Wireless Network Capacity Jamar Parris Xi Liu

Areas Covered Fixed Nodes Mobility of Nodes

Focus All wireless networks Causes issues: Medium access issues No centralized control complicates matters Physical layer issues Transmission power must be high enough to reach receiver whilst causing minimal interference to others. Fixed Nodes Mobility of Nodes

Useful Information Packets sent in multi-hop fashion Packets can be buffered at intermediate nodes Several nodes can transmit simultaneously provided no interference from others Two types of networks considered: Arbitrary Networks Random Networks Fixed Nodes Mobility of Nodes

Arbitrary Networks Node locations, destinations, traffic demands, range are all arbitrary. 2 models used to describe successful transmission from hop to hop: Protocol Model Physical Model Adds a signal to interference ratio Adds a ambient power level Fixed Nodes Mobility of Nodes

Arbitrary Networks Assume 1 bit meter is when one bit is transported the distance of 1 meter Multiple credit not given for same bit carried to several destinations e.g. multicast Sum of products of bits and distances over which they are carried indicates transport capacity Fixed Nodes Mobility of Nodes

Arbitrary Networks – Results Transport capacity under Protocol Model is This depends on: Nodes being optimally placed Traffic pattern optimally chosen Transmission range being optimally chosen. Fixed Nodes Mobility of Nodes

Transport & Throughput Capacity If the capacity were to be equally divided, each node would get Now if source and destination pair were 1m away Throughput and Transport Capacity would be equal It should be noted that transport capacity increases when the signal power decays more rapidly with distance Fixed Nodes Mobility of Nodes

Random Networks Each node randomly chooses destination Destination chosen independently as the node closest to a randomly located point All transmissions use the same range Nodes are randomly located either on the surface of a sphere or in a plane Fixed Nodes Mobility of Nodes

Random Networks Sphere: Every node in a cell is within range of every other node in its own cell or adjacent cells If two cells are not interfering neighbors than their transmissions cannot collide. Number of interfering neighbors are bounded so that each cell has chance to transmit. Each cell contains at least one node to make relaying feasible. Fixed Nodes Mobility of Nodes

Sphere Fixed Nodes Mobility of Nodes

Random Networks Also uses Protocol & Physical Model Uses Different Criteria for successful transmission Under Protocol Model - Results Results same for both the sphere and plane Throughput Capacity is Throughput constriction is caused by the need for all nodes to share the channel with other nodes Under Physical model, throughput capacity is Fixed Nodes Mobility of Nodes

Relay Nodes Idea is to add additional nodes who only relay packets and are not themselves sources This allows for an increase in throughput However, number of relay nodes to have an significant increase in capacity can be large. For example, with 100 nodes, to make capacity equal to five times its value when there are no relay nodes, you need 4476 relays. Fixed Nodes Mobility of Nodes

Trade-Offs Throughput versus range Increasing range of each node would reduce hops traversed. However, since nodes close to receiver need to be idle to avoid collision, throughput would actually decrease. Actually reducing range to as small as possible is what’s needed. However, range can only get so small before the network loses connectivity Fixed Nodes Mobility of Nodes

Inferences of the paper Maybe you should group nodes into cells and then designate one node to carry the burden of relaying multi-hop packets. Maybe connect base stations by wired links to improve capacity. If we assign a base station in each cell to communicate with other distant base stations wirelessly, base stations inherit same capacity limitation. Fixed Nodes Mobility of Nodes

Inferences of Paper According to tests, subdividing the channel W into W1, W2, etc. did not change anything. As number of nodes increase throughput will also decrease. Fixed Nodes Mobility of Nodes

Issues with this paper Interference is not factored in Access to wireless channel not coordinated Mobility not included Link failures not included Hence adapted and distributed traffic routing not included. Claims that the above will only reduce capacity. Not all of these is necessarily true Fixed Nodes Mobility of Nodes

Mobility of Nodes Follows the same model, only nodes are mobile as opposed to fixed Network Topology changes over time Incurs delay, good for applications that can tolerate delays of minutes to even hours. E-Mail Database Synchronization Fixed Nodes Mobility of Nodes

Mobility of Nodes Transmit only when nodes are close to each other. Reduces number of hops each packet must take, increasing throughput. Each node has an infinite stream of packets to send to its destination. The S-D association does not change over time, only the nodes themselves move. Fixed Nodes Mobility of Nodes

