Converge-Cast: On the Capacity and Delay Tradeoffs

1. Converge-Cast: On the Capacity and DelayTradeoffs Xinbing Wang Luoyi Fu Xiaohua Tian Qiuyu PengXiaoying Gan Hui Yu Jing Liu Department of Electronic EngineeringShanghai Jiao Tong University, China Congerve-Cast: On the Capacity Delay Tradeoffs

2. Outline Introduction Motivations Objectives Models and Definitions Converge-Cast Capacity of Stationary Network Converge-Cast Capacity and Delay in MANET Conclusion and Future Work Congerve-Cast: On the Capacity Delay Tradeoffs 2

3. Motivation • Capacity of wireless ad hoc network is not scalable: in a static • ad hoc wireless network with n nodes, the per-node capacity is • limited as . Interference is the main reason behind. • Mobility is utilized to increase the network capacity to . Interference is localized. [1] P. Gupta and P. R. Kumar, “The capacity of wireless networks”, in IEEETransaction on Information Theory, 2000. [2] M. Grossglauser and D. N. C. Tse, “Mobility increases the capacityof ad hoc wireless networks,” IEEE/ACM Transactions on Networking. 2002. Congerve-Cast: On the Capacity Delay Tradeoffs

4. Motivation • Converge-cast traffic is of significant value and has drawn much attention recently. • Monitoring & Alarming System [3] • Wireless sensor Network [4] [3] P. Zhang, C. M. Sadler, S. A. Lyon, and M. Martonosi,“Hardware designexperiences in zebranet,” in Proc. ACM SenSys 2004, NY, USA. [4] M. Zhao, M. Ma and Y. Yang, “Mobile data gathering withspace-division multiple access in wireless sensor networks,” in Proc. IEEE INFOCOM 2008, Phoenix, Arizona, Apr. 2008. Congerve-Cast: On the Capacity Delay Tradeoffs

5. Motivation • Converge-cast traffic pattern is a generalized version of unicast traffic and shares a similar configuration with multicast traffic [5] in that the information dissemination can both be modeled as a spanning tree. [5] Xiang-Yang Li, “Multicast Capacity of Wireless Ad Hoc Networks”, inIEEE/ACM Transaction on Networking, January, 2008. Congerve-Cast: On the Capacity Delay Tradeoffs

6. Objective • Both unicast and multicast capacity have been extensively studied in static & mobile ad hoc network. • There has been few works dealing with converge-cast network. What are the congverge-cast capacity and delay in stationary and mobile ad hoc network? Congerve-Cast: On the Capacity Delay Tradeoffs

7. Outline Introduction Models and Definitions Stationary network Mobile network Converge-Cast Capacity of Stationary Network Converge-Cast Capacity and Delay in MANET Conclusion and Future Work Congerve-Cast: On the Capacity Delay Tradeoffs 7

8. Stationary Network • n nodes are randomly distributed in the unit square and remain static. • A Common transmission range is adopted by all the nodes to guarantee network connectivity. • For each converge-cast session, k sources and 1 destination are randomly selected from the n nodes. There are n sessions existed in the network. Congerve-Cast: On the Capacity Delay Tradeoffs

9. Stationary Network • The network model is similar to the that of multicast network. The only difference is that the multicast spanning tree is reversed. Converge-cast Spanning Tree Multicast Spanning Tree Congerve-Cast: On the Capacity Delay Tradeoffs

10. Stationary Network • Transmission Protocol: Protocol Model Definition: Let denote the distance between node i and node j, and the common transmission range, then a transmission from i to j is successful if for any other node k transmitting simultaneously. Congerve-Cast: On the Capacity Delay Tradeoffs Heterogeneity Increases Multicast Capacity in Clustered Network 10

11. Mobile Network • n nodes are moving according to an independent identically distributed mobility model. • Cell partitioned model is assumed to model the interference, which is identical to [6]. • For each converge-cast session, k sources and 1 destination are randomly selected from the n nodes. There are n sessions existed in the network. (identical to stationary network) [6] M. J. Neely, and E. Modiano, “Capaicty and delay tradeoffs forad hoc mobile networks,” IEEE Transactions on InformationTheory, vol. 51, no. 6, pp. 1917-1937, Jun. 2005. Congerve-Cast: On the Capacity Delay Tradeoffs

12. Mobile Network • Mobility Model: independent identically distributed model • A simplified mobility model • Mathematical Tractability • Give an upper bound of the theoretical result Congerve-Cast: On the Capacity Delay Tradeoffs

13. Mobile Network • Transmission Protocol: Cell partitioned network • Nodes in the same cell are permitted to communicate • 9-TDMA is assumed to avoid inter-cell interference Congerve-Cast: On the Capacity Delay Tradeoffs

