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Issue No.06 - June (2012 vol.11)

pp: 970-982

Luoyi Fu , Shanghai Jiaotong University, Shanghai

Xiaohua Tian , Shanghai Jiaotong University, Shanghai

Yuanzhe Bei , Shanghai Jiaotong University, Shanghai

Qiuyu Peng , Shanghai Jiaotong University, Shanghai

Xiaoying Gan , Shanghai Jiaotong University, Shanghai

Hui Yu , Shanghai Jiaotong University, Shanghai

Jing Liu , Shanghai Jiaotong University, Shanghai

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TMC.2011.110

ABSTRACT

In this paper, we define an ad hoc network where multiple sources transmit packets to one destination as Converge-Cast network. We will study the capacity delay tradeoffs assuming that n wireless nodes are deployed in a unit square. For each session (the session is a dataflow from k different source nodes to 1 destination node), k nodes are randomly selected as active sources and each transmits one packet to a particular destination node, which is also randomly selected. We first consider the stationary case, where capacity is mainly discussed and delay is entirely dependent on the average number of hops. We find that the per-node capacity is \Theta (1/\sqrt{n\log n}) (given nonnegative functions f(n) and g(n){:} f(n) = O(g(n)) means there exist positive constants c and m such that f(n) \le cg(n) for all n \ge m; f(n)=\Omega (g(n)) means there exist positive constants c and m such that f(n)\ge cg(n) for all n \ge m; f(n) = \Theta (g(n)) means that both f(n) =\Omega (g(n)) and f(n) = O(g(n)) hold), which is the same as that of unicast, presented in [CHECK END OF SENTENCE]. Then, node mobility is introduced to increase network capacity, for which our study is performed in two steps. The first step is to establish the delay in single-session transmission. We find that the delay is \Theta (n\log k) under 1-hop strategy, and \Theta (n\log k/m) under 2-hop redundant strategy, where m denotes the number of replicas for each packet. The second step is to find delay and capacity in multisession transmission. We reveal that the per-node capacity and delay for 2-hop nonredundancy strategy are \Theta (1) and \Theta (n\log k), respectively. The optimal delay is \Theta (\sqrt{n\log k}+k) with redundancy, corresponding to a capacity of \Theta (\scriptstyle \sqrt{{1\over n\log k} }+{k\over n\log k} ). Therefore, we obtain that the capacity delay tradeoff satisfies delay/rate \ge \Theta (n\log k) for both strategies.

INDEX TERMS

Converge cast, capacity, delay.

CITATION

Luoyi Fu, Xiaohua Tian, Yuanzhe Bei, Qiuyu Peng, Xiaoying Gan, Hui Yu, Jing Liu, "Converge Cast: On the Capacity and Delay Tradeoffs",

*IEEE Transactions on Mobile Computing*, vol.11, no. 6, pp. 970-982, June 2012, doi:10.1109/TMC.2011.110REFERENCES

