Spatial and Temporal Relationship for Stochastic Networks 随机网络的时空观 Xinbing Wang Dept. of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

2 Related Work—A Partial View  At Year 2000, there are two ground breaking papers  A Partial View of Previous Work on Capacity Gupta & Kumar Grossglauser & Tse Neely Xiangyang Li Lei Ying Xiaojun Lin Guoqiang Mao, Pan Li, Zheng Wang, Chi Zhang, etc Garetto

3 Typical Related Work citation: 7640/6382  Scaling Laws (Gupta & Kumar [1]) citation: 7640/6382  Random placement  Protocol model  Random source-destination pairing  Result: maximal per node achievable rate scales as  Using multi-hop and geographic routing [1] P. Gupta, P. R. Kumar, “The Capacity of Wireless Network,” IEEE Trans. on Inf. Theory, vol. 46, no. 2, pp , Mar multi-hop transmission large scale wireless networks ground breaking work work pessimistic result

4 Typical Related Work  Mobile (Grossglauser & Tse [2]) citation: 2816/2134  i.i.d. mobility  Two-hop relay algorithm  Constant per-node capacity  Large delay [2] M. Grossglauser, D. Tse, “Mobility Increases the Capacity of Ad-hoc Wireless Networks,” in Proc. IEEE INFOCOM, vol. 3, pp , Apr Two-hop relay scheduling policy The first to achieve constant per-node capacity

5 Typical Related Work  Capacity-Delay Tradeoff (Neely [3]) citation: 257  i.i.d. mobility  Cell-partitioned network  Capacity vs Delay [3] M. J. Neely and E. Modiano, “Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks,” IEEE Transactions on Information Theory, vol. 51, no. 6, pp , June A cell-partitioned ad-hoc wireless network with C cells and N mobile users. The first to address the problem of capacity- delay tradeoff

6 Typical Related Work  Capacity in Heterogeneous Networks (Garretto [4]) citation: 34 citation: 34  Heterogeneous mobile network  Adjustable network size  Uniform and clustered model  Optimal per-node capacity in different heterogeneous level heterogeneous level [4] M. Garetto, P. Giaccone, and E. Leonardi, “Capacity scaling in delay tolerant networks with heterogeneous mobile nodes,” in ACM MobiHoc ’07, New York, NY, USA, 2007, pp. 41–50. Home point distribution of uniform and cluster model Per-node capacity vs network size n α The first to study capacity with heterogeneous mobility

7 Typical Related Work  Multicast (Xiangyang Li [5]) citation: 94  Static network  Manhattan routing tree  One source to k destinations  Capacity related to k [5] X. Li, “Multicast Capacity of Large Scale Wireless Ad Hoc Networks”, IEEE/ACM Trans. Networking, Vol.17, No. 3, pp , Jan The first to study multicast capacity Data copy Manhanttan Routing Tree

8 Other Related Work  Definition-based Capacity  [1] P. Gupta, P. R. Kumar, “The Capacity of Wireless Network,” IEEE Trans. on Inf. Theory, vol. 46, no. 2, pp , Mar  [2] P. Gupta, and P. R. Kumar, “Towards an Information Theory of Large Networks: An Achievable Rate Region,” IEEE Trans, Inf. Theory, IT -49,  [3] S. Toumpis, and A. J. Goldsmith, “Capacity Regions for Wireless Ad Hoc Networks,” IEEE Trans. Wireless Communications, V2, No. 4, July  [4] S. Ahmad, A. Jovicic, and P. Viswanath, “On Outer Bounds to the Capacity Region of Wireless Networks,” IEEE Trans, Inf. Theory, IT -52, No. 6, June  Interference-Model-based Capacity  [5] S. Li, Y. Liu, and X.-Y Li, “Capacity of large scale wireless networks under Gaussian channel model,” ACM MobiCom’08, Sep ,2008.  [6] M. Francescheti, O. Dousse, N. C. Tse and P. Thiran, “Closing the grap in the capacity of wireless network via percolation theory,” IEEE Trans, Inf. Theory, IT- 53, pp , No. 3, Mar., 2007.