Two Scenarios Used Mobile Nodes without Relaying Mobile Nodes with Relaying Fixed Nodes Mobility of Nodes

Mobile Nodes without Relaying The problem with fixed nodes is that throughput reaches zero because number of relay nodes packet must go through increases In this scenario, we expect that any two nodes can be expected to be close to each other from time to time. Improve capacity by not relaying at all and only let sources transmit directly to destinations. Fixed Nodes Mobility of Nodes

Results If the range is large (i.e. transmissions over long distances are allowed). many S-D pairs are within range. Interference however will limit the number of concurrent transmissions over long distances Makes throughput interference limited Also, if range is small, only a small fraction of S-D pairs will be close enough to transmit a packet. Makes throughput distance limited. Throughput per session decreases as n gets larger if only direct transmissions are allowed. Fixed Nodes Mobility of Nodes

Mobile Nodes With Relaying Problems with no relaying: Find a way to communicate only locally to overcome interference limitation Find a way to ensure that there are enough sender-receiver pairs to transmit to overcome distance limitation Proposed Solution: Direct communication not enough, so introduce relaying. Fixed Nodes Mobility of Nodes

Basic Idea Spread the traffic stream between the source and destination to a large number of intermediate relay nodes Each packet goes through one relay that buffers the packet until final destination delivery is possible For each S-D, every other node except S & D can serve as relay nodes Goal is packets of every source node will be distributed across all nodes in the network Fixed Nodes Mobility of Nodes

Basic Idea This ensures that every other node in the network will have packets buffered destined to every other node not including itself Hence, a sender-receiver pair always has a packet to send unlike in the case without relaying How many times must a packet be relayed in order to spread traffic uniformly? Fixed Nodes Mobility of Nodes

Number of Hops per packet It turns out only one The probability of an arbitrary node to be scheduled to receive a packet from source S in equal for all nodes and independent of S Each packet therefore has to make only two hops Source to relay Relay to destination Total achievable throughput is Fixed Nodes Mobility of Nodes

2 Phases Phase 1 Scheduling of packet transmissions from source to relays or from source to final destination in one hop if possible Phase 2 Scheduling of transmissions from relay to final destination or from source to destination if possible. When a receiver is identified, sender checks to see if it has any packets for which receiver is the destination, if it is, it transmits. In either phase, direct transmission is allowed since it is possible for a sender receiver pair to be a source destination pair as well. Fixed Nodes Mobility of Nodes

Phase 1 & Phase 2 Fixed Nodes Mobility of Nodes

Centralized vs. Distributed Implementation This model allowed for central coordinated scheduling, relaying and routing. Authors believe algorithm can be implemented in a distributed manner as well In this case: At each instant, node can randomly and independently determine if they want to be a sender or potential receiver Each sender seeks out a receiver close to it and attempts to send data to it Fixed Nodes Mobility of Nodes

Distributed Implementation Same phases as in centralized Multiple senders may attempt to send to same receiver Author’s analysis showed that probability of success is reasonable even with many users Fixed Nodes Mobility of Nodes

Problem Since capacity in both phases are identical, delay experienced from source to destination can be infinite even for a finite number of nodes if capacity in phase 1 fully used. Author Fix? Allow both source to relay and relay to destination transmissions to occur concurrently but give priority to relay to destination transmissions. Fixed Nodes Mobility of Nodes

Sender Centric versus Receiver Centric So far, sender selects the closest receiver to send to What if receiver selects the closest sender from which to receive? At first, it may seem that results should be the same, but in fact this is not the case Problems occur if several receivers select the same sender Fixed Nodes Mobility of Nodes

Two possible outcomes If the sender can only select one receiver to send to, sender-receiver pairs need to be eliminated, If sender can generate multiple signals for several receivers, we need to account for the fact the desired signal is only a fraction of unit power. Authors found no elegant want to integrate these complications into the proof Fixed Nodes Mobility of Nodes

Receiver centric approach preferable If there is a single receiver This is due to the fact that the selected sender always has the strongest signal In the receiver centric approach, interference is smaller. Signal to interference ratio is larger in receiver centric approach Throughput is also slightly higher than in the sender centric approach Fixed Nodes Mobility of Nodes

