We study the scaling properties of a georouting scheme in a wireless multi-hop network of @math mobile nodes. Our aim is to increase the network capacity quasi linearly with @math while keeping the average delay bounded. In our model, mobile nodes move according to an i.i.d. random walk with velocity @math and transmit packets to randomly chosen destinations. The average packet delivery delay of our scheme is of order @math and it achieves the network capacity of order @math . This shows a practical throughput-delay trade-off, in particular when compared with the seminal result of Gupta and Kumar which shows network capacity of order @math and negligible delay and the groundbreaking result of Grossglausser and Tse which achieves network capacity of order @math but with an average delay of order @math . We confirm the generality of our analytical results using simulations under various interference models.
In the context of @cite_15 , the number of relays a packet has to traverse to reach its destination is @math . Consequently, @math must be divided by @math to get the useful capacity: @math . In order to ensure connectivity in the network, so that every source is able to communicate with its randomly chosen destination, @math must satisfy the limit @math . This leads to Gupta and Kumar's maximum capacity of @math with hot potatoes'' routing.
@cite_15
2138203492 2114578240 2952542244 2105520014
The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cut-set arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cut-set upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source-channel coding problem, and it is well known that the source-channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance-it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source-destination pair, capacity grows with the logarithm of the number of nodes. We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every rational number in (0, 1] is the routing capacity of some solvable network. We also determine the routing capacity for various example networks. Finally, we discuss the extension of routing capacity to fractional coding solutions and show that the coding capacity of a network is independent of the alphabet used We study the problem of optimal sequential ("as-you-go") deployment of wireless relay nodes as a person walks along a line of random length (with a known distribution). The objective is to create an impromptu multihop wireless network for connecting a packet source to be placed at the end of the line with a sink node located at the starting point, to operate in the light traffic regime. As the deployment person walks along the line from the sink towards the source, at every step, he measures the channel quality to one (or more) previously placed relays, and places the relay nodes based on these measurements, so as to minimize either the sum power or the maximum power from the source to the sink node in the resultant network, subject to a constraint on the expected number of relays placed. For each of these two objectives, two different relay selection strategies are considered: (i) each relay communicates with the sink via its immediate previous relay, (ii) the communication path can skip some of the deployed relays. With appropriate modeling assumptions, we formulate each of these problems as a Markov decision process (MDP). We provide the optimal policy structures for all these cases, and provide illustrations, via numerical results, for some typical parameters. The author studies a simple strategy, proposed independently by E.L. Hahne and R.G. Gallager (1986) and M.G.H. Katevenis (1987), for fairly allocating link capacity in a point-to-point packet network with virtual circuit routing. Each link offers its packet transmission slots to its user sessions by polling them in round-robin order. In addition, window flow control is used to prevent excessive packet queues at the network nodes. As the window size increases, the session throughput rates are shown to approach limits that are perfectly fair in the max-min sense. If each session has periodic input (perhaps with jitter) or has such heavy demand that packets are always waiting to enter the network, then a finite window size suffices to produce perfectly fair throughput rates. The results suggest that the transmission capacity not used by the small window session will be approximately fairly divided among the large window sessions. The focus is on the worst-case performance of round-robin scheduling with windows. >