9 Other Related Work  Network-Topology- based Capacity  [7] P. Li, C. Zhang and Y. Fang, “Capacity and Delay of Hybrid Wireless Broadband Access Networks,” IEEE Journal on Selected Areas in Communications, vol. 27, No. 2, pp , Feb  [8] B. Liu, P. Thiran and D. Towsley, “Capacity of a wireless ad hoc network with infrastructure,” Proceeding of ACM MobiHoc, Montreal, Quebec, Canada, September  [9]M. Garetto, P. Giaccone, and E. Leonardi, “Capacity scaling in delay tolerant networks with heterogeneous mobile nodes,” in ACM MobiHoc ’07, New York, NY, USA, 2007, pp. 41–50.  [10] U. Niesen, P.Gupta and D.Shah, “On capacity scaling in arbitrary wireless networks”, IEEE Trans. on Inf. Theory, vol.55.no. 9, Sept,  Traffic-Pattern-based Capacity  [11] A. KeshavarzHaddad, V. Ribeiro and R. Riedi, “Broadcast Capacity in Multihop Wireless Networks,” MobiCom’06, September, pp 23–26, 2006, Los Angeles, California, USA.  [12] S. Shakkottai, X. Liu and R. Srikant, “The Multicast Capacity of Large Multihop Wireless Networks,” MobiHoc’07, September 9–14, 2007, Montréal, Québec, Canada.  [13] X. Li, S. Tang, and F. Ophir, “Multicast capacity for large scale wireless ad hoc networks,” Proc. ACM Mobicom  [14]  [14] Z. Wang, H. Sadjadpour, J. J. Garcia-Luna-Aceves, “A Unifying Perpective on the Capacity of Wireless Ad Hoc Networks”, IEEE Infocom 2008.

10 Other Related Work  Capacity Improvement  [15] M. J. Neely and E. Modiano, “Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks,” IEEE Transactions on Information Theory, vol. 51, no. 6, pp , June  [16] S. Yi, Y. Pei and S. Kalyanaraman, “On the Capacity Improvement of Ad Hoc Wireless Networks Using Directional Antennas,” MobiHoc’03, Annapolis, Maryland, USA, June,  [17] C. Zhang, Y. Fang, X. Zhu, “Throughput-Delay Tradeoffs in Large-Scale MANETs with Network Coding,” INFOCOM 2009,pp  [18] A. Ozgur, O. Leveque and David N. C. Tse, “Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks,” IEEE Transactions on Information Theory, vol. 53, no. 10, Oct.,  [19] H. R. Sadjadpour, Z. Wang, and J.J. Garcia-Luna-Aceves, “The capacity of Wireless Ad Hoc Networks with Multi-Packet Reception,” IEEE Transactions on Communications, Vol. 58, No. 2, pp , February,  [20] P. Kyasanur and N. H. Vaidya, “Capacity of Multichannel Wireless Networks Under the Protocol Model,” IEEE/ACM Trans. on Networking, vol.17, no. 2, April 2009.

11 Our Initial Results ToN, TPDS, TMC, MobiHoc, INFOCOM, ICC, etc  Capacity Delay Tradeoff (ToN, TPDS, TMC, MobiHoc, INFOCOM, ICC, etc)  Multicast, Converge-cast  Delay and Capacity Tradeoff  Capacity in Cognitive Radio Networks ICDCS 2011  Coverage (ICDCS 2011) Mobicom 2009  Connectivity (Mobicom 2009) INFOCOM 2012  Topology (INFOCOM 2012) INFOCOM 2012  Computation (INFOCOM 2012)

Delay and Capacity Tradeoff Analysis for MotionCast  In this paper, we study capacity and delay tradeoffs for MotionCast. We utilize redundant packets transmissions to realize the tradeoff, and present the performance of the 2-hop relay algorithm without and with redundancy respectively.  We find that the capacity of the 2-hop relay algorithm without redundancy is better than that of static networks when And our tradeoff is better than that of directly extending the tradeoff for unicast to multicast. [1] Xinbing Wang, W. Huang, S. Wang, J. Zhang, C. Hu, "Delay and Capacity Tradeoff Analysis for MotionCast," in IEEE/ACM Transactions on Networking, Relay-destinations transmission. (a) Each packet delivered to a relay. (b) Each relay can make a packet into k similar cppies.

