Group Mutual Excluion Baed on Prioritie Karina M. Cenci Laboratorio de Invetigación en Sitema Ditribuido Univeridad Nacional del Sur Bahía Blanca, Argentina kmc@c.un.edu.ar and Jorge R. Ardenghi Laboratorio de Invetigación en Sitema Ditribuido Univeridad Nacional del Sur Bahía Blanca, Argentina jra@c.un.edu.ar Abtract We propoe a ditributed olution for the group mutual excluion problem baed on prioritie, in a network with no hare memory whoe member only communicate by meage. The propoed algorithm i compoed by two player: group and procee, group are paive player while procee are active player. For the coordination acce to the reource, each group ha aigned a quorum. The group have aociated a bae priority in each tage, meanwhile the procee have the ame level priority. An important feature i that procee have aociated a time to participate in the group in each tage. The meage complexity obtain, in the bet cae, where the group doe not yield the permiion, i 3l+3(q 1) meage, where l denote the procee linked and q denote the quorum ize. The maximum concurrency of the algorithm in, which implie that all procee have linked to the ame group. Keyword-Mutual Excluion - Group Mutual Excluion - Concurrency - Ditributed Sytem I. INTRODUCTION In ditributed ytem there are procee that compete in uing reource and other that cooperate and hare reource for olving a tak. The main problem to olve i to recognize it a a mutual excluion one. Thi problem arie in multiprogramming environment becaue procee require excluive acce for uing reource, e.g. printer, databae. Different olution have been propoed to olve thi problem, e.g. [1], [6]. When ome procee cooperate and other compete, a difference from the original problem appear, known a group mutual excluion. The concept of group mutual excluion (GME) can be applied to a variety of area, e.g., concurrent data tructure, ditributed data bae, communication, video conference, wirele ytem. In GME two propertie are important: excluion among competing procee and concurrence among cooperative procee. There are different approache for thi problem uing different paradigm and implementation. GME problem i firt propoed by Joung [3], in which an aynchronou algorithm for hared memory parallel computer ytem i propoed. Wu- Joung [13], propoed a olution to the group mutual excluion on ring network. Several quorum-baed algorithm [4] [12] [7] have been propoed for aynchronou meage paing. The Manabe-Park [7] algorithm prevent the unneceary blocking, defined a the cae that two procee are prevented from entering a critical ection imultaneouly even if they are capable of doing o. Kakugawa et al [5] propoed a privileged token approach, with two clae of token -main and ubtoken-, and ued coterie for communication tructure to reduce meage complexity. Singh-Su [9] propoed a olution to the region ynchronization problem (uch a mutual excluion, group mutual excluion, reader/writer) uing meage and atifying the property of abence of unneceary blocking. There are alo olution for mobile ad hoc network like [11], [8], [10]. In thi paper, we propoe a ditributed olution to the problem of group mutual excluion coordination, conidering that the procee require a time to hare the reource in a group. We conider that every group ha an aociated priority. II. PRELIMINARIES Let be a et of n procee P 0, P 1,..., P n 1 ; a et of m group G 0, G 1,..., G m 1 and a unique, non hareable, reource among the m group. The procee may work alone or in cooperation with other procee in a group. Any of the n procee i able to participate in a group. Only one group at a time i allowed to ue the reource. Initially each proce work alone. When the proce want to work in a team, it elect a group. Each proce may elect any of the different group with a finite time of work in the team. Figure 1 how an example of relation between the group and the 21
