Converge-Cast: On the Capacity and DelayConverge-Cast: On the Capacity and DelayTradeoffsTradeoffs

Xinbing Wang Luoyi Fu Xiaohua Tian Qiuyu Peng Xiaoying Gan Hui Yu Jing Liu

Department of Electronic EngineeringShanghai Jiao Tong University, China

04/20/23 Congerve-Cast: On the Capacity Delay Tradeoffs 1

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OutlineOutline

IntroductionIntroduction MotivationsMotivations ObjectivesObjectives

Models and DefinitionsModels and Definitions

Converge-Cast Capacity of Stationary NetworkConverge-Cast Capacity of Stationary Network

Converge-Cast Capacity and Delay in MANETConverge-Cast Capacity and Delay in MANET

Conclusion and Future WorkConclusion and Future Work

Congerve-Cast: On the Capacity Delay Tradeoffs 2

MotivationMotivation

Capacity of wireless ad hoc network is not scalable: in a staticCapacity of wireless ad hoc network is not scalable: in a static

ad hoc wireless network with n nodes, the per-node capacity is ad hoc wireless network with n nodes, the per-node capacity is

limited as . Interference is the main reason behind.limited as . Interference is the main reason behind.

Mobility is utilized to increase the network capacity to . Mobility is utilized to increase the network capacity to . Interference is localized. Interference is localized.

[1]1( )

logO

n n

[1] P. Gupta and P. R. Kumar, “The capacity of wireless networks”, in IEEE Transaction

on Information Theory, 2000.

Congerve-Cast: On the Capacity Delay Tradeoffs 3

[2] M. Grossglauser and D. N. C. Tse, “Mobility increases the capacity of ad hoc wireless

networks,” IEEE/ACM Transactions on Networking. 2002.

[2](1)O

Congerve-Cast: On the Capacity Delay Tradeoffs 4

MotivationMotivation Converge-cast traffic is of significant value and has drawn much Converge-cast traffic is of significant value and has drawn much

attention recently. attention recently. Monitoring & Alarming System [3]Monitoring & Alarming System [3] Wireless sensor Network [4]Wireless sensor Network [4]

[3] P. Zhang, C. M. Sadler, S. A. Lyon, and M. Martonosi, “Hardware design experiences in zebranet,” in

Proc. ACM SenSys 2004, NY, USA.

[4] M. Zhao, M. Ma and Y. Yang, “Mobile data gathering with space-division multiple access in wireless

sensor networks,” in Proc. IEEE INFOCOM 2008, Phoenix, Arizona, Apr. 2008.

MotivationMotivation

Converge-cast traffic pattern is a generalized version of unicast Converge-cast traffic pattern is a generalized version of unicast traffic and shares a similar configuration with multicast traffic [5] traffic and shares a similar configuration with multicast traffic [5] in that the information dissemination can both be modeled as a in that the information dissemination can both be modeled as a spanning tree. spanning tree.

[5] Xiang-Yang Li, “Multicast Capacity of Wireless Ad Hoc Networks”, in IEEE/ACM Transaction on

Networking, January, 2008.

Congerve-Cast: On the Capacity Delay Tradeoffs 5

Congerve-Cast: On the Capacity Delay Tradeoffs 6

ObjectiveObjective

Both unicast and multicast capacity have been extensively Both unicast and multicast capacity have been extensively studied in static & mobile ad hoc network.studied in static & mobile ad hoc network.

There has been few works dealing with converge-cast network.There has been few works dealing with converge-cast network.

What are the congverge-cast capacity and delay in What are the congverge-cast capacity and delay in stationary and mobile ad hoc network? stationary and mobile ad hoc network?

