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Fuzzy causal order

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Se presenta un nuevo orden de eventos para sistemas distribuidos. …

Se presenta un nuevo orden de eventos para sistemas distribuidos.

A new event ordering for distributed systems is presented.

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    • 1. Congreso Internacional de Informática AplicadaDistributed Multimedia SynchronizationBased on Fuzzy Causal Relations Luis Alberto Morales Rosales Misantla, Veracruz, a 25 de Abril del 2012
    • 2. Overview• Practical Aspect (application area) – Distributed multimedia synchronization in real time • Distributed sources • Heterogeneous data (discreet and continuous) • Loss of data • Transmission delay• Theoretical Aspect – Development of a flexible causal relation for distributed systems unlike the one proposed by Lamport (1978) • For applications where certain degradation of the system is allowed is not necessary to assure a strict causal delivery, for example, multimedia, scheduling, cooperative work and planning 2
    • 3. Outline1. Introduction2. Related work3. Problem description4. Research proposal5. Results6. Conclusions INAOE 3
    • 4. Introduction• Distributed systems – Absence of a global clock – Concurrency – Fail tolerance – Examples: cooperative applications, mobile systems, multimedia applications, etc.• Distributed multimedia systems – The exchange of big volumes of multimedia data in a communication network among a group of participants 4
    • 5. Introduction• Multimedia synchronization – The preservation of temporal dependencies among the application data from the time of generation to the time of presentation Audio Video Multimedia Text, slides, images, etc. Multimedia data 5
    • 6. Introduction A V V P1 P2 A A V S S A V V V A- Audio (Voice) P1 – Participant 1 V- Video P2 - Participant 2 S- Slides P3 P3 - Participant 3 Example of a multimedia scenario 6
    • 7. Introduction AP1 V VP2 A VP3 SA- Audio (Voice) P1 – Participant 1V- Video Time Line P2 - Participant 2S- Slides P3 - Participant 3 Representation of a multimedia scenario 7
    • 8. Related Work Synchronization Synchronous AsynchronousCommon reference Logical dependenciesPhysical clock DisadvantagesDisadvantages Introduction of random delays Bottlenecks Discard of messages Introduction of random delays Halt of the system Not scalable 8
    • 9. Related work: Synchronous• Works that use fuzzy logic – Zhou et al. [6] • Temporal model based on fuzzy petri networks to represent the multimedia synchronization • Video on demand – Ramaprabhu et al. [3] • Broadcast transmission of video on demand • Consider the parameters: available bandwidth, network delay and buffer space 9
    • 10. Related work: Synchronous (Cont.)• Works that use fuzzy logic – Coelho et al. [1] • Methodology for the high level specification and decentralized coordination of temporal interdependences among objects of multimedia documents previously stored • Membership function to calculate the lifetime of the data • Strict causal relation for event ordering • Global time reference 10
    • 11. Related work: Asynchronous Causal and ∆-causal algorithms• The causal and ∆-causal algorithm use the causal relation proposed by Lamport – Main works: Baldoni [2] et al., Tomoya et al.[5] and Pomares et al. [4] – Introduce delays and/or discard of messages (packets) a b c Time Line Strict delivery order ∆-causal order b→c b→c and ∆c < ∆max ( b, c) ( b, c ) Infinite halt Deliver c and discard b 11
    • 12. Context problem• Distributed multimedia synchronization in real time by considering: • Asynchronous sources • Heterogeneous data • Communication network characteristics – Loss of the data and transmission delay • Without previous knowledge of the system behaviorHow can we ensure the temporal dependencies among events in this kind of enviroments? 12
    • 13. Research proposal• As hypothesis we claim that for systems where some degradation of the system is allowed, it is not necessary ensuring a strict causal order of the data, which is associated with a binary value• We propose the fuzzy causal relation and the fuzzy causal consistency to relax the order delivery• We show that relaxing the causal delivery order of the data can improve the performance of the synchronization 13