P 0 Fig. 1. P 1 P 2 P 7 Reource G 0 G 1 G m-1 Player Proce i Fig. 2. P 8 Group Example of Relation between the player Select Ok Finih Communication between the player P n-1 Procee Player Group k procee; where P 1, P 2 and P 7 are linked to the group G 1, thi i active and ha the permiion to ue the reource. That mean that all the procee are uing the reource concurrently. Procee P 0 and P 8 are linked to the group G 0 that i competing to gain the acce to the reource. The model of two player, poed in [2], propoed a general olution to thi problem uing two player: group and procee. Figure 2 how the communication between the player. The procee are active player and the group are paive player. The relation between the player i temporary. When the player group i activated, the competition to acce the reource begin. The deign of a olution for thi problem require an algorithm that atifie the following requirement. Mutual Excluion: if ome proce i in a group, then no other proce can be in a different group imultaneouly. Bounded Delay: a proce attempting to participate in a group will eventually ucceed. Progre: when the reource i available (the critical ection i empty), and ome group are waiting. At ome later point one group gain the acce to the reource. Concurrent Entering: if ome procee are intereted in a group and no proce i intereted in a different group. Then the procee can participate in the group concurrently. A. Coterie Definition 2.1: Coterie [1]. Let U = {G 1,..., G m } be a et. A et C of ubet of U i a coterie under U if and only if the following three condition are atified. 1) Non-emptine: for each S i C, S i i not empty and S i U. 2) Interection property: for any S i, S j C, S i S j i not empty. 3) Minimality: for any S i, S j C, S i i not a ubet of S j. Coterie i a et of quorum, and a quorum i a ubet of procee. By the interection condition, the coterie can be ued to develop algorithm for mutual excluion in a ditributed ytem. To enter the critical ection, a node i required to receive permiion from all the member of ome quorum in the ytem. Since any pair of quorum have at leat one member in common, mutual excluion i then guaranteed. III. ALGORITHM GBP (GROUP BASE PRIORITY) Thi ection preent a olution to the problem of group mutual excluion including time aociated with the player (group and procee), uing meage for the communication. Applying the model of the two player [2] to thi ituation, we obtain the following: When the player proce want to participate in a group, firt pecifie hi time and then elect the group. Wait until the group allow the acce. At the moment the player group activate, it aign the time of the firt proce to ue the reource. While the player group i waiting to acce to the reource (entry ection): When a requet from a player proce arrive, add the requet to the active queue and compare the duration of the proce with the group duration. If it i greater, then et the duration to the maximum duration of the new player proce. While the player group i uing the reource (critical ection): When a requet from a player proce arrive, compare if the duration of the proce in not greater than the remainder (group duration - elaped duration). Then add the requet to the active queue and accept the requet. Otherwie add the requet to the waiting queue until the next tage. The time aociated with each player doe not repreent deadline time but repreent it duration in the critical ection. In ditributed environment, we have to conider the communication time (time delay). We aume a reliable network, with a etimated 22
communication time tc, and a finite time of ue of the reource. The communication time i neceary to adjut the remainder time, to accept or not a new player proce while the player group i in the critical ection. We define the following variable: tc i,k : Delay etimation of the communication between the group and the proce : Proce time aociated to the group in a tage : Group time in a tage When the player group receive a requet from a proce and it i in the critical ection, the acceptance control for a new proce i the following: < (remainder time k - tc i,k ), where remainder time k = ( - tpoue k ) When the time group finihe, we conider the following option: 1) Wait until all the aociated procee releae the group. 2) Inform the aociated procee in order to finih their aociation. We could conider different poibilitie. a) Waiting for all of the proce acknowledgment. The delay time could be unpredictable. b) Releae the critical ection (releae the reource) and allow another group to acce. Thi option avoid the waiting time, but the notification could be delayed to a aociated proce and till continue uing the reource while a different group gain the acce to the critical ection. Thi ituation doe not guarrantee the group mutual excluion property. In accordance with the contrain impoed for allowing the active aociation in the group, we aume that the group doe not take into account it own time. When each proce finihe, the group i inform. When the group i empty of participant