Basic Limits on Protocol Information & Capacity Deficit in Computer Networks

1. Basic Limits on Protocol Information & Capacity Deficit in Computer Networks Rensselaer Polytechnic Institute Prof. Alhussein Abouzeid RPI.edu/~abouza

2. Ack: CISE NSF Projects • NR: Routing Overhead in Random Topology Networks: A Theoretical Framework with Practical Implications (8/2003-8/2006) • What are the basic limits on scalability of various protocol classes? • CAREER: Multi-Layer Modeling and Design of Wireless Ad Hoc Networks (2/2006-2/2011) • Whether we cross-layer or not, we need models that capture the behavior when multiple layers interact (which they do!).

3. 1. Information theory 2. Queuing Networks Proactive routing protocol overhead [INFOCOM05]; [IT04] Random Access Ad Hoc Networks [IWCMC06] Geographic routing protocol overhead [Allerton06]; [IT06] Random Access Mesh Networks [ICC’06] 4. Stochastic Decision 3. Probabilistic Models Reactive protocols overhead vs. traffic pattern [JSAC05], [Mobicom03] Spatial Diversity Forwarding [MASS’06] Random walk search [Hotp2p05], [Elsevier06] Optimal Stopping In Data Aggregation [INFOCOM’07]? Mobile Sensor Networks [MobiCom06]

4. 1. Information theory 2. Queuing Networks Proactive routing protocol overhead [INFOCOM05]; [IT04] Random Access Ad Hoc Networks [IWCMC06] Geographic routing protocol overhead [Allerton06]; [IT06] Random Access Mesh Networks [ICC’06] 4. Stochastic Decision 3. Probabilistic Models Reactive protocols overhead vs. traffic pattern [JSAC05], [Mobicom03] Spatial Diversity Forwarding [MASS’06] Random walk search [Hotp2p05], [Elsevier06] Optimal Stopping In Data Aggregation [INFOCOM’07]? Mobile Sensor Networks [MobiCom06]

5. What is a good routing protocol? • Routing in MANETs is one of the most researched problems in the networking literature since the inception of MANETS in the 1980s. • Paradoxically, this has strengthened the belief among many researchers in the community that MANET routing is not well understood. • Indeed, the fact that there currently exists no reference curve (a la Shannon capacity for a wireless AWGN channel) defining the feasible domain for routing protocols is indicative of the current state of affairs. • Can we even ask this question?...Can we view all protocols in one context?...one framework?

6. B B A A Single path Multi- path ? y y B B C C E E A A D D Geographic Geographic x x Data to send Find Path Find Path Data to Send t t A G D H B C E F S J K View: At the core of a routing protocol is a problem of maintaining state • Single Path, Multi-Path • Link-staterouting • Distance-vector routing • Source routing • “Stateless” geographic routing • still needs to maintain destination state `location information’ through some geographic service entities • On-Demand, Proactive • When to update state? • Flat, Hierarchical • Where to store state?

7. From Thermodynamics to Infodynamics • The first law of thermodynamics can be interpreted as “you cannot get something from nothing, because matter and energy are conserved .” [C.P. Snow] • So if a protocol that forwards data around needs to know some information about how to forward it, how much work (overhead) does the protocol need to exert? • Considering a variable topology network, such as for example a mobile ad hoc network; It is a dynamic system in a certain state. • So, we may, in information theoretic framework: • characterize the variability (or uncertainty) of the network • and then relate it to the (minimum) routing overhead • and hence discover some basic limits on routing effort a.k.a overhead? • …and maybe these limits could be used as reference curves (similar to Shannon’s Capacity for error free communication)

8. Location Server Location Update Beacon Transmission Geographic Routing Overheads • A MANET with 2-dimensional Brownian motion • Two components of geographic routing overheads: • Location update overheads for maintaining consistent states at the location servers • Beacon overheads for maintaining consistent local neighborhood information • Two Rate-Distortion Problems: • Minimum location update overhead problem: What is the minimum rate at which a node must transmit its location information to the location servers such that a the deviation between actual and perceived locations is bounded? • Minimum beacon overhead problem: What is minimum rate at which a node must transmit beacons such that all the nodes in the network know their neighborhood with high probability? • Hence evaluate lower bounds for the minimum overhead incurred • Publications: Allerton 2006 (to appear); joint work with N. Bisnik

