Mobile Ad hoc Networks COE 549 Delay and Capacity Tradeoffs II Tarek Sheltami KFUPM CCSE COE 8/6/20151

Outline Multi-user in Mobile Network Static vs. Mobile Ad Hoc Networks Direct Contact vs. Simple Replication Why multi-hop relaying in static networks? Tradeoff between delay and capacity

Typical Scenario n nodes communicate in random S-D pairs All nodes are mobile, no fixed base station Applications are delay tolerant Database Synchronization Control message to Explorer on Mars Topology may change during packet delivery

Multi-user in Mobile Network Direct contact: The source holds the packet until it comes in contact with the destination Minimal resource, but long delay This idea is very simple, but does not perform very well. In fact, any scheme that does not use relaying can not do better than: Where is the minimum simultaneously successful transmissions

Scheduling Policy We slot time, and index slots by t. In each slot, each node transmits with probability Each transmitter transmits to its closest neighbor There will be a lot of collisions: The expected number of successful receptions N t is on the order of n: With n nodes, it is possible to have around successful transmissions, with S/N requirements

Multi-user in Mobile Network Simple replication: S sends a replicate to as many different nodes as possible. These relays hand the packet off to D when it gets close Each packet goes through at most one relay node  Higher throughput, relatively shorter delay

Methodology Using the previous scheduling policy as a building block. Nodes only transmit to their nearest neighbors. In odd slots, each node transmits to its nearest neighbor a packet for its destination. The neighbor will act as a relay. In even slots, each node will relay to its nearest neighbor a packet destined for that node (if it has such a packet).

Each of the n − 2 intermediate queues has arrival and departure rate equal to packets/slot The link directly from the source to the destination has rate packets/slot. The aggregate throughput per node is packets/slot Multi-user in Mobile Network..

The Book Analogy Imagine a large number of people moving around in a city Each one carries a stack of books for a friend of his. The stack is very high Whenever I bump on any other person on the street: I either give him a book for him to give to my buddy, or I give him a book that his buddy gave to me some time in the past Chances that I bump on my own buddy are negligible Question: What is the average number of people that their destinations are also nearest neighbors? This is related to the famous hat problem!

Model Assumptions Session Each of the n nodes is an S node for one session and a D node for another session Each S node i has an infinite stream of packets to send to its D, d(i) The S-D association does not change with time Each node has an infinite buffer to store relayed packets Central Scheduler At any time t, the scheduler chooses which nodes will transmit which packet, and its power level

Transmission Model

Random Topology

Static vs. Mobile Ad Hoc Networks When # of users per unit area n increases Static: The throughput per S-D pair decreases approximately like Long-range direct communication limited due to interference. Most comm. has to occur between nearest neighbors  Distances of order  Hops to D of order  Actual useful traffic per pair is small Best performance achievable with optimal scheduling, routing  Traffic rate per S-D pair can actually go to zero Mobile:The avg. long-term throughput per S-D pair can be kept constant

Direct Contact vs. Simple Replication Mobile Nodes w/ direct contact Transmission are long range  interference prevents more concurrent transactions For sufficient large N, throughput goes to 0 Mobile Nodes w/ relaying (simple replication) Overcame interference and distance limitation Possible to schedule O(n) concurrent successful transmissions per time slot w/ local communication Achieved a throughput per S-D pair of O(1)

Numerical Results

Receiver Centric Results

What is capacity here? Not traditional information-theoretic notion Notion of network capacity under interference Modulation and coding scheme is fixed In this notion of capacity, space is resource d S D d IN No other transmission in this area of

Capacity of static ad hoc networks Gupta and Kumar [IEEE Trans. IT, 2000] Uniform distribution of n nodes within a disk of unit area Randomly chosen sender-destination pairs Same power level for all transmissions Per-node throughput as with multi-hop relaying Agarwal and Kumar [ACM CCR, 04] Per-node capacity of with power control

Why multi-hop relaying in static networks? Direct transmission is bad Transmission over distance d costs Short transmission is better than long transmission Multi-hop relay (via nearest neighbor) is best Best possible is to transmit only to neighbors hops VS For each hop Required area = Network capacity = Per-node capacity = S D S D

Capacity of mobile ad hoc networks Grossglauser and Tse [IEEE INFOCOM, 01] Similar model as Gupta and Kumar, but with mobile nodes Per-node capacity of is achievable with two- hop relay Why two-hop relay in mobile networks? Direct transmission cannot exploit mobility More than two-hop decreases capacity

Capacity scaling of ad hoc networks Number of nodes Per-node Capacity Gupta, Kumar -Static nodes -Common power level Francheschetti, Dousse - Static nodes - Power control allowed Grossglausser, Tse - Mobile nodes

What is ‘price’ for capacity? Two ways to send a packet to D Wireless transmission Node mobility (=relay movement) For given distance d between S and D d = (sum of distances by transmission) + (sum of distances by relay movement) To minimize first term is to maximize second term Time taken for node mobility: Delay Sum of distances by mobility results in time delay

Why tradeoff between delay and capacity? Tradeoff between delay and capacity d = (sum of distances by transmission) + (sum of distances by relay movement) For capacity, reduce distances by transmission For delay, reduce distances by relay movement For given value of d Can not reduce both distances!  tradeoff

Illustration of tradeoff between delay and capacity Assume appropriate scheduling One transmission = distance of S D R1 R2 S D d Total movement of relays = Delay Capacity # of transmissions = 3

Critical Delay and 2-Hop Delay Critical Delay: Minimum delay that must be tolerated under a given mobility model to achieve a per-node throughput of 2-Hop Delay: Delay incurred by the 2-hop relaying scheme The delay-capacity tradeoff exists for values of delay between critical delay and 2-hop delay

Hybrid Random Walk Models The network is divided into n 2β cells for β between 0 and ½ Each cell is divided into n 1-2 β sub-cells Each node jumps from its current sub-cell to a random sub-cell in one of the adjacent cells β=1/2  random walk model

Random Direction Models Parameterized by β between 0 and ½ Each node moves a distance of n -β with a speed of n -1/2 in a random direction Can pause for some time between steps

Lower Bound for Critical Delay Main idea If average delay is smaller than a certain value, packets travel average distance of to reach destination Then show that this result in throughput of HRW: Critical delay scales as RD: Critical delay scales as

04/26/0629 Calculating Critical Delay using Exit Time Study exit time for a disk of radius r=1/8 centered at nodes initial position Derive a lower bound on exit time that holds with high probability r = 1/8

Details of lower bound: Exit time Let ς hrw and ς rd denote exit times for a disk of radius 1/8 in case of HRW and RD model with parameter β Lemma (Lower Bound on Exit Time for HRW models): Lemma (Lower Bound on Exit Time for RD models): C = slot duration

04/26/0631 From Exit Time to Critical Delay? 1 1/4 s d r

Upper Bound for Critical Delay Need to develop a scheme that achieves a throughput of Delay can be upper bounded by first hitting time for HRW models and for RD models

Summary of Main results 2-Hop delay is roughly for all models Critical delay scales as roughly for HRW models Critical delay scales as roughly for RD models

Conclusions Node mobility has strong impact on delay-capacity tradeoff There exists minimum value of delay (critical delay) which makes capacity better than that of static ad hoc networks Nodes change directions over shorter distances exhibit higher critical delay values Nodes moving in same direction over longer distances shows a wider delay-capacity tradeoff