reference 38 for more details). They propose to use approximation approaches from economic theory to maximize the ratio. The solution of the optimal allocation problem is static and does not change over time because it is assumed that the underlying path failure probability does not change over time. Instead of optimally allocating a xed portion of the coded blocks on each path from source to destination, it is proposed in reference 39 that coded blocks with replication factor r are equally split among the rst mr relays (or contacts), for some constant m. And those relays must deliver the coded blocks to the destination directly. The original message can be decoded as soon as m contacts deliver their data (that is, as soon as 1/r of the coded blocks have been received). The difference between this approach and the one presented in reference 38 is that this approach sends data dynamically to the rst m contacts the node meets (in other words, the allocation of the coded blocks is not xed). It also differs from the estimation-based approaches discussed in Section 8.3.2 in that it does not attempt to nd which contacts have better chances to deliver the data. Instead, it simply forwards to the rst m contacts the node meets (all contacts are equally good relays). Both analytic and simulation results show that the erasure coding-based forwarding in DTNs signi cantly improves the worst-case delay (compared with several other simple forwarding schemes). To further improve the performance of the forwarding protocols-based erasure coding, Liao et al. [41] propose to combine erasure coding and estimation based forwarding, which is referred to as estimation-based erasure coding (EBEC). The original messages are rst encoded (using an erasure coding scheme). The encoded messages are forwarded to different relays that have a higher chance of delivering the messages. Numerical results show that EBEC outperforms the scheme studied in reference 39. A probabilistic forwarding approach based on network coding is proposed for DTNs in reference 40. Recently, network coding has drawn a lot of attention in the networking research community. Instead of simply forwarding packets received,
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intermediate nodes can combine some of the packets received so far and send out as a new packet. For example, suppose that there are three nodes, A, B, and C. Nodes A and C want to exchange information through the middle node B. Node A rst transmits packet x to node B, and node C transmits packet y to node B. Node B broadcasts x or y (not x and y in sequence). Since node A has packet x and node C has packet y, node A can decode y and node C can decode packet x. For this example, it is easy to see that the number of transmissions is reduced when network coding is used. The basic idea in reference 40 is to use network coding to generate new packets. A coding vector is attached to each new packet. When a packet is received at a node, d new packets are generated and broadcast to the neighbors of the node, where d is referred to as a forwarding factor. When enough packets are received at the receiver, the original packet can be decoded. The value of d depends on the node density. Simulation results show that, for the given network setting in reference 40, for example, the packet deliver ratio using network coding is much higher than that under probabilistic forwarding and most of the packets are delivered with lower forwarding factor, see Figure 8.11 (originally shown in [40]).
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8.4 DISCUSSIONS AND FUTURE RESEARCH ISSUES In the previous sections, we classify routing protocols into different categories: deterministic routing, random forwarding, history-based forwarding, and so on. Based on the existing work and the unique characteristics of the DTN, it is apparent that many research issues remain to be solved in the area of DTNs. In this section, we list some of research issues that should be addressed and we hope that this will stimulate activity in the research community.
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