14. Mobile Network • The traffic pattern is also similar to the that of multicast network. The only difference is that the information is sent from k mobiles to the common destination. Congerve-Cast: On the Capacity Delay Tradeoffs Congerve-Cast: On the Capacity Delay Tradeoffs 14

15. Mobile Network • Sending Pool: packets that are sampled by the node itself. When a new session starts, a new packet is produced and duplicated m times if the node is selected as source. • Relaying pool: packets that are sampled by other node and will be sent to other destinations. When this node meets another node which is the destination of one of the packets P in the relaying pool, the packet P will be delivered to the receiving pool. • Receiving pool: packets that are designated for itself. When this node meets another node which contains a packet P, the packet P will be delivered to the receiving pool in this node. Congerve-Cast: On the Capacity Delay Tradeoffs

16. Introduction • Models and Definitions • Converge-Cast Capacity of Stationary Network • Converge-Cast Capacity and Delay in MANET • Conclusion and Future Work Congerve-Cast: On the Capacity Delay Tradeoffs

17. Capacity of Stationary Network • Delay is usually not considered in static network because it only relates with the number of hops. • An efficient way to estimate the upper bound in static converge-cast networks is to study its redundancy under the pattern. Theorem 5.1: The total capacity for random stationary ad hoc network with one-hop strategy is with per-node throughput . Congerve-Cast: On the Capacity Delay Tradeoffs

18. Capacity of Stationary Network • Relays are necessary according to protocol model, yet Theorem 5.1 only shows the capacity of static ad hoc network with no relays. Then the whole transmission route can be treated as a chain whose length can be treated as redundancy because the whole transmission utilizes the same number of transmissions. • For unicast, the average redundancy is ,then the total capacity is ; For multicast, the average number of edges of the spanning tree is • , then the total capacity is • For Converge-cast network, we get the same result as unicast network, so the total capacity is identical to unicast network. Congerve-Cast: On the Capacity Delay Tradeoffs

19. Introduction • Models and Definitions • Converge-Cast Capacity of Stationary Network • Converge-Cast Capacity and Delay in MANET • Delay of Single Session in MANET • Delay and Capacity of Multi-session in MANET • Conclusion and Future Work Congerve-Cast: On the Capacity Delay Tradeoffs Congerve-Cast: On the Capacity Delay Tradeoffs 19

20. Delay of Single Session in MANET • In mobile ad hoc network, delay should be taken into consideration and it deals with both routing scheme and mobility pattern. • The delay consists of two types of delays: transmission delay and queuing delay. However, transmission delay can be ignored since there are at most 2 hops in this model and such assumption does not change the order of the result. • The total delay is defined as the maximum of k delays: Congerve-Cast: On the Capacity Delay Tradeoffs

21. Delay of Single Session in MANET • Delay estimation of 1-hop algorithm • Only source-destination transmission is allowed. • Delay estimation of 2-hop algorithm • Both source-relay and relay-destination transmission are allowed and taken into consideration. Congerve-Cast: On the Capacity Delay Tradeoffs

22. Capacity Delay of Multi-Session • Case I: without redundancy • The delay is the same as the 1-hop algorithm • It does not improve the delay and capacity in ad hoc networks. • The per-node capacity is , which is identical to unicast network in MANET. Congerve-Cast: On the Capacity Delay Tradeoffs

23. Capacity Delay of Multi-Session • Case II: with redundancy • The delay is the same as the 2-hop algorithm • delay and capacity tradeoff is improved in ad hoc networks. • We obtain an optimal per-node capacity and delay tradeoff as follows: Congerve-Cast: On the Capacity Delay Tradeoffs

24. Introduction • Models and Definitions • Converge-Cast Capacity of Stationary Network • Converge-Cast Capacity and Delay in MANET • Conclusion and Future Work Congerve-Cast: On the Capacity Delay Tradeoffs Congerve-Cast: On the Capacity Delay Tradeoffs 24

25. Conclusion • For stationary network, we find that the achievable capacity is the same as the unicast case. The comparison is as follows: • For mobile network, we derive the capacity and delay with and without redundancy. The comparison is as follows: Congerve-Cast: On the Capacity Delay Tradeoffs

26. Conclusion • We make a comparison among the unicast, multicast, converge-cast capacity delay tradeoffs of both stationary and mobile ad hoc network. Congerve-Cast: On the Capacity Delay Tradeoffs

27. Conclusion • The impact of base station is investigated in both unicast and multicast network. However, it is still unknown whether it can improve the performance in converge-cast network. • We assume a fast mobility model in this work, which means the time scale of node moving is identical to the time slot for data transmission. When the node speed is not that fast, multihop transmission is allowed. • In this work, we only consider i.i.d mobility pattern, which is unreal for the real world. We can also investigate the capacity under some more practical mobility model, e.g. random walk, random way point mobility models. Congerve-Cast: On the Capacity Delay Tradeoffs

28. Thank you for listening Congerve-Cast: On the Capacity Delay Tradeoffs