An Adaptive Compulsory Protocol for Basic Communication in Ad-hoc Mobile Networks

1. An Adaptive Compulsory Protocolfor Basic Communicationin Ad-hoc Mobile Networks Ioannis Chatzigiannakis Sotiris Nikoletseas April 2002

2. I. Chatzigiannakis - S. Nikoletseas Ad-Hoc Mobile Networks • A collection of mobile hosts with wireless network interfaces forming a temporary network WITHOUT any established infrastructure or centralized administration. • Ease of Deployment • Speed of Deployment • No Infrastructure is used • Instant Networking

3. I. Chatzigiannakis - S. Nikoletseas The Basic Communication Problem • Send information from some Sender S to some Receiver R. • Adverse conditions: • Poor Resources (computational and battery power) • Highly dynamic variable connectivity • Connections are constantly forming and breaking • Hosts may be far away • Difficult to avoid broadcasting and thus flooding • Is there a more efficient technique – other than notifying every station that the sender meets, in the hope that some of them will then eventually meet the receiver (i.e. Flooding) ?

4. I. Chatzigiannakis - S. Nikoletseas Previous research • Use a Dynamic Graph Model: • The network is modeled as an undirected graph. • Vertices correspond to Mobile Hosts • Edges (virtual links) correspond to temporary communication between pairs of hosts • Algorithms try to maintain data structures on connectivity, such as sets of paths of intermediate nodes that lie within one another’s transmission range. • M. Adler and C. Sheideler: “Efficient Communication Strategies for Ad-hoc Wireless Networks”, in SPAA 1998. • Y. Ko and N. Vaidya: “Location-Aided Routing (LAR) in Mobile Ad-hoc Networks”, in MOBICOM 1998. • N. Malpani, J.Welch and N. Vaidya: “Leader Election Algorithm for Mobile Ad-hoc Networks”, in DIALM 2000.

5. I. Chatzigiannakis - S. Nikoletseas Limitations of Such Approaches • Proof of correctness requires • A bound on the rate of virtual link changes • Good Results in static graphs and in quasi-static graphs (of low or medium mobility rate) • In case of very high mobility rate (i.e. very high rate of topology changes) such approaches may fail to react fast enough. • Broadcasting techniques for communication in small area networks or dense networks of many users are efficient but • In wider area networks? • In sparse networks of less users? • Impractical (path formation may not be feasible), Not Efficient (very long paths) and Not Fault-tolerant (if any one path exists)

6. I. Chatzigiannakis - S. Nikoletseas tr tc An Explicit Model Of Motions We assume that each mobile host has a transmission range represented by a sphere tr centered by itself. We approximate this sphere by a cube tc with volume V(tc), where V(tc) < V(tr) • Any other host within tr can receive any message broadcasted by the host. • Given that the mobile hosts are moving in the space S, S is divided into consecutive cubes of volume V(tc).

7. I. Chatzigiannakis - S. Nikoletseas The “Support” Approach • We envision networks where the highly dynamic movement of hosts makes “maintenance” of valid paths inconceivable • We propose the idea of using a small team of nodes to move as per the needs of the protocol – we call these nodes the Support () of the network • The Support acts as a moving (sweeping the entire network area) intermediate pool for storing and forwarding messages • We take advantage of the hosts natural movement by exchanging information whenever hosts meet accidentally • We additionally take special care of users in remote areas that do not move beyond these areas • Our scheme follows the “2-tier” principle – try to move communication and computation to the fixed part of the network [Imielinski+Korth96] – in our case  simulates the fixed part

8. I. Chatzigiannakis - S. Nikoletseas Previous Work: The Snake Protocol • At the Set-up phase, a set of k hosts become the support andelect a leader (the head of ) • The nodes of the support move fast enough to cover (in sufficiently short time) the entire motion graph moving as a chain of nodes (in a snake-like formation) • When some node of gets within communication range of a sender, an underlying sensor sub-protocol P2 notifies the sender to send its message(s). • The messages are then propagated within  structure using a synchronization sub-protocol P3. • When a receiver node comes within communication range of a node of , the underlying sensor sub-protocol P2 notifies the node of , and the pending messages are forwarded to the receiver.