[2] Xinbing Wang, Y. Bei, Q. Peng, L. Fu, "Speed Improves Delay-Capacity Tradeoff in MotionCast," to appear in IEEE Transactions on Parallel and Distributed Systems, Speed Improves Delay-Capacity Tradeoff in MotionCast  In this paper, we study the relationship between mobility speed R and delay- capacity tradeoff ratio with multicast traffic pattern.  We show that there is a special turning point when mobility speed varies from zero to the scale of network.  In both LSRM and GSRM, as the number of destinations of each multicast session increases, the impact of mobility is more significant. Local-based Speed-Restricted Model (LSRM) Global-based Speed-Restricted Model (GSRM)

[3] W. Huang, Xinbing Wang, "Throughput and Delay Scaling of General Cognitive Networks," in IEEE INFOCOM 2011, Shanghai, China. 14 Throughput and Delay Scaling of General Cognitive Networks  All previous works consider specific primary networks with predefined communication schemes, and then design secondary protocols accordingly.  What is the performance of a general cognitive networks with arbitrary primary users?  In this paper, we show that the cognitive networks can perform as well as standalone networks under some general conditions.  Primary network operates at a SINR level slightly larger than reception threshold  Primary network employs round- robin TDMA like scheduling schemes or its traffic flows  The TX ranges of primary and secondary networks satisfy a condition

[4] Q. Peng, Xinbing Wang, H. Tang, "Heterogeneity Increases Multicast Capacity in Clustered Network," in IEEE INFOCOM 2011, Shanghai, China. 15 Heterogeneity Increases Multicast Capacity in Clustered Network  In this paper, we investigate the multicast capacity for static network with heterogeneous clusters. We study the effect of heterogeneities on the achievable capacity from two aspects, including heterogeneous cluster traffic (HCT) and heterogeneouscluster size (HCS). HCT means cluster clients are more likely to appear near the cluster head, instead of being uniformly distributed across the network and HCS means each cluster is also not equal in size as most prior literatures assume.  For this class of networks, we find that HCT increases network capacity for all the clusters and HCS only increases capacity for small clusters. Our work can generalize various results obtained under non- heterogeneous networks in the literature.

16  Our cooperative MIMO scheme in static networks breaks the bottleneck and can achieve an aggregate throughput of order 1.  Our cooperative MIMO scheme in MANETs can achieve a per-node throughput of Θ(1) while the delay is reduced to Θ(k) where k is the number of sources.  Our results well cover other traffic patterns and act as a generalization. Converge-Cast with MIMO [5] L. Fu, Y. Qin, Xinbing Wang, X. Liu, "Converge-Cast with MIMO," in IEEE INFOCOM 2011, Shanghai, China. Step 1: Preparing for cooperation with recursion Step 2: Multi-hop MIMO Transmission Step 3: Cooperative Reception

[6] Y. Wang, X. Chu, Xinbing Wang, Y. Cheng, "Optimal Multicast Capacity and Delay Tradeoffs in MANETs: A Global Perspective," in IEEE INFOCOM 2011, Shanghai, China. 17 Optimal Multicast Capacity and Delay Tradeoffs in MANETs: A Global Perspective  In our work, we give a global perspective of multicast capacity and delay analysis in Mobile Ad-hoc Networks (MANETs).  Specifically, we consider four node mobility models: 1. two-dimensional i.i.d. mobility; 2. two-dimensional hybrid random walk; 3. one-dimensional i.i.d. mobility; 4. one-dimensional hybrid random walk.  Two mobility time-scales are included: 1. Fast mobility; 2. Slow mobility.  We generalize the optimal delay-throughput tradeoffs in unicast traffic pattern and generalize the multicast capacity result under delay constraint when considering the two- dimensional i.i.d. fast mobility model.

18 Fundamental Lower Bound for Node Buffer Size in Intermittently Connected Wireless Networks  We study the lower bounds for node buffer in intermittently connected network.  In supercritical case, the achievable lower bound does not increase as the network size grows.  In subcritical case, the achievable lower bound is, where n is the number of nodes in the network.  In both cases, lower bounds for buffer occupation scales linearly to the length of time slot. [7] Y. Xu, Xinbing Wang, "Fundamental Lower Bound for Node Buffer Size in Intermittently Connected Wireless Networks," in IEEE INFOCOM 2011, Shanghai, China. Supercritical Case: active giant exists in each time slot Subcritical Case: no active giant in each time slot

19 Mobility Increases the Connectivity of K-hop Clustered Wireless Networks  We study the critical transmission range for conncecivity, k-hop clustered networks, random walk mobility with non-trivial velocity and i.i.d. mobility model.  Our results show that Mobility does improve connectivity in k-hop clustered networks, and it also significantly decreases the energy consumption and the power-delay trade-off. [8] ACM Mobicom 2009 [8] Q. Wang, X. Wang, X. Lin, "Mobility Increases the Connectivity of K-hop Clustered Wireless Networks," in Proc. of ACM Mobicom 2009, Beijing, September A summary of all the results achieved in this work.