procee it releae the critical ection. Thi option implifie the olution and it i acceptable becaue the aociated time i not critical. Figure 3 how the action of the player proce. The proce, in each tage, end two meage to the group and receive one meage from the group. Req-Proce (,, topdur i ): the proce end a requet meage to the group to participate in during a period topdur i. Rep-Proce (, ): the proce receive the reply of hi requet from, that allow the acce to the reource. Rel-Proce (, ): the proce end a meage to the group to inform that the period in the group ha finihed and it i unlinked. The time that the proce tay in the critical ection i and then releae it aociation proce RemainderSection... EntrySection = choen group = choen the time to ue the reource end Req-Proce (,, topdur i) receive Rep-Proce (, ) CriticalSection... duration ExitSection end Rel-Proce (, ) Fig. 3. Action of Player Proce Variable tate (INACTIVE, ACTIVE, CS, EXIT) LP: keep information of all the linked proce. LG: keep information of all waiting requet of lock. : keep the time to ue the reource. priori: keep the bae priority of the group in the tage. Fig. 4. Variable Group with the group. Figure 4 how the variable of the group. Figure 5 how the action of the player group aociated with the proce and figure 6 how the action with the other group. The tate of the group are the following: INACTIVE: i waiting for participating procee, ACTIVE: i waiting to acce the reource, CS i uing the reource and EXIT i releaing the reource. Each linked proce ha the ame priority, and each group ha an aociated priority. Two different group could have the ame priority. The propoed protocol i baed on priority without prompt meanwhile the group with lower priority i uing the reource. The group communicate with the aociated procee and with the other group. The meage received from the proce are: Req-Proce(,, ) thi meage i received from a proce, if the group i INACTIVE then change it tate to ACTIVE, add the requet to the lit LP and et the length of time of the group ( ) with the length of time of the proce ( ). If the group i ACTIVE the requet i added, and the length time of the group i checked with the length of time of the proce. If it i lower then it et it current time length with the proce time length. If the group i in CS it add the requet and check the remaining time group with the length of time proce. If it i greater it accept the proce requet and allow to participate in thi tage. Otherwie the proce ha to wait for the next tage. Rel-Proce(, ) thi meage come from a proce to releae hi link with the group. Remove the requet from the lit LP. If the 23
group Receive Req-Proce(,, ) cae tate of Inactive : = ; tate = Active ; conj = ; priori = choen priority; AddLp(LP, ); AddLG(LG,, priori); end multicat Req-Grupo(, prior); Active : if > then = ; AddLp(LP, ); SC : AddLp(LP, ); if ( - tpoue k - tc i,k ) then end Rep-Proce(, ); Exit : AddLp(LP, ); Fig. 5. Receive Rel-Proce(, ) DeleLp(LP, ) if activeempty(lp) then tate = Exit ; end multicat Lib-Group( ); G l = SelectGroup(LG); end Rec-Group(G l, ); tate = Inactive ; if not empty(lg) then tate = Active ; conj = ; priori = choen priority; end multicat Req-Group(, priori) Action of Player Group with Player Proce lit L empty of active proce then releae the reource. If waiting procee exit in the lit then the group begin a new tage. The meage received from the other group are: Req-Group(G l, priori) thi meage come from group G l that require the lock. The group grant the lock if available. If the lock i not available two different cae may occur: (a) The priority of the received meage i le than the priority of the meage given the lock then the requet i delayed. (b) If the priority i greater then call the lock to the appropriate group and then grant it the highet priority. Rec-Group(G l, ) thi meage come from group G l, affirmative repone to the meage Req-Group of requirement lock. If the group have all the lock then change the tate to CS and tell all the procee that are linked to the group. Rel-Group(G l, ) thi meage come grom group G l requiring the lock, thi will be ucceful if the group i not in the critical ection. Rep-Rel-Group(G l, ) thi meage come from group G l releaing the lock that had given Fig. 6. Receive Req-Group(G l, priori) if empty(lg) then AddLitGroup(LG, G l, priori); end Rec-Group(, G l ) ele if HigherPriori(LG, G l, priori) then G = findhigh(lg); end Rel-Group(G, ); AddLitGroup(LG, G