    • 14. Results Fuzzy causal relation (FCR)• Fuzzy causal relation (FCR) denoted by “a λ b” → – The FCR is based on a notion of “distance” among the events – The distance can be established considering three main domains: spatial (RS), temporal (RT) and/or logical(RL) – Using the notion of distance, the FCR establishes a cause-effect degree that indicates “how long ago” an event a happened before an event b – One assumption considered for the FCR is that “closer” events have a stronger cause-effect relation, according to the addressed problem 14
    • 15. Results (Cont.) Fuzzy causal relation (FCR)• The distance between events is determined by the fuzzy relation DR: E × E → [0, 1] DR(a,b) = RS ∪ RT ∪ RL Where: RS=(R1 ∪ R2∪... ∪ Rs) RT=(R1 ∪ R2∪... ∪ Rt) RL=(R1 ∪ R2∪... ∪ Rl) Ri = membership function• The fuzzy union operator chosen for intra and inter domains is the max operator 15
    • 16. Results (Cont.) Fuzzy causal relation (FCR)• Distance relation – The DR grows monotonically and it is directly proportional to the spatial, temporal and/or logical distances between a pair of events – DR(a,b) with a value tending to zero indicates that the events a and b are “closer” – The DR cannot determine precedence dependencies among events, it only indicates certain distance among them 16
    • 17. Results (Cont.) Fuzzy causal relation (FCR)• The fuzzy causal relation “ λ on a set of events E satisfies →” the two following conditions:3. a λ b If a→ b ∧ 0 ≤ DR(a,b) < 1 → FCR between two events λ6. a → c If ∃b  a→b→c ∧ DR(a,b) ≤ DR(a,c) : DR(a,b), DR(a,c) < 1 Transitivity•The fuzzy concurrency (FCNR) is defined as follows: The value of the fuzzy causal relationa λbetween a pair of events is represented as: FCR(a,b) b If ¬ (a→b ∨ b→a) ∧( (DR(a, b)= DR(b, a) )< 1) 17
    • 18. Results(Cont.) Example of the FCR and the FCNR 2 FCR(a,e) b e 1a c f d Example of fuzzy precedence among causal messages FCR(a,e) λ a → e If ∃b  a→b→e ∧ DR(a,b) ≤ DR(a,e) : DR(a,b), DR(a,e) ) < 1 18
    • 19. Results(Cont.) Fuzzy Causal Consistency• The Fuzzy Causal Consistency (FCC) is based on the FCR• The goal of the FCC is to indicate “how good” the performance of the system is in a certain time• The meaning of the performance can be indicated according to the problem to solve 19
    • 20. Results(Cont.) Fuzzy Causal Consistency FCRp (b,a) b c d FCRp(c,a) ∑ GP(b) FCR (b, a) p Fuzzy causalH(a) FCRp(d,a) b∈H ( a ) FCC p (a) = consistency FCRp( w,a) ∑ GP(b) FCCp(a) w b∈H ( a ) Calculation of the Fuzzy causal consistency b GP(b) is a weighting degree used to determine priorities or weight FCRp( b,d) a for every fuzzy causal relation when it is needed d Average FCRp( c,d) FCCp(a) Weight c Example of calculation of the FCC 20
    • 21. Results (Cont.) Fuzzy causal delivery order• The fuzzy causal delivery order must satisfy the following condition: λ If send(m) → send(m’) then ∀p ∈ dests(m)∩dests(m’), FCCp(m’)≤ FCCmax – deliveryp(m) → deliveryp(m’) or – deliveryp(m’) → deliveryp(m) 21
    • 22. Results Causal order vs fuzzy causal order a+ c+ = xn a -→a +i =Part(X) A C a- = x1 c- a+→ d- d = y1 - B b =yp +j =Part(Y) D Causal delivery order of events a+ d - Fuzzy causal deliveryk =Part(Z) Synchronization Period Example of a fuzzy causal delivery Fuzzy causal order Strict order delivery ∆-causal order delivery delivery a+→d - a+→d - y ∆d < ∆max + λ a →d - ( a+, d - ) ( a+, d - ) Deliver: (a+, d - ) or Infinite halt Deliver d and discard a (d -, a+) 22
    • 23. Synchronization Scheme of the Distributed Multimedia Mechanism Model Fuzzy Causal Component Fuzzy Causal Temporal Fuzzy Causal Relations Consistency Distance FCRp(m) ∀m ∈ H(a) FCCp(a) RN Performance of the SystemCausal Distance RD Fuzzy Control System Weighting Degree Fuzzy GP Control Network Adjustment and Conditions Selective Discard System NCComponent of Current State ofinput variables the System 23
    • 24. Synchronization model A E C E’ i =Part(X) j =Part(Y) F D F’ B i≠j Synchronization periods Fuzzy causal delivery A → I EF → I (C ||| D) → I E F → I BFormally a period is defined as: EF λ f ∨ eλ ⇒ ∀(e, f) ∈ (E x F), e → f 24
    • 25. Synchronization model 25