- [1] M.J. Neely and E. Modiano, “Capacity and Delay Tradeoffs for Ad Hoc Mobile Networks,”
IEEE Trans. Information Theory, vol. 51, no. 6, pp. 1917-1937, June 2005.- [2] X. Wang, W. Huang, S. Wang, J. Zhang, C. Hu, “Delay and Capacity Tradeoff Analysis for MotionCast,”
IEEE/ACM Trans. Networking, vol. 19, no. 5, pp. 1354-1367, Oct. 2011, doi:10.1109/TNET.2011.2109042. - [3] P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks,”
IEEE Trans. Information Theory, vol. 46, no. 2, pp. 388-404, Mar. 2000.- [4] F. Xue and P. Kumar,
Scaling Laws for Ad-Hoc Wireless Networks: An Information Theoretic Approach. Now Publishers Inc., 2006.- [5] X.-Y. Li, S.-J. Tang, and O. Frieder, “Multicast Capacity for Large Scale Wireless Ad Hoc Networks,”
Proc. ACM MobiCom, Sept. 2007.- [6] M. Grossglauser and D.N.C. Tse, “Mobility Increases the Capacity of Ad Hoc Wireless Networks,”
IEEE/ACM Trans. Networking, vol. 10, no. 4, pp. 477-486, Aug. 2002.- [7] X. Lin and N.B. Shroff, “The Fundamental Capacity-Delay Tradeoff in Large Mobile Wireless Networks,” technical report, http://cobweb.ecn.purdue.edu/linxpapers.html , 2004.
- [8] S. Shakkottai, X. Liu, and R. Srikant, “The Multicast Capacity of Large Multihop Wireless Networks,”
Proc. ACM MobiHoc, Sept. 2007.- [9] S. Zhou and L. Ying, “On Delay Constrained Multicast Capacity of Large-Scale Mobile Ad-Hoc Networks,”
Proc. IEEE INFOCOM, 2010.- [10] P. Li, Y. Fang, and J. Li, “Throughput, Delay, and Mobility in Wireless Ad Hoc Networks,”
Proc. IEEE INFOCOM, 2010.- [11] X.-Y. Li, S.-J. Tang, and O. Frieder, “Multicast Capacity for Large Scale Wireless Ad Hoc Networks,”
Proc. ACM MobiCom, Sept. 2007.- [12] L.-L. Xie and P.R. Kumar, “On the Path-Loss Attenuation Regime for Positive Cost and Linear Scaling of Transport Capacity in Wireless Networks,”
IEEE Trans. Information Theory, vol. 52, no. 6, pp. 2313-2328, June 2006.- [13] X. Lin, G. Sharma, R.R. Mazumdar, and N.B. Shroff, “Degenerate Delay-Capacity Trade-Offs in Ad Hoc Networks with Brownian Mobility,”
Joint Special Issue of IEEE Trans. Information Theory and IEEE/ACM Trans. Networking on Networking and Information Theory, vol. 52, no. 6, pp. 2777-2784, June 2006.- [14] G. Sharma and R. Mazumdar, “Scaling Laws for Capacity and Delay in Wireless Ad Hoc Networks with Random Mobility,”
Proc. IEEE Int'l Conf. Comm., 2004.- [15] J. Mammen and D. Shah, “Throughput and Delay in Random Wireless Networks with Restricted Mobility,”
IEEE Trans. Information Theory, vol. 53, no. 3, pp. 1108-1116, Mar. 2007.- [16] G. Zhang, Y. Xu, X. Wang, and M. Guizani, “Capacity of Hybrid Wireless Networks with Directional Antenna and Delay Constraint,”
IEEE Trans. Comm., vol. 58, no. 7, pp. 2097-2106, July 2010.- [17] S. Shakkottai, X. Liu, and R. Srikant, “The Multicast Capacity of Large Multihop Wireless Networks,”
Proc. ACM MobiHoc, Sept. 2007.- [18] L. Ying, S. Yang, and R. Srikant, “Coding Achieves the Optimal Delay-Throughput Tradeoff in Mobile Ad Hoc Networks: A Hybrid Random Walk Model with Fast Mobiles,”
Proc. Information Theory and Application Workshop (ITA), 2007.- [19] U. Lee, S.-Y. Oh, K.-W. Lee, and M. Gerla, “RelayCast: Scalable Multicast Routing in Delay Tolerant Networks,”
Proc. ACM Int'l Conf. Network Protocol (ICNP '08), Oct. 2008.- [20] L. Ying, S. Yang, and R. Srikant, “Optimal Delay-Throughput Trade-Offs in Mobile Ad-Hoc Networks,”
IEEE Trans. Information Theory, vol. 9, no. 54, pp. 4119-4143, Sept. 2008.- [21] X. Wang, Y. Bei, Q. Peng, and L. Fu, “Speed Improves Delay-Capacity Tradeoff in MotionCast,”
IEEE Trans. Parallel and Distributed Systems, vol. 22, no. 5, pp. 729-742, May 2011, doi: 10.1109/TPDS.2010.126. - [22] S. Toumpis and A.J. Goldsmith, “Large Wireless Networks under Fading, Mobility, and Delay Constraints,”
Proc. IEEE INFOCOM, Mar. 2004.- [23] A. El-Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Optimal Throughput-Delay Scaling in Wireless Networks - Part I: The Fluid Model,”
IEEE Trans. Information Theory, vol. 52, no. 6, pp. 2568-2592, June 2006.- [24] A. El-Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Optimal Throughput-Delay Scaling in Wireless Networks - Part II: Constant-Size Packets,”
IEEE Trans. Information Theory, vol. 52, no. 11, pp. 5111-5116, Nov. 2006.- [25] P. Zhang, C.M. Sadler, S.A. Lyon, and M. Martonosi, “Hardware Design Experiences in Zebranet,”
Proc. ACM Int'l Conf. Embedded Networked Sensor Systems (SenSys), 2004.- [26] M. Zhao, M. Ma, and Y. Yang, “Mobile Data Gathering with Space-Division Multiple Access in Wireless Sensor Networks,”
Proc. IEEE INFOCOM, Apr. 2008.- [27] K. Ota, M. Dong, and X. Li, “TinyBee: Mobile-Agent-Based Data Gathering System in Wireless Sensor Networks,”
Proc. IEEE Int'l Conf. Network, Architecture, and Storage, 2009.- [28] L. Ying, S. Yang, and R. Srikant, “Optimal Delay-Throughput Trade-Offs in Mobile Ad Hoc Networks,”
IEEE Trans. Information Theory, vol. 54, no. 9, pp. 4119-4143, Sept. 2008.- [29] M. Garetto, P. Giaccone, and E. Leonardi, “Capacity Scaling in Ad Hoc Networks with Heterogeneous Mobile Nodes: The Super-Critical Regime,”
IEEE/ACM Trans. Networking, vol. 17, no. 5, pp. 1522-1535, Oct. 2009.- [30] M. Garetto, P. Giaccone, E. Leonardi, “Capacity Scaling in Ad Hoc Networks with Heterogeneous Mobile Nodes: The Sub-Critical Regime,”
ACM/IEEE Trans. Networking, vol. 17, no. 6, pp. 1888-1901, Dec. 2009.- [31] D. Ciullo, V. Martina, M. Garetto, E. Leonardi, “Impact of Correlated Mobility on Delay-Throughput Performance in Mobile Ad-Hoc Networks,”
Proc. IEEE INFOCOM, Mar. 2010. |