9. I. Chatzigiannakis - S. Nikoletseas Previous Work: Communication Times The time needed for two mobile usersto communicate is: X time for the sender to reach a node of  Τ time for the message to propagate inside  Y time for the receiver to meet , after the propagation of the message inside  Theorem : The total communicate time for the snake protocol is bounded above by the following: The above upper bound is minimized when

10. I. Chatzigiannakis - S. Nikoletseas The Runners Protocol • At the Set-up phase, a set of k hosts become the support  • Each member of performs an independent random walk on the network area. Thus all support hosts sweep the area “in parallel” by moving independently of each other. • When some node of gets within communication range of a sender, an underlying sensor sub-protocol P2 notifies the sender to send its message(s). • The messages are then propagated within  structure using a synchronization sub-protocol P3. • When a receiver node comes within communication range of a node of , the underlying sensor sub-protocol P2 notifies the node of , and the pending messages are forwarded to the receiver.

11. I. Chatzigiannakis - S. Nikoletseas The Synchronization Sub-protocol P3 • When 2+ members of (runners) meet, a two-phase commit protocol is initiated • Let the members of that reside on the same area of the network be MS1, MS2,…, MSj • Let S1(i) be the set of undelivered messages and S2(i) be the set of delivery receipts (i.e. we assume a generic storage scheme) of runner MSi where 1≤i≤j. • Phase 1: Using the sensor sub-protocol P2, identify the runner with the lowest ID (i.e. MS1) and transmit S1 and S2. • MS1 collects all the sets and combines them with its own to compute its new sets S1 and S2: and • Phase 2: MS1 broadcasts its decision to all the other runners. • All hosts that received the broadcast apply the same rules (as MS1 did) to join their S1 and S2 sets. • Any host that receives a message in phase 2, and which has not participated in phase 1, accepts the values received in that message as if it had participated in phase 1.

12. I. Chatzigiannakis - S. Nikoletseas Protocol Correctness • Theorem 1:Assuming that the motions of the hosts of the network which are not member of are independent of the motion of the runners, the runners protocol is correct. • Proof: Under this independence assumption, any mobile host will eventually meet some node of  with probability 1. • By using Borel-Cantelli Lemmas for infinite sequences of trials, given an unbounded period of (global) time each station will meet the support infinitely often with probability 1. • This guarantees delivery of a message onto  and, then, reception by a destination when it meets the support.

13. I. Chatzigiannakis - S. Nikoletseas Fault Tolerance • Theorem 2:The runners protocol is t-fault tolerant, where t<k and k the size of . Hosts need to re-transmit messages until a receipt of delivery is received by a member of . • Proof: Let’s assume that a sender S transmits some messages to the first runner R that it encounters, and let’s assume further that this runner is distant from the rest of . • Thus copies of the original messages are only stored in R and they will not propagate within for some time  (i.e. until R meets other members of ). • In a worst case, if a fault occurs on R during this period , the only copies of the messages will be lost and not delivered to their final destination. • Thus S retransmits the messages until finally a receipt is received by a member of .

14. I. Chatzigiannakis - S. Nikoletseas Highly Changing Ad-Hoc Mobile Networks • First Time Considered • Stronger Model • Mobile Hosts can expand or Shrink the Area of the Network • Possible Obstacles Appear such as rumbles, destroyed bridges… • New Paths Discovered due to rumble removal • Exploration of New Areas due to the mobility of the hosts • We study such changes by using the number of vertices n=|V| of the motion graph G. • At any time instance, the motion graph G will undergo certain changes by • adding or removing one or more vertices • adding or removing one or more edges • These changes are unpredictableand are not known in advance.

15. I. Chatzigiannakis - S. Nikoletseas The Need for Adaptation • The Snake + Runners protocols assume that the area of deployment (motion graph G) remains fixed throughout the execution of the protocol. • The execution and performance analysis provided assume a fixed G • Selection of an optimal support size (k) implied by the analysis assumes that the network size (n) is known in advance • But in highly-changing network the network size (n) can change → the optimal support size (k) can change • This leads to big communication times OR unnecessary high number of support (k) • What if the initial network size is not known in advance? • We need a mechanism to modify (adapt) the size of to the (current) optimal by periodically measuring the communication times