9. Geographic Routing Overheads: Results • For small packet arrival times and large uncertainty in node locations, routing overhead may be prohibitively high • Impact of decrease in packet inter-arrival time: Both location update and beacon overheadsincrease • Impact of increase in node mobility (): • Location update overhead increases • Beacon overhead decreases after a certain threshold – A node belonging to a neighborhood is more likely to leave it under high mobility

10. Geographic Routing Overheads: Capacity Deficit • Routing overheads lead to deficit in the effective capacity available to network users • Characterizing the deficit is important for understanding the true scaling laws of wireless networks • We characterize the minimum deficit in the transport capacity caused by geographic routing overheads • The deficit is highly sensitive to packet arrival rate and number of nodes • If network size or packet arrival rate is above certain threshold then complete capacity is used up by routing overheads

11. Conclusion: Basic Limits on Protocols What is the minimum capacity deficit for well known classes of protocols? What is the best routing protocol? • This parallels another successful story; finding scaling laws for the total transport capacity (vis-à-vis the capacity itself). • Information theory is one promising approach; but not the only one (see attached slides on Queuing Theory).

12. 1. Information theory 2. Queuing Networks Proactive routing protocol overhead [INFOCOM05]; [IT04] Random Access Ad Hoc Networks [IWCMC06] Geographic routing protocol overhead [Allerton06]; [IT06] Random Access Mesh Networks [ICC’06] 3. Probabilistic Models 4. Stochastic Decision Reactive protocols overhead vs. traffic pattern [JSAC05], [Mobicom03] Spatial Diversity Forwarding [MASS’06] Random walk search [Hotp2p05], [Elsevier06] Optimal Stopping In Data Aggregation [INFOCOM’07]? Mobile Sensor Networks [MobiCom06]

13. Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks • For Ad Hoc / Mesh Networks with Random Access, how does delay scale with throughput? • How throughput scales with network size? • How delay including queuing scales with network size? • Relation between delay and throughput? • What are the tradeoffs as a function of the MAC, traffic pattern, node density and packet arrival process? • For WMNs: • Achievable per-node bit rate (throughput) if m routers with l available channels deployed to serve n clients? • How many clients can m routers with n available channels serve so that desired bit rate is achievable? • What end-to-end delay to expect?

14. Approach and results • Developed queuing network models for multi-hop wireless ad hoc networks • Used diffusion approximation to evaluate average delay and maximum achievable per-node throughput • Investigated the deviation of results from real life networks • Publications: • Secon’06/IWWAN’06 • ICC’06 • IWCMC’2006 • Future work: • Extend analysis to many to one cases • Taking deterministic routing into account • Sleep MAC and other MAC algorithms

15. 1. Information theory 2. Queuing Networks Proactive routing protocol overhead [INFOCOM05]; [IT04] Random Access Ad Hoc Networks [IWCMC06] Geographic routing protocol overhead [Allerton06]; [IT06] Random Access Mesh Networks [ICC’06] 3. Probabilistic Models 4. Stochastic Decision Reactive protocols overhead vs. traffic pattern [JSAC05], [Mobicom03] Spatial Diversity Forwarding [MASS’06] Random walk search [Hotp2p05], [Elsevier06] Optimal Stopping In Data Aggregation [INFOCOM’07]? Mobile Sensor Networks [MobiCom06]

16. Reactive Routing Results • Discovered certain traffic patterns for which the reactive routing overhead scales with n as O(1): infiniteley scalable conditions. The results hold for many types of connected networks. • Intuition: if long paths are updated only rarely, then the network will seem clustered “on the average” • Pubs: JSAC05; MobiCom3; • Future work: what if traffic does not obey the condition – view hierarchy as one solution…Inject enough state (weak state) to reduce overhead (at expense of successful delivery) • these concepts we plan to use for recently funded DTN project. • Towards a Distortion Tolerant Opportunistic Internet (8/2006-8/2009); with S. Kalyanaraman (PI), P. Drineas & M. Yuksel. • Building networks where disconnection is the norm

17. Popularity Estimate Popularity Estimator Module Parameter Selection Module Network (k,T) Delay (Update Window) Success Rate Adaptive Random Walk Search • Considered k random walkers, each with TTL T, searching for a resource with popularity p. • Adapt the aggressiveness (k, T) as a function of changing p to maintain a target performance criteria (success rate, delay, overhead) • Feedback from previous searches used to maintain popularity estimates (Popularity Estimator Module) • Analytical expressions for avg delay, overhead and success rate used to set k and T for future searches (Parameter Selection Module) • Pubs:hotp2p; Elsevier

18. Performance of Adaptive Random Walk Search • Adaptive random walk (EBAS) outperforms non-adaptive random walk • EBAS maintains minimal state information (popularity estimate of resources) • Future Work: solution…Inject enough state (weak state) to reduce overhead (at expense of successful delivery) – these concepts we plan to use for recently funded DTN project.

