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R` Global state S`;Show problem of slicing state when something is in transit T*`?Define local state;  send ( m ij )     LS i  iff time of  send ( m ij ) < current time of  LS i ; similar for receive Uh =transit( LS i ,  LS j ); inconsistent( LS i ,  LS j ); consistent state is one with inconsistent set empty for all pairs  LS i , @ LS j VUU`)Consistent global state: Chandry-Lamport W*`Termination detection X`Haung we`,Differences with non-distributed algorithms `"no shared memory, no common clock /`unpredictable message delays `Types of algorithms 0``Vfairness (requests executed in the order made, or in the order they arrive in system) ?`Xfault tolerance (if a system fails, the algorithm can recover and continue to function) @wH`Performance measures A`,Performance under varying loads (low, high) B`&Best, average, worst case performance C`*Terminology for non-token based protocols D*`Request set  R i  for a process  p i :set of nodes from which  p i  must obtain permission to enter critical section EUU2`qRequests ordered bytimestamps: ( time ,  pid ); the pid is used to disambiguate equal timestamps F2`/Request sets satisfy the following conditions: G*`:pairwise non-null intersection property : for all 1   i ,  j   n  with  i   j ,  R i      R j    H J`^equal effort rule : for all 1   i   n , |  R i  | =  K I`kequal responsibility rule :  p j  is contained in  D  number of  R i . J`Xfor all 1   i   n ,  p i      R i  KUU5 `1Obvious solution: pick a single controlling site LB!`SAdvantages: 3 messages per request (site REQUEST, controller REPLY, site RELEASES) MN!`QDisadvantages: single point of failure, congestion, controller does all the work NZn` Lamports O`Request set is all processes Qrk`'Performance: 3( n 1) messages QY6`Ricart and Agrawalas HHˆ;6HHˆ 66 lH$ @5!:H$ 99l H$ @6!H$ 8Wlm Ricart and Agrawalas Distributed Mutual Exclusion ProtocolECS 251 Winter 2001Page  7  HUV @7!8HHUV GGlHTsUVXuuUVM{񻈣Q Q  s1ફ"EWUUiUUXx;=?ફ"EWUUiUUફ"E8ow &MXy;>@&M&Qw&Qws2UUzXz ;?AUUzUUUUUUzX{ ;@JUUzUUUU}?H =x1C?H FW-e¢ }H =zB2H FW.e d=~EEd=DdFF l d=Dd& zrE zupkfa\WRMHC>vCFILORUX[^adgjmpsy| %).12/,)&# HUV @8!HUV :WlBLast modified at 7:04 pm on Tuesday, February 27, 2001 HHˆ@9!:HHˆII l HHˆ@:!HHˆHW` UUazX| ;AKUUazUUaUUaRUU X};JLRUU UVV6 X~;KMUVV6 V5 X;LNV5 UVV6 X;MOUVV6 fUU^V6 X;NPfUU^V6 0UUV6 X;OQ0UUV6 zUU] X;PRzUU] w X;QSw ^"GwX;RT^"Gw P 1 ,"GwX;SU,"Gw^ᢪ^P 2 \^"GwX;TV\^"Gwe e P 3 SUU%݈X;UWSUU%݈SUU5SUU5e11 ʪ%݈X;VXʪ%݈ʪ5ʪ5e12 ]݈X;WY]݈^^e21 UU]݈X;XZUU]݈UU^UU^e22 UU]݈X;Y[UU]݈UU^UU^e23 ZS{݈X;Z\ZS{݈ZW ZW e31 u{݈X;[]u{݈u u e13UU6PUUX ;\^UU6PUUUU6 ƪ^UU X ;]_ƪ^UU ƪ^w^7^B&X ;^`7^B&7^z^^l5"(X ;_al5"(l_55V6 X;`bV6 <5p@X ;a<5p@< < e24H*XxdyĀUUX ceĀUU@o*UUX cdf@o*UU>IUUX ceg>IUUpo*UUX cfhpo*UUoUVc~UUX cgioUVc~UUĂUVX chjĂUVĂ@Ko-ENĂUVX cikENĂUVENĂqUUeo-o-UVX cjlo-UVo-Bo-GUUo-UUX ckmGUUo-UUGUUJĂro- E^ X clnE^ @؄@P0 J X cmoJ Jo-Jo-P1 UU X cnpUU UUo-UUo-P2 t X coqt tĂtĂP5 tS X cptS tZĂtZĂP4dXtt HHˆXrHHˆt\ `/Chandy-Lamport Global State Recording Protocol ],` Introduction ^ vThe goal of this distributed algorithm is to capture a consistent global state. It assumes all communication channels I@\are FIFO. It uses a distinguished message called a  marker  to start the algorithm. _b` Protocol `*t`P i  sends marker a`/Pi  records its local state  LS i b` For each  C ij  on which  P i  has not already sent a marker,  P i  sends a marker  before  sending other messages. c`/P i  receives marker from  P j d`;If  P i  has  not  recorded its state: e`0Record the state of  C ji  as empty fUU`#Send the marker as described above g*Ԑ`:If  P i  has recorded its state  LS i h Record the state of  C ji  to be the sequence of messages received between the computation of  LS i  and the Pg@ marker from  C ji . HHˆXrHHˆ wss ldXww HHˆXuHHˆa;;wi h Example  j* Here, all processes are connected by communications channels  C ij . Messages being sent over the channels are repreUUR@(sented by arrows between the processes. k*Q`Snapshot  s 1 : l`_P 1  records  LS 1 , sends markers on  C 12  and  C 13 m JP 2  receives marker from  P 1  on  C 12 ; it records its state  LS 2 , records state of  C 12  as empty, and sends marker on  C 21  @and  C 23 n JP 3  receives marker from  P 1  on  C 13 ; it records its state  LS 3 , records state of  C 13  as empty, and sends markers on  C 31  @and  C 32 . o`#P 1  receives marker from  P 2  on  C 21 ; as  LS 1  is recorded, it records the state of  C 21  as empty. p`#P 