16. I. Chatzigiannakis - S. Nikoletseas The Adaptive Runners Protocol (1) • At the Set-up phase, the set of k hosts of elect a leader • The leader executes the adaptation sub-protocol Padapt • The protocol Padapt evolves in phases of possible adaptation • At the beginning of each such phase, the protocol tries to sense the need (or not) of possible adaptation • Does not assume knowledge on the network size (n) • This is sensed explicitly by measuring the communication times • Let tmeas be the time needed to measure (accurately enough) the communication times of the network • Such measurements may indicate that • Communication times becomes significantly bigger → Increase k • Communication times becomes significantly smaller → Reduce k

17. I. Chatzigiannakis - S. Nikoletseas The Adaptive Runners Protocol (2) • Adaptation is done progressively by adding (or removing) support members in each step of the adaptation procedure • Let tchange-size be the time needed to change the support size • This progressive adaptation allows to sense reaching a new optimal size – since further increase of the Σ size (k) will not significantly affect the communication times • Previous research (both analytical and experimental) on the performance of the Support approach indicate such a threshold behavior for the support size (k) and its effect on communication times • Let tsteps be the number of adaptation steps • Then the overall time to adapt is

18. I. Chatzigiannakis - S. Nikoletseas The Adaptation Procedure Padapt (1) • Let x0,x1,…,xi be the performance measure at the end of step i, where x0 is an initial value and step i is the current execution step • Let xi = |xi - xi-1| ≥ xi-1 be the “sensed” alteration and is the “sensitivity factor” and is set to a fixed small percentage constant (i.e. =0.1) • We use the sensitivity factor to avoid non-necessary adaptation in cases of trivial changes in the network • When sensitivity threshold (xi-1) is crossed a new adaptation phase is initiated. • At the step t of the procedure, the leader of Σ will increase or decrease k by c·t where c is a small constant (for initialization purposes) and

19. I. Chatzigiannakis - S. Nikoletseas The Adaptation Procedure Padapt (2) • Let tsensebe the last i such xi≥ xi-1– i.e. tsense is the last step of the last adaptation • At the end of each adaptation phase, the leader stores xtsense for further use • Then for any sensing of subsequent adaptation phases, the following rule is used: • Let xi = |xi - xtsense| ≥ xtsensethe next “sensed” alteration since the last adaptation phase tsense • Remark that xi measures the performance measures over short time intervals • xi is used to prevent our protocol from not detecting a sequence of small changes that do not cross the sensitivity factor but whose cumulative effect over a long time period leads to an adaptation need

20. I. Chatzigiannakis - S. Nikoletseas Analysis of the Adaptation Speed • The overall time to adapt is • Let n=|V| of the motion graph at the beginning of Padapt, i.e. at tsenseand n’ be the number of vertices at the end of the adaptation phase. • Remark that both n and n’ are not known by the protocol but implied by the performance measurements taken • Let k, k’ be the “optimal” support sizes for n and n’ respectively. • If the optimal support size then the number of steps is upper bounded by

21. I. Chatzigiannakis - S. Nikoletseas Analysis of the Time to Increase the Size of Σ • Note that the analysis holds only in the case where the hosts not in perform concurrent and independent random walks on G. • Remark that runners also perform concurrent and independent random walks on G. • Theorem 4:In the case of adapting by increasing the support size, the expected time is: • Theorem 5:Assuming uniform spread of the h hosts into the n cubes of the network area, the expected time is:

22. I. Chatzigiannakis - S. Nikoletseas Analysis of the Time to Decrease the Size of Σ • We work using similar arguments as in the case of increasing the support size. • Theorem 6:In the case of adapting by decreasing the support size, the expected time is: • Theorem 7:Assuming uniform spread of the k runners into the n cubes of the network area, the expected time is:

23. I. Chatzigiannakis - S. Nikoletseas Concluding Remarks & Future Work • We presented a new adaptive, compulsory protocol for the basic communication problem in highly-changing ad-hoc mobile networks. • Provided correctness and fault-tolerance proofs • Investigated analytically its performance • There are several directions for future work: • Provided tighter bounds for the performance of the Runners protocol (probably using advanced analytic techniques from Physics, such as theory of interacting particles) • Implement the protocol and experimentally validate its superiority over the static implementation of the runners protocol.