Throughput Comparison Sender Centric Receiver Centric Fixed Nodes Mobility of Nodes

Downlink & Uplink Throughput Downlink: from source to all relays Uplink: from relays to destination Due to multi-user diversity, throughput of downlink is high due to fact that at any one time a relay node is likely to be close to source The same also applies for uplink This is in essence a statistical multiplexing effect due to a large number of network users Fixed Nodes Mobility of Nodes

Implications & Conclusions Make use of delay tolerance of applications to improve throughput in a mobile wireless network Impossible to support a high throughput per source-destination pair using direct communication, they are too far apart most of the time This idea must be combined with a two hop strategy to achieve high throughput Drastic improvement in throughput over fixed nodes in previous paper Fixed Nodes Mobility of Nodes

Problems with this model Nodes have entirely random mobility patterns. What if mobility is constrained? Delay increases as the system gets larger but at the same time so does throughput No constraint on delay imposed This implies that with a constraint on delay imposed the maximum achievable throughput must decrease. Must balance throughput and delay Fixed Nodes Mobility of Nodes

Capacity of Ad Hoc Network Examine the capacity at a detailed level Single Cell Capacity Capacity of a Chain of Nodes Capacity of a Regular Lattice Network Capacity of Random Network Some conditions that per-node capacity scales Local traffic pattern

Capacity of A Single Cell All nodes can hear each other Four-way handshake 2Mbps Expect to see 1.8Mbps for 1500B data packet if control overhead is counted 1.7Mbps if IFS is counted

Capacity of A Chain of Nodes - Analysis 1 2 3 4 6 Radio Range of Node (200 m) Interference Range of Node 4 5

Capacity of A Chain of Nodes - Analysis 1 2 3 5 6 4 Radio Range of Node Interference Range of Node 4

Capacity of A Chain of Nodes - Analysis Total Max. Channel Utilization = 1/4 1 2 3 5 6 4 Radio Range of Node Interference Range of Node 4

Capacity of A Chain of Nodes – Simulation Node 1 sends as fast as its MAC allows With Longer Chains, Utilization levels go substantially low. For a 1500 Byte packet size, it is as low as 15% (1/7) of 1.7Mbps It is possible to achieve ¼ under 802.11 MAC 802.11 failed to find an optimal schedule Backoff waste 500 B 1500 B 64 B

Discrepancy Backoff wastage: large backoff at node 1 (5.4%) 1 2 3 4 6 Radio Range of Node Interference Range of Node 5

Capacity of A Regular Lattice Network Two communication patterns Scenario #1 Scenario #2

Capacity of A Regular Lattice Network Scenario #1 Internode Distance = 200 m Interference radius = 550 m Every third row can operate Without interference to give a Maximum throughput of 1/4 Thus flow in such a lattice network is expected (theoretically) to reach 1/12

Capacity of A Regular Lattice Network Expected: (1/12) * 1.7 = 0.14 Mbps Observed: 0.1 Mbps Discrepancy: Same as in chain

Capacity of A Regular Lattice Network Traffic flow direction Scenario #2 1) Optimal Scheduling possible with predetermined routes. 2) Overall throughput can be maximized (in theory) with one vertical flow in one time unit and horizontal flows in another 3) Per-flow throughput is expected to be (1/24)

Capacity of A Regular Lattice Network Slightly less than half of the per-flow throughput without cross traffic Possible Problem : Head of queue block

Capacity of Random Network Expect to see similar total capacity to lattice network No dramatically loss 1) Hole in area 2) Center is more susceptible to congestion

Traffic Pattern Random traffic pattern Scalable traffic pattern The capacity available to each node is O(1/sqrt(n)) Scalable traffic pattern Exactly local traffic: fixed distance Power law distance distribution: if the distance distribution decays more rapidly than the square of distance The basic idea is that the average path length in scalable traffic pattern should be kept constant

Impact of Interference on Multi-hop Wireless Network Performance Framework to answer questions about the capacity of specific topologies with specific traffic pattern Assumptions No mobility Fluid model Centralized scheduler The basic idea is to model as a standard network flow problem with wireless constraints

Network Flow Model Connectivity graph Each vertex represents a wireless node Directed edge from A to B if B is within range of A Linear programming that solves the MAXFLOW problem