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OutlineOutline

IntroductionIntroduction

Models and DefinitionsModels and Definitions Stationary networkStationary network Mobile networkMobile network

Converge-Cast Capacity of Stationary NetworkConverge-Cast Capacity of Stationary Network

Converge-Cast Capacity and Delay in MANETConverge-Cast Capacity and Delay in MANET

Conclusion and Future WorkConclusion and Future Work

Congerve-Cast: On the Capacity Delay Tradeoffs 7

Congerve-Cast: On the Capacity Delay Tradeoffs 8

Stationary NetworkStationary Network

n nodes are randomly distributed in the unit square and remain n nodes are randomly distributed in the unit square and remain static.static.

A Common transmission range is adopted by all the A Common transmission range is adopted by all the nodes to guarantee network connectivity.nodes to guarantee network connectivity.

For each converge-cast session, For each converge-cast session, k k sources and sources and 11 destination are destination are randomly selected from therandomly selected from the n n nodesnodes. . There are There are nn sessions sessions existed in the network.existed in the network.

log( )

nr

n

Congerve-Cast: On the Capacity Delay Tradeoffs 9

Stationary NetworkStationary Network

The network model is similar to the that of multicast network. The The network model is similar to the that of multicast network. The only difference is that the multicast spanning tree is reversed. only difference is that the multicast spanning tree is reversed.

Multicast Spanning TreeMulticast Spanning Tree Converge-cast Spanning TreeConverge-cast Spanning Tree

Congerve-Cast: On the Capacity Delay Tradeoffs 10

Stationary NetworkStationary Network Transmission Protocol: Protocol ModelTransmission Protocol: Protocol Model

ijd

(1 )

ij T

kj T

d R

d R

TR

Definition: Let denote the Definition: Let denote the distance between node i and distance between node i and node j, and the common node j, and the common transmission range, then a transmission range, then a transmission from i to j is transmission from i to j is successful ifsuccessful if

for any other node k transmitting for any other node k transmitting simultaneously.simultaneously.

Heterogeneity Increases Multicast Capacity in Clustered Network 10

Congerve-Cast: On the Capacity Delay Tradeoffs 11

Mobile NetworkMobile Network

nn nodes are moving according to an independent identically nodes are moving according to an independent identically distributed mobility model.distributed mobility model.

Cell partitioned model is assumed to model the interference, Cell partitioned model is assumed to model the interference, which is identical to [6].which is identical to [6].

For each converge-cast session, For each converge-cast session, k k sources and sources and 11 destination are destination are randomly selected from therandomly selected from the n n nodesnodes. . There are There are nn sessions sessions existed in the network. (existed in the network. (identical to stationary networkidentical to stationary network))

[6] M. J. Neely, and E. Modiano, “Capaicty and delay tradeoffs for ad 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 NetworkMobile Network

Mobility Model: independent identically distributed modelMobility Model: independent identically distributed model A simplified mobility modelA simplified mobility model Mathematical TractabilityMathematical Tractability Give an upper bound of the theoretical resultGive an upper bound of the theoretical result

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Transmission Protocol: Cell partitioned networkTransmission Protocol: Cell partitioned network Nodes in the same cell are permitted to communicateNodes in the same cell are permitted to communicate 9-TDMA is assumed to avoid inter-cell interference9-TDMA is assumed to avoid inter-cell interference

Mobile NetworkMobile Network

Congerve-Cast: On the Capacity Delay Tradeoffs 14Congerve-Cast: On the Capacity Delay Tradeoffs 14

Mobile NetworkMobile Network

The traffic pattern is also similar to the that of multicast 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 The only difference is that the information is sent from k mobiles to the common destination.to the common destination.

Congerve-Cast: On the Capacity Delay Tradeoffs 15

Mobile NetworkMobile Network

Sending Pool: packets that are sampled by the node itself. When Sending Pool: packets that are sampled by the node itself. When a new session starts, a new packet is produced and duplicated m a new session starts, a new packet is produced and duplicated m times if the node is selected as source. times if the node is selected as source.