[9] X. Wang, Xinbing Wang, J. Zhao, "Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks,“ in IEEE ICDCS 2011, Minneapolis, Minnesota, USA, Impact of Mobility and Heterogeneity on Coverage and Energy Consumption in Wireless Sensor Networks  In this paper, we have studied coverage in mobile and heterogeneous wireless sensor networks. Specifically, we have investigated asymptotic coverage under uniform deployment model with i.i.d. and 1-dimensional random walk mobility model, respectively.  Mobility is found to decrease sensing energy consumption. On the other hand, we demonstrate that heterogeneity increases energy consumption under 1-dimensional random walk mobility model but imposes no impact under the i.i.d. model. The k-coverage under Poisson deployment scheme with 2-dimensional random walk mobility model has been discussed, which also identifies the coverage improvement brought by mobility. Coverage Under 1-Dimensional Random Walk Mobility Model Coverage Under I.I.D Model

21 In-network computation:Preliminaries  Network Computation Overview  Recovery Random projections Transform basis Coefficient Random matrix (1) (2)

22 Problem Formulation  Computation Formulation  Measurements of n sensor nodes  Random Projections:  Compressive Sensing:  The target function can be represented as a : a random Gaussian or Bernoulli matrix. Multiround Random Linear Function:

Tree-based computation protocol with CS 23  Protocol  Intra-cell Protocol  Inter-cell Protocol Each cell head generates random coefficients receives the values from its child cell heads, computes the value of and transmits the result to the parent cell head. Computation is repeated for m rounds using different random coefficients.

24  通信 : 以传递真实信息为目的，对源信息比特进行的调制解调、 编解码、重传等操作。过程中不涉及对源信息的改变，网络传递的 是信息流（ information flow ）  计算 : 以处理信息为目的，对信息进行函数化操作。过程中涉及 的是信息函数（ information function ）  计算通信：以传递信息函数为目的，通过信息传递和信息处理的深 度耦合，同时运用计算和通信资源在网络传递函数流（ function flow ） 计算 通信 计算通信

25 Our Future Work—A New Perspective  The network structure in all the previous work is fixed and given in prior, ignoring both the spatial and temporal dynamic evolution:  Ad-hoc wireless network  Uniformly and independently distributed users  Independent mobility pattern between users  Network with both ad-hoc users and infrastructure support  The fixed network size and area  A new type of hybrid network is emerging with the development of Internet:  The combination of both wireless and wire lined devices.  New protocol design requirement on such new hybrid networks.  The feature of heterogeneity and variability of such networks.

26 Our Future Work—A New Perspective The previous work lacks the good understanding of the nature of wireless network:  The assumption of fixed network model.  Not applicable to other types of networks.  No deep reflection on inner relationship between capacity and delay. Study a new spatial and temporal based network model can help us better understand the nature of network topology and his temporal and spatial relationship as well as a more generalized model. Study a new spatial and temporal based network model can help us better understand the nature of network topology and his temporal and spatial relationship as well as a more generalized model. Why study such a new network?

27 Our Future Work—A New Perspective Our Goal of the Study Capacity in static hybrid network (the spatial relationship of information flow) Capacity in static hybrid network (the spatial relationship of information flow) Capacity (the spatial relationship of information flow), delay (the temporal relationship of information flow) and tradeoff in mobile hybrid network (the spatial and temporal relationship of information flow) Capacity (the spatial relationship of information flow), delay (the temporal relationship of information flow) and tradeoff in mobile hybrid network (the spatial and temporal relationship of information flow) Coverage of hybrid network (the spatial end-to- end relationship of network) Coverage of hybrid network (the spatial end-to- end relationship of network) Connectivity of hybrid network (the spatial and temporal end-to-end relationship of network) Connectivity of hybrid network (the spatial and temporal end-to-end relationship of network) Explore: Spatial, Temporal, Frequency, and Content’s correlations Explore: Spatial, Temporal, Frequency, and Content’s correlations The spatial impact node A has on its adjacent nodes and the temporal impact it has during the dynamic changing of its position.

28 Our Future Work—A New Perspective Challenges and open questions How to extract such new hybrid networks into mathematical models How to extract such new hybrid networks into mathematical models  Modeling of temporal and spatial relationship between nodes and information flows  Modeling of such new hybrid system Mathematical analysis of such networks may be very complicated. Mathematical analysis of such networks may be very complicated.  Difficult to analyze the inter-dependency of nodes’ behavior and information transfer

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