Gaurav Sharma,Ravi Mazumdar,Ness Shroff Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective Gaurav Sharma,Ravi Mazumdar,Ness Shroff IEEE/ACM Transaction on Networking, Vol 15,No 5. 2007, pp981-991 d96725002 蕭 鉢 d96725011 黃文莉 r96725035 林意婷 指導老師: 林永松 教授

Is node mobility a “liability” or an “asset” in ad hoc networks?

Liability Hand-off protocols for cellular networks [Toh & Akyol] Adverse effect on the performance of traditional ad hoc routing protocols [Bai, Sadagopan and Helmy] Asset Grossglauser and Tse showed node mobility can increase the capacity of an ad hoc network, if properly exploited. The delay related issues were not considered.

To Provide better understanding of the delay and capacity trade-offs in mobile ad hoc networks (MANET) from a global perspective

Outlines Critical Delay and 2-hops Delay Introduction Capacity scaling of ad hoc networks Mobility can increase capacity Main contributions Main Results Overview The Models Hybrid random walk model i.i.d mobility model Random walk model Hybrid random direction model Discrete random direction model Brownian motion mobility Critical Delay and 2-hops Delay Critical Delay and 2-hops Delay Under Various Mobility Models Lower bound on critical delay for hybrid random walk models Upper bound on critical delay for hybrid random walk models Lower bound on critical delay for discrete random direction models Upper bound on critical delay for discrete random direction models Discussion Characteristic path length Conclusion

Introduction

Capacity scaling of ad hoc networks Study fundamental properties of large wireless networks [Gupta & Kumar] Derive asymptotic bounds for throughput capacity To derive upper bounds, use: Interference penalty—nodes within range need to be silenced for successful communication Multi-hop relaying penalty— a node that traverses a distance of d needs to use order of d hops. To derive constructive lower bounds, use: Geographic routing strategic along great circles Greedy coloring schedules.

Capacity scaling of ad hoc networks Number of nodes Per-node Capacity [Grossglauser & Tse] - Nodes are mobile [Francheschetti &Dousse] - Nodes static - Power control allowed [Gupta & Kumar] Nodes static Interference model: protocol or physical model Common power level across network

Mobility can increase capacity [Grossglauser & Tse] achieve constant capacity scaling by two-hop relaying [Gupta & Kumar] allow for constant capacity scaling if the traffic pattern is purely local. Source uses one of all possible mobile nodes as a relay. Source splits stream uniformly across all relays. When a mobile forwarder nears the destination, it hands off packet.

Mobility can increase capacity Why does mobility increase capacity? By choosing a random intermediate relay, the traffic is diffused uniformly throughout the network. Thus, on average, every mobile node has a packet for every other destination and can schedule a packet to a nearby destination in every slot. (For those who took randomized algorithms, this is akin to permutation routing algorithms) Catch: forwarding strategy improves capacity at the expense of introducing delay. Need to study the delay-capacity tradeoff!!

Main contributions Delay-capacity tradeoff: increasing the maximum allowable average delay increases the capacity. Delay-capacity tradeoff depends on network setting, mobility patterns. Different mobility models have been studied in the literature i.i.d Brownian motion Random way-point Random walk Difficult to compare results across paper because network setting are quite different. How does the mobility model affect the delay capacity trade-off?

Main Results: Notion of critical delay to compare mobility modes For each mobility model, there is a critical delay below which node mobility cannot be exploited for improving capacity. Critical delay depends mainly on mobility pattern, not on network setting

Overview Mobility can increase capacity. Delay-capacity tradeoff depends on network setting, mobility models. Some questions arises How representative are these mobility models in this study? Can the delay-capacity relationship be significantly different under the mobility models? What sort of delay-capacity trade-off are we likely to see in real world scenario?

Main Results A new hybrid random walk model Propose and study a new family on hybrid random walk models, indexed by a parameter in [0, ]. For the hybrid random walk model with parameter ,critical delay is As approaches 0, the hybrid random walk model approaches an i.i.d mobility model. As approaches , the hybrid random walk model approaches a random walk mobility model.

Main Results A new hybrid random walk model Number of nodes Critical Delay random walk model Hybrid random walk model 1 i.i.d

Main Results A new hybrid random direction model Propose and study a new family on hybrid random direction models, indexed by a parameter in [0, ]. For the hybrid random direction model with parameter , the critical delay is As approaches 0, this hybrid random direction model approaches a random way-point model. As approaches , this hybrid random direction model approaches a Brownian mobility model.

Main Results A new hybrid random direction model Number of nodes Critical Delay Brownian mobility Hybrid random direction model Random Way-point 1

The Models

Hybrid random walk model Divide the unit square into cells of area Divide each cell into sub cells of area In each time slot, a node is in one of sub cells in a cell. At the beginning of a slot, node jumps uniformly to one of the sub cells of an “Adjacent cell”

i.i.d mobility model As approaches 0, we get i.i.d mobility. One big cell with n sub-cells. In each slot, a node is in one of the sub-cells. At the beginning of a time slot, a node jumps uniformly to one of the n subcells.