19. r Critical Velocities Motion Strategies in Mobile Sensor Networks • Does mobility always lead to better coverage? • The answer is No! Depends on velocity of mobile sensors, characteristics of the phenomenon being covered and the motion strategy • For simplistic motion strategies, we evaluate expressions for coverage quality in terms of event characteristic, velocity pattern and number of mobile sensors • Results help decide whether to move or not to move

20. Motion Strategies • Given information about the event dynamics and quality of coverage constraint (bound on event loss probability): • What is the minimum velocity with which a single sensor may satisfy QoC (MV-BELP problem) • For a fixed velocity, what is the minimum number of sensors that may satisfy QoC (MS-BELP problem) • We develop algorithms for solving MV-BELP and MS-BELP problems • For special cases, where event occur along a line or closed curve, we develop optimal algorithms for MV-BELP and 2-approx algorithms for MS-BELP problem • For general MV and MS-BELP we present heuristic algorithms and bound their performance with respect to the optimal. • If the event dynamics are uniform throughout the field, the performance of heuristic algorithms is close to the optimal • Publication: MOBICOM 2006

21. 1. Information theory 2. Queuing Networks Proactive routing protocol overhead [INFOCOM05]; [IT04] Random Access Ad Hoc Networks [IWCMC06] Geographic routing protocol overhead [Allerton06]; [IT06] Random Access Mesh Networks [ICC’06] 4. Stochastic Decision 3. Probabilistic Models Reactive protocols overhead vs. traffic pattern [JSAC05], [Mobicom03] Spatial Diversity Forwarding [MASS’06] Random walk search [Hotp2p05], [Elsevier06] Optimal Stopping In Data Aggregation [INFOCOM’07]? Mobile Sensor Networks [MobiCom06]

22. Applications of Optimal Decision Theory • In many situations, a node needs to take a decision based on its local information e.g. • To send its local samples or wait for more to aggregate before sending • Which node to select for forwarding packets if the channel conditions are different to maximize throughput through spatial diversity • Solution in terms of optimal policies

23. Sample arrival X3 X2 X1 Transmission Epoch … …… … … … …… Time s=X1 a=0 s=X1+X2 a=0 s=sn a=1 Decision Horizon Optimal Policies for Distributed Data Aggregation in WSN • Distributed Data Aggregation • No fixed tree-based structure; global information available on each node; • Robust to node failures, topology changes, etc; • Asynchronous information exchange & update; • A Decision Perspective for Intrinsic Energy-Delay Tradeoff • At each available transmission epoch, decide to stop current aggregation operation or continue for a possible higher degree of aggregation – An Optimal Stopping Problem; • A Semi-Markov Decision Process (SMDP) model

24. Solutions • Policies from Real-time Learning • Based on a finite-state approximation of the original SMDP model; • Adaptive Real-Time Dynamic Programming (ARTDP); • Real-Time Q-learning (RTQ); • Control-limit Type Policies • Search for control limit s*; • Easy to implement, but optimality is restrictive; • Evaluation in Distributed Data Aggregation • Example: 25 nodes, tracking maximal values of a time-varying phenomenon; • Metrics: Reward, Energy and Delay; • Key Results: • Learning algorithms ARTDP and RTQ achieve the best balance between delay and energy, but slower convergence and higher complexity in computation; • Control-limit type policies is sub-optimal, but the performance loss is small and much simpler in implementation; • Significant performance gain over traditional fixed degree of aggregation and on-demand schemes. • Future Work • Many sensor resource management problems naturally fit into sequential decision models; • SMDP provides a more realistic model than MDPs by considering real time.