Relaying pool: packets that are sampled by other node and will Relaying pool: packets that are sampled by other node and will be sent to other destinations. When this node meets another be sent to other destinations. When this node meets another node which is the destination of one of the packets P in the 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.relaying pool, the packet P will be delivered to the receiving pool.

Receiving pool: packets that are designated for itself. When this Receiving pool: packets that are designated for itself. When this node meets another node which contains a packet P, the packet node meets another node which contains a packet P, the packet P will be delivered to the receiving pool in this node.P will be delivered to the receiving pool in this node.

Congerve-Cast: On the Capacity Delay Tradeoffs 16

IntroductionIntroduction

Models and DefinitionsModels and Definitions

Converge-Cast Capacity of Stationary NetworkConverge-Cast Capacity of Stationary Network

Converge-Cast Capacity and Delay in MANETConverge-Cast Capacity and Delay in MANET

Conclusion and Future WorkConclusion and Future Work

Congerve-Cast: On the Capacity Delay Tradeoffs 17

Capacity of Stationary NetworkCapacity of Stationary Network

Delay is usually not considered in static network because it only Delay is usually not considered in static network because it only relates with the number of hops.relates with the number of hops.

An efficient way to estimate the upper bound in static converge-An efficient way to estimate the upper bound in static converge-cast networks is to study its redundancy under the pattern.cast networks is to study its redundancy under the pattern.

Theorem 5.1: Theorem 5.1: The total capacity for random stationary ad hoc The total capacity for random stationary ad hoc network with one-hop strategy is with per-node network with one-hop strategy is with per-node throughput .throughput .

( )log

n

n

1( )log n

Congerve-Cast: On the Capacity Delay Tradeoffs 18

Capacity of Stationary NetworkCapacity of Stationary Network

Relays are necessary according to protocol model, yet Theorem Relays are necessary according to protocol model, yet Theorem 5.1 only shows the capacity of static ad hoc network with no 5.1 only shows the capacity of static ad hoc network with no relays. Then the whole transmission route can be treated as a relays. Then the whole transmission route can be treated as a chain whose length can be treated as redundancy because the chain whose length can be treated as redundancy because the whole transmission utilizes the same number of transmissions.whole transmission utilizes the same number of transmissions.

For unicast, the average redundancy is ,then the For unicast, the average redundancy is ,then the total capacity is ; For multicast, total capacity is ; For multicast, the average number of edges of the spanning tree is the average number of edges of the spanning tree is

, , then the total capacity isthen the total capacity is

For Converge-cast network, we get the same result as unicast For Converge-cast network, we get the same result as unicast network, so the total capacity is identical to unicast network.network, so the total capacity is identical to unicast network.

( )log

nm

n

( / log ) ( / log )n m n n n

( / log )m k n n ( / log )n k n

Congerve-Cast: On the Capacity Delay Tradeoffs 19Congerve-Cast: On the Capacity Delay Tradeoffs 19

IntroductionIntroduction

Models and DefinitionsModels and Definitions

Converge-Cast Capacity of Stationary NetworkConverge-Cast Capacity of Stationary Network

Converge-Cast Capacity and Delay in MANETConverge-Cast Capacity and Delay in MANET Delay of Single Session in MANETDelay of Single Session in MANET Delay and Capacity of Multi-session in MANETDelay and Capacity of Multi-session in MANET

Conclusion and Future WorkConclusion and Future Work

Congerve-Cast: On the Capacity Delay Tradeoffs 20

Delay of Single Session in MANETDelay of Single Session in MANET

In mobile ad hoc network, delay should be taken into In mobile ad hoc network, delay should be taken into consideration and it deals with both routing scheme and mobility consideration and it deals with both routing scheme and mobility pattern.pattern.

The delay consists of two types of delays: transmission delay and The delay consists of two types of delays: transmission delay and queuing delay. However, transmission delay can be ignored queuing delay. However, transmission delay can be ignored since there are at most 2 hops in this model and such since there are at most 2 hops in this model and such assumption does not change the order of the result.assumption does not change the order of the result.