Random walk model As approaches , we get the random walk. n cells, one sub-cell in each cell. In any slot, a node is in particular cell. At the beginning of a slot, node jumps uniformly to one of the adjacent cells.

Hybrid random direction model Motion of a node is divided into trips. In a trip, node chooses a direction in [0,360] and moves a distance Speed of movement (for scaling reasons). The average neighborhood size scales as

Discrete random direction model. Divide the square into cells of area tours of size Time divided into equal duration slots At the beginning of a slot, a node jumps uniformly to an adjacent cell. During a slot, the node chooses a start and end point uniformly inside the cell, and moves from start to end. Velocity of motion is made inversely proportional to distance.

Brownian motion mobility For , the discretized random direction model degenerates to the random walk discrete equivalent of a Brownian motion with variance

Critical delay and 2-hop delay

Definition of critical delay We know that in the static node case, per node capacity is . Capacity achieving scheme is the multi-hop relaying scheme of Gupta & Kumar. If mobility is allowed, the two-hop relaying strategy achieves per node capacity of [Grossglauser & Tse] The two hop relaying strategy has an average delay of , under most mobility models. Mobility increase capacity at the expense of delay.

Definition of critical delay (conti) Suppose we impose the constraint that the average delay can not exceed . Under this constraint, relaying strategy that use mobility will achieve a capacity , somewhere between and For some critical delay bound , this capacity will be equal to capacity of static node networks. Below this critical delay , there is no benefit from using mobility based relaying.

An illustration of critical delay [Gupta & Kumar] Critical delay Capacity Two hop delay [Grossglauser & Tse] 2 hop relaying scheme has been shown to incur an average delay of about under many different mobility models Critical delay is the minimum delay that must be tolerated Maximum average delay

More on the critical delay It depends on the mobility mode. It provides a basic to compare mobility model. If mobility model A has lower critical delay than mobility model B , then A provides more leeway to achieve capacity gains from mobility than B. Critical delay also depends on what scheduling strategies are allowed.

Critical Delay and 2-hops Delay Under Various Mobility Models

Lower bound on critical delay for hybrid random walk models Obtain a value such that if average delay is below this value than (on average) packets travel a constant distance using wireless transmissions before reaching their destinations. For the hybrid random walk model , this value is Show that if packets are on average relayed over constant distance using wireless transmission, this results in a throughput of ,with the protocol model of the interference. Thus, the critical delay can not be any lower than this value.

Lower bound on critical delay for hybrid random walk models (cont) Step1: Establish a lower bound on the first exit time from a disc of radius Step2: If average delay is smaller than , than packets must on average be relayed over a distance no smaller than Pigeonhole argument Exit lemma Union Bound Motion arguments for successful relaying.

Upper bound on critical delay for hybrid random walk models Develop a scheduling and relaying scheme that provides a throughput of while incurring a delay of Consider a scheme where relay node transfer the packet to destination when it is in the same cell as destination Delay=(approx) time for delay node to move into destination node’s cell. Packet arrivals are independent of mobility delay is the same as mean first hitting time on a torus of size This first hitting time=

Upper bound on critical delay for hybrid random walk models (conti) With this strategy, multi-hop relaying is only used once we reach the destination’s cell, ie., at most distance Each hop travels a distance Throughput loss from multihop relaying = Since each wireless transmission travels ,nodes within this range must stay silent. An additional throughput loss of Combining the two, throughput=

Discussion on hybrid random walk models As increases, the critical delay increases, thereby shrinking the delay-capacity trade-off region. Two extreme cases: i.i.d model: when the static node capacity can be achieved even with a constant delay constraint. Random walk model: where delay on the order of is required to achieve the static node capacity.

Lower bound on critical delay for hybrid discretized random direction models Same approach as before to obtain lower bound on critical delay as Step1: derive a lower bound on exit time from a disc of radius 8 under the random direction model Step2: If average delay is smaller than packets must on average be relayed over a distance on smaller than

Same strategy as before Upper bound on critical delay for hybrid discretized random direction models Same strategy as before Replicate and give to relay node Relay node hands off to destination when it is in the cell of the destination Can obtain a throughput of with a delay of Provides an upper bound on critical delay for discreted random direction model.

Discussion

Discussion : Characteristic path length Critical delay seems to be inversely proportion to characteristic path length of a mobility model. Characteristic path length is the average distance traveled before changing direction under the model. For example, with hybrid discretized random ditection model, characteristic path length is and the critical delay is

Discussion : Characteristic path length(cont) Thus, a scenario with nodes moving long distance before changing direction provides more opportunities to harness delay-capacity trade-off, e.g., random way point model vs. Brownian model.

Conclusion

Conclusion Motivate capacity-delay tradeoff in MANET（Mobile Ad-hoc NETworks ）. Define critical delay to compare capacity-delay tradeoff region across mobility models. Define a parameterized set of hybrid random walk models and hybrid random direction models that exhibit continuous critical delay behavior from minimum possible to maximum possible.

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