    • 26. Results (Cont.) The FCR applied to the intermedia synchronization• The FCR for the intermedia synchronization problem gives a qualitative measure of the temporal and logical dependencies between two events with regard to a partial view of a participant• The value of the FCR is calculated by: λ FCR (a, b) = DR (a, b) if a  →b  DR (a, b) = max( RD , RN ) 26
    • 27. Results (Cont.) The FCR applied to the intermedia synchronization• The meaning of the values obtained by the FCR(a, b) is as follows: – When FCR(a, b) tends to zero indicates that the events a and b are “closer”, which means that the network present low transmission delay and low loss of messages – When FCR(a, b) tends to the unit indicates the opposite 27
    • 28. Results (Cont.) FCC applied to the intermedia synchronization• FCC gives a qualitative measure of the synchronization error, according to the temporal and logical dependencies in the whole system in a certain time, with regard to the partial view that every participant has – When FCCp(a) tends to zero, this indicates that the performance of the system is good – When FCCp (a) tends to the unit, this indicates that the system performance is regular or bad 28
    • 29. Results (Cont.) Fuzzy control system Fuzzy Causal Current State Consistency, FCCp(a) µ= delivery time Fuzzy of the System Control System Network Conditions (CS) NC(a) Diagram of the fuzzy control system• The NC determines the network condition• TheThe NC consider:control will bedelays, jitter among messages, loss of – actions that the transsmision able to execute are: – the immediate delivercongestion and message aavailable messages, network of the received bandwith or its delay, and – the determination whether a selective discard of the messages contained – in the causal history of the messageto is carried out When the value of NC(a) is near a zero, this means that the network• Theconditions are good is used as inference mechanism Mandami’s model• – When membership one, this are included the network conditions TriangularNC(a) tends to functions represents that as part of the fuzzy control bad are 29
    • 30. Results (Cont.) Test of a multimedia scenario• The Host from W to Y send: – Audio – Video, and – Animation Host Z• Host Z only listens • We simulated three scenarios: • Soft, Medium and Hard Host Host Host W X Y• 100,000 simulations• Fuzzy causal order vs. ∆-causal order •When Lamport’s relation is used the system halts if a message is lost 30
    • 31. Results (Cont.)Test: Fuzzy causal order vs. ∆-causalSoft case Big without discard Medium without discard Classification of delivered messages 31
    • 32. Results (Cont.)Test: Fuzzy causal order vs. ∆-causalSoft case ∆-Causal Order Fuzzy causal order Classification of messages loss INAOE 32
    • 33. Results (Cont.)Test: Fuzzy causal order vs. ∆-causalMedium case Medium without Small with discard discard Classification of delivered messages 33
    • 34. Results (Cont.)Test: Fuzzy causal order vs. ∆-causalMedium case ∆-Causal Order Fuzzy causal order Classification of messages loss 34
    • 35. Results (Cont.)Test: Fuzzy causal order vs. ∆-causalHard case ∆-Causal Order Fuzzy causal order Classification of messages loss 35
    • 36. Conclusions• The definitions of FCR and FCC permits to establish a more asynchronous ordering for application where certain degradation of the system is allowed• The FCO allows a more asynchronous delivery of events compared with the causal delivery order based on the happened-before relation introduced by Lamport• The FCR and FCC allow a measure of the performance of the application by a participant at runtime without halt the system 36
    • 37. Conclusions• A novel fuzzy control for intermedia synchronization that works in a distributed manner was presented• By using the fuzzy control and FCC the mechanism discard fewer messages than the ∆-causal mechanism