The total delay is defined as the maximum of k delays:The total delay is defined as the maximum of k delays:

Congerve-Cast: On the Capacity Delay Tradeoffs 21

Delay of Single Session in MANETDelay of Single Session in MANET

Delay estimation of 1-hop algorithmDelay estimation of 1-hop algorithm Only source-destination transmission is allowed. Only source-destination transmission is allowed.

Delay estimation of 2-hop algorithmDelay estimation of 2-hop algorithm Both source-relay and relay-destination transmission are Both source-relay and relay-destination transmission are

allowed and taken into consideration. allowed and taken into consideration.

Congerve-Cast: On the Capacity Delay Tradeoffs 22

Capacity Delay of Multi-SessionCapacity Delay of Multi-Session

Case I: without redundancyCase I: without redundancy The delay is the same as the 1-hop algorithmThe delay is the same as the 1-hop algorithm It does not improve the delay and capacity in ad hoc It does not improve the delay and capacity in ad hoc

networks.networks. The per-node capacity is , which is identical to The per-node capacity is , which is identical to

unicast network in MANET. unicast network in MANET.

(1)

Delay/capacity ( log )n k

Congerve-Cast: On the Capacity Delay Tradeoffs 23

Capacity Delay of Multi-SessionCapacity Delay of Multi-Session

Case II: with redundancyCase II: with redundancy The delay is the same as the 2-hop algorithmThe delay is the same as the 2-hop algorithm delay and capacity tradeoff is improved in ad hoc delay and capacity tradeoff is improved in ad hoc

networks.networks. We obtain an optimal per-node capacity and delay tradeoff We obtain an optimal per-node capacity and delay tradeoff

as follows:as follows:

Congerve-Cast: On the Capacity Delay Tradeoffs 24Congerve-Cast: On the Capacity Delay Tradeoffs 24

IntroductionIntroduction

Models and DefinitionsModels and Definitions

Converge-Cast Capacity of Stationary NetworkConverge-Cast Capacity of Stationary Network

Converge-Cast Capacity and Delay in MANETConverge-Cast Capacity and Delay in MANET

Conclusion and Future WorkConclusion and Future Work

Congerve-Cast: On the Capacity Delay Tradeoffs 25

ConclusionConclusion

For stationary network, we find that the achievable capacity is the For stationary network, we find that the achievable capacity is the same as the unicast case. The comparison is as follows:same as the unicast case. The comparison is as follows:

For mobile network, we derive the capacity and delay with and For mobile network, we derive the capacity and delay with and without redundancy. The comparison is as follows:without redundancy. The comparison is as follows:

Congerve-Cast: On the Capacity Delay Tradeoffs 26

ConclusionConclusion

We make a comparison among the unicast, multicast, converge-We make a comparison among the unicast, multicast, converge-cast capacity delay tradeoffs of both stationary and mobile ad hoc cast capacity delay tradeoffs of both stationary and mobile ad hoc network.network.

Congerve-Cast: On the Capacity Delay Tradeoffs 27

ConclusionConclusion

The impact of base station is investigated in both unicast and The impact of base station is investigated in both unicast and multicast network. However, it is still unknown whether it can multicast network. However, it is still unknown whether it can improve the performance in converge-cast network.improve the performance in converge-cast network.

We assume a fast mobility model in this work, which means We assume a fast mobility model in this work, which means the time scale of node moving is identical to the time slot for the time scale of node moving is identical to the time slot for data transmission. When the node speed is not that fast, data transmission. When the node speed is not that fast, multihop transmission is allowed.multihop transmission is allowed.

In this work, we only consider i.i.d mobility pattern, which is In this work, we only consider i.i.d mobility pattern, which is unreal for the real world. We can also investigate the capacity unreal for the real world. We can also investigate the capacity under some more practical mobility model, e.g. random walk, under some more practical mobility model, e.g. random walk, random way point mobility models.random way point mobility models.

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