25. Optimal Polices for Spatial Diversity Forwarding • Inherent spatial diversity in wireless ad hoc networks • A packet at a node can be usually forwarded via multiple alternative next-hop relays towards its destination, which can be utilized to combat fading; • Previous schemes are proposed based on some heuristic which explore the following two extreme cases: • FSR (First Stopping Relaying): selecting the first relay that replies to the forwarding node. (Problem: though minimum overheads incurred, the selected relay may be poor in quality.); • LSR (Last Stopping Relaying): collecting CSI from all candidate relays and then selecting the best one. (Problem: though the selected relay might be (if CSI is not outdated) the best, it incurs the maximum overheads.) • Formulate the next-hop selection at a forwarding node as an optimal stopping problem • OSR (Optimal Stopping Relaying): to achieve a target trade-off between channel probing overhead and the quality of the selected relay.

26. Results and Future Work • Optimal Stopping theory in OSR • IE (Information Efficiency: progress towards destination X the link rate) is chosen as the reward function that the forwarding node wants to maximize; • Given Rayleigh-fading) channel statistics, a threshold-based policy is derived. • A Cross-layer implementation for OSR • GPSR Routing: selecting the set of candidate next-hop relays; • PHY: passing CSI to upper layers; • Modified 802.11 MAC: performing the calculated policy on the relay side and selecting the “optimal” next-hop (if any). • Summary of results • OSR outperforms FSR/ LSR in terms of IE given a single forwarding node and multiple relays analytically; • OSR outperforms FSR/LSR in terms of (FTP) throughput, (CBR) packet delivery ratio, end-to-end delay and jitter in regular grid/random/mobile topologies via extensive simulations. • Future Work • Enable nodes to learn the fading channel characteristics online instead of relying on a channel model; • Extend such a decision framework to also include flow selection from a queue to see whether the forwarding capability can be further improved.

27. References • [Allerton06] N. Bisnik, A. A. Abouzeid, “Rate-Distortion Bounds on Location-Based Routing Protocol Overheads in Mobile Ad Hoc Networks” Proceedings of Forty Fourth Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 2006. • [INFOCOM05] N. Zhou and A. Abouzeid, “Routing in Ad Hoc Networks: A Theoretical Framework with Practical Implications,” in Proceedings of 24th IEEE Conference on Computer Communications (INFOCOM’2005), Miami, FL, USA, March 2005. • [IT04] N. Zhou and A.A. Abouzeid, “Routing in Ad Hoc Networks: A Theoretical Framework with Practical Implications,” IEEE Transactions on Information Theory, submitted April 2004, revised August 2006. • [IWCMC06] N. Bisnik and A.A. Abouzeid, “Queuing Network Models for Delay Analysis of Multihop Wireless Ad Hoc Networks,” Proceedings of International Symposium on Wireless Local and Personal Area Networks, International Wireless Communications and Mobile Computing Conference (IWCMC 2006), July 2006, Vancouver, Canada. • [IWWAN06] N. Bisnik and A.A. Abouzeid, “Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks,” Proceedings of The 2006 IEEE International Workshop on Wireless Ad-hoc and Sensor Networks (IWWAN 2006), June 2006, New York, NY. • [ICC06] N. Bisnik and A.A. Abouzeid, “Delay and Throughput in Random Access Wireless Mesh Networks,” Proceedings of The 2006 IEEE International Conference on Communications (ICC’2006), June 2006, Istanbul, Turkey. • [JSAC05] N. Zhou, H. Wu and A. A. Abouzeid, “The Impact of Traffic Patterns on the Overhead of Reactive Routing Protocols,” IEEE Journal on Selected Areas in Communications, Special Issue on Mobile Ad-Hoc Networks, 23(3):547-60, March 2005. • [Hotp2p05] N. Bisnik and A. Abouzeid, “Modeling and Analysis of Random Walk Search Algorithms in P2P Networks,” in Proceedings of IEEE Second International Workshop on Hot Topics in Peer-to-Peer Systems (Hot-P2P 05), San Diego, CA, July, 2005. • [Elsevier06] N. Bisnik and A. Abouzeid, “Optimizing Random Walk Search in P2P Networks,” Computer Networks, submitted August 2005, accepted August 15 2006. • [MobiCom06] N. Bisnik, A.A. Abouzeid and V. Isler, “,”Proceedings of The Twelfth Annual International Conference on Mobile Computing and Networking (ACM MobiCom 2006), Los Angeles, CA, Sept. 2006. • [MASS06] J. Ai, Z. Ye and A. A. Abouzeid, “Cross-layer Optimal Decision Policies for Spatial Diversity Forwarding in Wireless Ad Hoc Networks,” in Proceedings of The Third IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS’06), October, 2006, Vancouver, Canada.