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An Adaptive Compulsory Protocol for Basic Communication in Ad-hoc Mobile Networks Ioannis Chatzigiannakis Sotiris Nikoletseas April 2002

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Ad-Hoc Mobile Networks I. Chatzigiannakis - S. Nikoletseas WITHOUTA 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

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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) ? 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) ? I. Chatzigiannakis - S. Nikoletseas

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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 anothers 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. I. Chatzigiannakis - S. Nikoletseas

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Limitations of Such Approaches I. Chatzigiannakis - S. Nikoletseas 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)

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Any other host within tr can receive any message broadcasted by the host.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). An Explicit Model Of Motions tr tc sphere tr We assume that each mobile host has a transmission range represented by a sphere tr centered by itself. cube tc We approximate this sphere by a cube tc with volume V(tc), where V(tc) < V(tr) I. Chatzigiannakis - S. Nikoletseas

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The Support Approach I. Chatzigiannakis - S. Nikoletseas 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

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Previous Work: The Snake Protocol I. Chatzigiannakis - S. Nikoletseas At the Set-up phase, a set of k hosts become the support and elect 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 P 2 notifies the sender to send its message(s). The messages are then propagated within structure using a synchronization sub-protocol P 3. When a receiver node comes within communication range of a node of, the underlying sensor sub-protocol P 2 notifies the node of, and the pending messages are forwarded to the receiver.

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

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The Runners Protocol I. Chatzigiannakis - S. Nikoletseas 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 P 2 notifies the sender to send its message(s). The messages are then propagated within structure using a synchronization sub-protocol P 3. When a receiver node comes within communication range of a node of, the underlying sensor sub-protocol P 2 notifies the node of, and the pending messages are forwarded to the receiver.

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The Synchronization Sub-protocol P 3 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 MS 1, MS 2,…, MS j Let S 1 (i) be the set of undelivered messages and S 2 (i) be the set of delivery receipts (i.e. we assume a generic storage scheme) of runner MS i where 1ij. Phase 1: Using the sensor sub-protocol P2, identify the runner with the lowest ID (i.e. MS 1 ) and transmit S 1 and S 2. –MS 1 collects all the sets and combines them with its own to compute its new sets S 1 and S 2 : and Phase 2: MS 1 broadcasts its decision to all the other runners. –All hosts that received the broadcast apply the same rules (as MS 1 did) to join their S 1 and S 2 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. I. Chatzigiannakis - S. Nikoletseas

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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. any mobile host will eventually meet some node of with probability 1.Proof: Under this independence assumption, any mobile host will eventually meet some node of with probability 1. infinitely oftenBy 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. This guarantees delivery of a message onto and, then, reception by a destination when it meets the support. I. Chatzigiannakis - S. Nikoletseas

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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: Lets assume that a sender S transmits some messages to the first runner R that it encounters, and lets 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. I. Chatzigiannakis - S. Nikoletseas

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Highly Changing Ad-Hoc Mobile Networks I. Chatzigiannakis - S. Nikoletseas 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 unpredictable and are not known in advance.

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The Need for Adaptation I. Chatzigiannakis - S. Nikoletseas 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

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The Adaptive Runners Protocol (1) I. Chatzigiannakis - S. Nikoletseas At the Set-up phase, the set of k hosts of elect a leader The leader executes the adaptation sub-protocol P adapt The protocol P adapt 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 t meas 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

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The Adaptive Runners Protocol (2) Adaptation is done progressively by adding (or removing) support members in each step of the adaptation procedure Let t change-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 t steps be the number of adaptation steps Then the overall time to adapt is I. Chatzigiannakis - S. Nikoletseas

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The Adaptation Procedure P adapt (1) Let x 0,x 1,…,x i be the performance measure at the end of step i, where x 0 is an initial value and step i is the current execution step Let x i = |x i - x i-1 | x i-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 ( x i-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 I. Chatzigiannakis - S. Nikoletseas

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The Adaptation Procedure P adapt (2) Let t sense be the last i such x i x i-1 – i.e. t sense is the last step of the last adaptation At the end of each adaptation phase, the leader stores x t sense for further use Then for any sensing of subsequent adaptation phases, the following rule is used: Let x i = |x i - x t sense | x t sense the next sensed alteration since the last adaptation phase t sense Remark that x i measures the performance measures over short time intervals x i 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 I. Chatzigiannakis - S. Nikoletseas

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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 t sense and 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 I. Chatzigiannakis - S. Nikoletseas

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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: I. Chatzigiannakis - S. Nikoletseas

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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: I. Chatzigiannakis - S. Nikoletseas

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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. I. Chatzigiannakis - S. Nikoletseas

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