Conflict Graph (Contention Graph) Each edge in the connectivity graph (link) represented by a vertex in conflict graph An undirected edge between two vertices (links) if one link will interfere with the other If there are an edge between two links, then the two links cannot transmit together

Clique Constraints Cliques in conflict graph At most one link in a clique can be active at any instance Augment MAXFLOW LP to get upper bound

Properties of Clique Constraints Finding all cliques takes exponential time Even if all cliques are found, no optimality is guaranteed More cliques added, more tight the bound Tradeoff between computation and performance

Independent Set Constraints All links belong to an independent set can be active together No two independent sets can active at the same time Augment MAXFLOW LP to get lower bound

Properties of Independent Set Constraint Lower bound is always feasible LP can output a schedule Finding all independent sets takes exponential time The lower bound is optimal is all independent sets are found Lower bound will increase if we add more independent sets If upper and lower bound converge, the optimality is guaranteed

Some Generalizations Multiple radio on orthogonal channels Multiple, non-interfering links between nodes Directional antenna Appropriate edges in connectivity graph Conflict graph can also accommodate Multiple sender/receiver Multi-commodity flow problem for LP

Routing Shortest path is not enough Interference-aware routing Channel quality should be considered May introduce congestion Interference-aware routing Prefer routes that use up minimum amount of spectrum resource Advantageous sometimes even with 802.11 MAC

Limitations Computation cost 2-5 minutes for ~100 nodes No guarantee to get optimal schedule in polynomial time Change in conflict graph Slow vs. fast change Fairness is bad

Capacity of Multi-Channel Wireless Networks Multiple channels share a fixed bandwidth Consider multiple channels and multiple interfaces in networks # of channel c, # of interface m per node What if we use less interfaces than channels m < c Intuitively, capacity degradation may occur

Results The capacity is dependent on the ratio c/m, and not on the exact value of either c or m For Arbitrary network: There is always a capacity loss

Results No degradation when c/m = O(log n) If c = O(log n), then m = 1 suffices For Random network:

Capacity of Power Constrained Ad-hoc Network Consider model with low spectral efficiency Arbitrary large bandwidth Power constrained Two applications UWB Sensor network The result is that throughput increases with node enter the network

Intuition SINR = Signal / (Noise + Interference) Noise = noise density * bandwidth In bandwidth-constrained scenario, SINR is dominated by interference In low spectral efficiency, SINR is mainly affected by ambient noise

Question: What are the fundamental limitations of wireless network?

Summary – Factors Influencing Capacity Node placement Traffic pattern Static / Mobile Available Bandwidth Multi-Channel Infrastructure support Directional / Omnidirectional antenna

Thanks! Question? Suggestion?

Reference P. Gupta and P. R. Kumar, " The capacity of wireless networks,'' IEEE Transactions on Information Theory , vol. IT-46, no. 2, pp. 388-404, March 2000 Capacity of power constrained ad-hoc networks , Arjunan Rajeswaran, Rohit Negi, IEEE Infocom 2004, Hong Kong, March 2004. Jinyang Li, Charles Blake, Douglas S. J. De Couto, Hu Imm Lee, and Robert Morris, Capacity of Ad Hoc Wireless Networks, Proceedings of the 7th ACM International Conference on Mobile Computing and Networking (MobiCom '01), Rome, Italy, July 2001, pages 61-69 Kamal Jain, Jitendra Padhye, Venkata N. Padmanabhan, and Lili Qiu. Impact of Interference on Multi-hop Wireless Network Performance. In Proc. of ACM MOBICOM, San Diego, CA, September 2003 Matthias Grossglauser and David Tse. Mobility Increases the Capacity of Mobile Ad-hoc Wireless Networks. IEEE/ACM Transactions on Networking, Vol. 10, No. 4, Aug. 2002 Pradeep Kyasanur and Nitin Vaidya. Capacity of Multi-Channel Wireless Networks: Impact of Number of Channels and Interfaces In Proc. of ACM MobiCom 2005, Aug. - Sept. 2005 Abbas El Gamal, James Mammen, Balaji Prabhakar, and Devavrat Shah. Throughput-Delay Trade-off in Wireless Networks. Proc. of IEEE INFOCOM, March 2004.