    • 38. References1. André L. V. Coelho, Alberto B. Raposo, Ivan L. M. Ricarte. “Bringing Flexibility to the Specification and Coordination of Temporal Dependencias among Multimedia Components”. VII Simposio Brasileiro de Sistemas Multimídia e Hipermídia, Florianópolis, Brazil, SBC. 2001, pp. 37-52.2. Roberto Baldoni, Achour Mostéfaoui, Michel Raynal. “Efficient Causally Ordered Communications for Multimedia Real-Time Applications”. The 4th International Symposium on High Performance Distributed Computing (HPDC 95), Washington, DC, USA, August 2-4, 1995, pp. 140-1473. Ramaprabhu Janakiraman, Marcel Waldvogel and Lihao Xu. “Fuzzycast: Efficient Video-on-demand over Multicast”. Proceedings INFOCOM 2002, New York, NY, USA, June 2002.4. Saul E. Pomares Hernandez, Luis A. Morales Rosales, Jorge Estudillo Ramirez, and Gustavo Rodriguez Gomez, “Logical Mapping: An Intermedia Synchronization Model for Multimedia Distributed Systems,” Journal of Multimedia, Eds. Academy Publisher, Vol. 3 No.5, 2008, ISSN: 1796-2048, pp. 33-41.5. Tomoya Enokido, Sei-ichi Hatori, Takuya Tojo Makoto Takizawa. “Group Communication in Distributed Multimedia Objects”. Proceeding of The Eighth IEEE International Workshop on Object-Oriented Real-Time Dependable Systems (WORDS 2003), 2003, pp. 258.6. Yi Zhou, Tadeo Murata. “Modeling and Analysis of Distributed Multimedia Synchronization by Extended Fuzzy-Timing Petri Nets”. Transactions of the Society for Desing and Process Science, Volume 5, Number 4, December 2001, pp. 23-37. 38
    • 39. Thanks !Questions? 39
    • 40. Resultados 1 Causalidad estricta Relación causal difusa y consistencia causal difusa 0 Línea del tiempo Restricciones de una causalidad estricta vs. relación causal difusa y consistencia causal difusa INAOE 40
    • 41. Related work Characteristics Coelho et. al Proposal Predefined synchronization points Yes No Decisions Centralized Distributed Real time No Yes Communications Producer-Consumer Group Time Constraints No Yes Quality of services No Yes Clocks to order the events Physics Logics Comparison of characteristics between the work done by Coelho et al. in [3] and our proposed research INAOE 41
    • 42. Algoritmo Periodo 1 A a’ Part(w), C Historia Causal H(m) de a’: a {d,f,z} D d B E Part(x) Periodo 2 f G Part(y) F H g z Part(z) 6.- Calculo del estado actualPart(y) orden de entrega causal:1.- Calculo de los Periodos de cada elemento contenido en H(m) 7.- Calculo de CR2.- Obtención de los parámetros RTT, Bw, jitter p/c evento de H(m) 8.- Paso de parámetros3.- Calculo de la Distancia Temporal: t(a’)-t(a) al control difuso (CR y CCD) 9.-Salida del control difuso4.- Calculo de la Distancia Causal (a’): {d,f,z} •Retrasar5.- Calculo de RCD(a’) y CCD a partir de H(a’)={d,f,z} •Entregar INAOE •Descarte Selectivo 42
    • 43. • The GP variable is the weighting grade that determines the degradation of a channel (participant) according to the best channel of the system  ( RTTi + jitteri ) + PPi  GPi =    BChannel  BChannel = min in=1 [ ( RTTi + jitteri ) + PPi ]
    • 44. 95 190 250 Global Time 0 mj-1 mi H(mi)={mj, mk}i =Part(A) audio A mj Bj =Part(B) videok =Part(C) audio C mk-2 mk-1 mk Δ(mk-2) Δ(mj-1) m1l
    • 45. Media Mode, application Maximum Error synchronization (QoS, dmax)Video Animation Correlated ±120ms Audio Lip synchronization ±80ms Image Overlay ±240ms No-overlay ±500ms Text Overlay ±240ms No-overlay ±500msAudio Animation Event correlation (e.g. dancing) ±80ms Audio Tightly coupled(stereo) ±11ms Loosely coupled (dialogue mode with ±120ms various participants) Loosely coupled (e.g. background ±500ms Image music) coupled (e.g. music with notes) Tightly ±5ms Loosely coupled (e.g. slide show) ±500ms Text Notes of text ±240ms Pointer Audio related to the item ±700ms Tabla 2. Maximum error tolerable for multimedia synchronization INAOE 45
    • 46. Algorithm A a’ Part(w), C Historia Causal H(m) de a’: a {d,f,z} D d B E Part(x) f G Part(y) F H g z Part(z)Part(y) orden de entrega causal: 6.- Calculo del estado actual 7.- Calculo de CR1.- Calculo de los Periodos de cada elemento contenidoen H(m) 8.- Paso de parámetros2.- Obtención de los parámetros RTT, Bw, jitter p/c evento de H(m)3.- Calculo de la Distancia Temporal: t(a’)- al control difuso (CR y CCD)t(a)Calculo de la Distancia Causal (a’): 9.-Salida del control difuso4.- •Retrasar{d,f,z}5.- Calculo de RCD(a’) y CCD a partir de •EntregarH(a’)={d,f,z} INAOE •Descarte Selectivo 46
    • 47. 95 190 250 Global Time 0 mj-1 mi H(mi)={mj, mk}i =Part(A) audio A mj Bj =Part(B) videok =Part(C) audio C mk-2 mk-1 mk Δ(mk-2) Δ(mj-1) m1l