1  receives marker from  P 3  on  C 31 ; as  LS 1  is recorded, it records the state of  C 31  as empty. q`#P 2  receives marker from  P 3  on  C 32 ; as  LS 2  is recorded, it records the state of  C 32  as empty. r`#P 3  receives marker from  P 2  on  C 23 ; as  LS 3  is recorded, it records the state of  C 23  as empty. s`fSnapshot  s 2 : now messages are in transit on  C 12  and  C 21 . t`_P 1  records  LS 1 , sends markers on  C 12  and  C 13 u LP 2  receives marker from  P 1  on  C 12  after the message from  P 1  arrives; it records its state  LS 2 , records state of  C 12  as @Aempty, and sends marker on  C 21  and  C 23 v JP 3  receives marker from  P 1  on  C 13 ; it records its state  LS 3 , records state of  C 13  as empty, and sends markers on  C 31  @and  C 32 . w :P 1  receives marker from  P 2  on  C 21 ; as  LS 1  is recorded, and a message has arrived since  LS 1  was recorded, it records @ 0,  W j  > 0. ( W i  is the new weight of  P i .) L`4Send  B ( W j ) to  P j `WP j  receives a computation message  B ( W ) from  P i  D*`*W j  =  W j  +  W   fH`?If  P j  is idle,  P j  becomes active  `P i  becomes idle:  )]`4Send  C ( W i ) to  P 0 7`W i  = 0 `P i  becomes idle `BP i  receives a control message  C ( W ): ad`*W i  =  W i  +  W o`9If  W i  = 1, the computation has completed. *`Example * `The picture shows a process  P 0 , designated the  controlling agent , with 2f& W 0  = 1. It asks  P 1 ,  P 2 , and  P 3  to do some computation. It sets  W 1  to 0.3, W 2  to 0.2, and  W 3  to 0.5.  P 2  in turn asks  P 4  and  P 5  to do some computa@Ftions. It sets  W 4  to 0.1 and  W 5  to 0.1.  When  P 5  terminates, it sends C( W 3 ) = C(0.1) to  P 0 , which changes  W 0  to UU@0 + 0.1 = 0.1. *m When  P 3  terminates, it sends C( W 3 ) = C(0.5) to  P 0 , which changes  W 0  to UU@0.1 + 0.5 = 0.6. * When  P 4  terminates, it sends C( W 4 ) = C(0.1) to  P 0 , which changes  W 0  to UUf@0.6 + 0.1 = 0.7. *!f When  P 1  terminates, it sends C( W 1 ) = C(0.3) to  P 0 , which changes  W 0  to UU/;a@0.7 + 0.3 = 1. *;;``CP 0  thereupon concludes that the computation is finished. [UUI`vTotal number of messages passed: 9 (one to start each computation, one to return the weight to the controlling node). HHˆXxHHˆw}yy ldY<}} HHˆY={HHˆ|,,}P `0Lamports Distributed Mutual Exclusion Protocol ,` Introduction  qLamports scheme uses distributed clocks. Every process notifies all others when it wants to enter the region of I@smutual exclusion. The process desiring to go in, enters when all others trying to get in made their request later. b` Notation *t`4n  processes  p 1 , ,  p n `t j  timestamp  ` Protocol !*UL`To enter the critical section,  p i  sends REQUEST( t i ,  i ) to all sites and puts the request on its queue. "wj`?When  p i  receives a REQUEST( t j ,  j ) message, it returns a REPLY( t j ,  j ) to  p j  and puts the request on its queue. #` When  p i  receives a RELEASE( t j ,  j ) message, it deletes  p j s request from the queue. $`Up i  enters the critical section when both of the following conditions hold: %`}p i  has received a message with timestamp larger than ( t i ,  i ) from each of the other sites &``4p1receivesR(13,3)p313Q(10,1)P(10,2)P(10,3) ?`p1enters Q(10,1) @`p1leaves  A`p1sendsR(13,1)p1,p214 B` p2receivesR(13,1)p114 AC` p3receivesR(13,1)p115 HHˆY?{HHˆz|| ldY@ HHˆYA~HHˆ@N&&D 3Ricart and Agrawalas Distributed Mutual Exclusion $@ Protocol ED` Introduction FU`sRicart and Agrawalas protocol is an optimization of Lamports. They piggyback the release message onto the reply. Gn` Notation H*`4n  processes  p 1 , ,  p n I`t j  timestamp J` Protocol K*UM`mTo enter the critical section,  p i  sends REQUEST( t i ,  i ) to all sites. Lwk`SWhen  p i  receives a REQUEST( t j ,  j ) message: M`if it is not trying to enter the region of mutual exclusion, it returns REPLY( t j ,  j ) to  p j . Nn`'if it is trying to enter the region of mutual exclusion, and if ( t i ,  i )    ( t j ,  j ), it retains the REQUEST. O`Uotherwise it returns a REPLY( t j ,  j ) to  p j .. PfK`xWhen  p i  has received a REPLY message from every other process, it enters the region of mutual exclusion. Q`When  p i  leaves the region of mutual exclusion, it sends REPLY( t i ,  i ) to all processes with deferred requests. R-`Example S*?]`5There are three processes,  p 1 ,  p 2 , and  p 3 .  p 1  and  p 3  seek mutually exclusive access to a shared resource. 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