    • 48. Example of a synchronization multimedia scenario 95 165 253 Global Time 0 mj-1 mi H(mi)={mj, mk}i =Part(A) audio A mj Bj =Part(B) videok =Part(C) animated C mk-2 mk-1 mk images Δ(mk-2) Δ(mj-1) m1l
    • 49. Results(Cont.) Fuzzy causal relation 1 1Cause-effect Cause-effect Temporal cause-effect Logical cause-effect degree degree INAOE 49
    • 50. Related work Characteristics Coelho et. al Proposal Predefined synchronization points Yes No Decisions Centralized Distributed Real time No Yes Communications Producer- Group Consumer Time Constraints No Yes Quality of services No Yes Clocks to order the events Physic Logic Comparison of characteristics between the work done by Coelho et al. in [3] and our proposed research INAOE 50
    • 51. Results(Cont.) The FCR applied to the intermedia synchronization• The membership functions, “RN” and “RD” can be calculated by a triangular function 1 defined as: 0 If x< f x− f A(x) If f≤ x< hO f h h− f 1 If x≥h INAOE 51
    • 52. Results(Cont.) The FCR applied to the intermedia synchronization 1 1Cause-effect Cause-effect dmax Causal distance Temporal cause-effect degree Logical cause-effect degree dmax is assigned according to the maximum error allowedCausal distance is established to four events INAOE 52
    • 53. Results (Cont.) Input value for the fuzzy causal relation• Temporal distance m m’ Part(X) ∆(m) Part(Y) Local physical clock of Part(Y)∆(m)= time_arrival(m) – time_arrival(m’) ∀p∈ H(m) ∧ m = last_messagep INAOE 53
    • 54. Results(Cont.) FCC applied to the intermedia synchronization  GP is the weighting grade that determines the degradation of a channel (participant) according to the best channel of the system  ( RTTi + jitteri ) + PPi • RTT is the Round trip time of a message GPi =    BChannel • Jitter is the fluctuation of end to end of a message with the next message inside the same stream BChannel = min in=1 [ ( RTTi + jitteri ) + PPi ]• PP is the number of lost messages in a synchronization period• n is the number of channels (participants) which are causally related to the event a INAOE 54
    • 55. Results (Cont.)Input value for the fuzzy control system• NC is calculated by the following formula: n  2 Bi  ( PEi − PRi )  ∑  RTT  i =1  +  PEi  * GPi i   NC (a ) = S GP• Where – B is the bandwidth available in the network. – RTT is the round trip time of a message a across the network. – PE is the number of expected messages inside the synchronization period. – PR is the number of received messages inside the synchronization period. – SGP is the sum of the weighted grades of the channels. – n is number of channels(participants) which are causally related with the message a, known as the causal history of a. INAOE 55
    • 56. Results (Cont.) Fuzzy control system• The set of rules used by the fuzzy control to adjust the delivery time of the message a has the form: If NC(a) ∈ Ai y FCCp(a) ∈ Bi then µ ∈Ci• Where: – NC(a), FCCp(a) and µ are the enter parameters of the fuzzy control system – Ai = {good, regular, bad} are the linguistic labels for NC(a) – Bi = {good, regular, bad} are the linguistic labels for the FCCp(a) – Ci = {big, medium, short} are the linguistic labels for the output µ INAOE 56
    • 57. Results (Cont.) Fuzzy control system• The set of rules that the fuzzy control system considers is the following3. If NC(a)= bad and FCCp(a)= good, then µ= medium (delivery without discard)4. If NC(a)= bad and FCCp(a) = regular, then µ= short (delivery with discard)5. If NC(a)= bad and FCCp(a) = bad, then µ= short (delivery with discard)6. If NC(a)= regular and FCCp(a) = good, then µ= medium (delivery without discard)7. If NC(a)= regular and FCCp(a) = regular, then µ= medium (delivery without discard)8. If NC(a)= regular and FCCp(a) = bad, then µ= short (delivery with discard)9. If NC(a)= good and FCCp(a) = good, then µ= big (delivery without discard)10. If NC(a)= good and FCCp(a) = regular, then µ= big (delivery without discard)11. If NC(a)= good and FCCp(a) = bad, then µ= medium (delivery without discard)• The Mamdani model has been selected as the inference mechanism• The centroide function has been selected for the defuzzyfication of the output of the fuzzy control system INAOE 57

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