l, priori); upgrade(priori); ele AddLitGroup(LG, G l, priori); Receive Rec-Group (G l, ) if G l / conj then conj = conj {G l } if conj = S k then tate = CS For each proce in LP do end Rep-Proce(,) Receive Rel-Group (G l, ) if tate CS then conj = conj - {G l }; end Rep-Rel-Group(, G l ); Receive Rep-Rel-Group (G l, ) G = findhigher(lg); end Rec-Group(, G ) Receive Lib-Group (G l ) DeleLitGroup(LG, G l ) if not emptylitgroup(lg) then G = findhigher(lg); end Rec-Group(, G ) Action of Player Group the group. The lock i granted the highet priority requirement. Lib-Group(G l ) thi meage come from the group G l that releae the lock. If there are outtanding requirement, then chooe the highet priority and give the lock. Figure 7 (a) how the tate of the group (ACTIVE) with their linked procee, and, the time of the group i equal to the time of proce. Figure 7 (b) how when arrive a new requet from proce P to link the group with a time (tpodur > ), ince the group i in the ACTIVE tate, et the value of it time with the time of P, figure 7 (c) how thi modification. Figure 7 (d) how the tate of the group (CS) with their linked procee, and, and the tpoue k > 0. Figure 7 (e) how when arrive a new requet from proce P to link the group with a time tpodur. Since the time tpodur i greater than ( - tpoue k - tc,k ) and the group i in SC then the proce P ha to wait for the next tage, figure 7 (e) how thi cae. The meage among the group correpond to the competition to gain the acce of the reource. The algorithm ue meage to obtain the permiion 24
P P (a) Group k Active -Entry Section tpodur (b) Group k Active -Entry Section. Requet from p tpodur (c) Group k Active -Entry Section. Requet accepted of p tpoue k (d) Group k CS -Critical Section tpoue k from the other group. Each group ha aociated a quorum (et of group) to requet the permiion of acce (S k ). To elect the quorum, we ue the Maekawa method [6], the ize of the quorum i m, where m i the number of group. When the group obtain all the permiion the reource can be ue and thi i informed to hi aociated procee. IV. CORRECTNESS In thi ection, we how the correctne of the propoed algorithm. The algorithm atifie the propertie of mutual excluion, progre and concurrent entering. Theorem 4.1: The propoed algorithm enure mutual excluion. Suppoe procee and can acce the critial ection at the ame time, where, G l, G l. Thu, two procee are in the critical ection linked with different group. If thi occur, then the group receive all the lock from hi quorum S k and the group G l receive all the lock from hi quorum S l. For the condition (2) of the definition of coterie, S k S l, then occur that the member of the two quorum grant the lock to 2 requirement. Thi i a contradiction. Theorem 4.2: The propoed algorithm enure bounded delay. Suppoe a proce make a requet to the group and i waiting indefinitely. Each requet ha aociated a priority (, t, priori). Thi priority eventually will be the higher and grant the acce to the critical ection. Beide, we conider that each group doe not tay indefinitely in the critical ection for the arrival of new procee, through the time of the proce (topdur i ) and the remainder time of the group ( - tpoue k - tc i,k ). P P tpodur (e) Group k CS -Critical Section. Requet from p tpoue k tpodur wait (f) Group k CS -Critical Section. Requet of p ha to wait To reduce the waiting time, we conider: When a group with a lower priority i uing the reource, the other group with higher priority that want to acce mut wait. When a group i uing the reource (tate = CS ) accept new requet of procee only if the time aociated i le than hi remainder time. With thi conideration, none of the group tay indefinitely uing the reource. Theorem 4.3: The maximun concurrency of the propoed algorithm i n. When each proce make a requet for the ame group imultaneouly, all of the requet are added to the active queue. When the group grant the lock of hi quorum can acce concurrently the n procee. Fig. 7. Concurrency V. COMPLEXITY The complexity of the algorithm can be meaured uing different topic, like the number of acce to 25
hared memory, the delay time between entrie in the critical ection and the number of exchanged meage. The election of the meaure depend on the type of the algorithm. The complexity of the algorithm i meaured in function of the number of the meage require. Let q = S k, in the bet cae, each group require for gain the acce and releae 3(q 1) meage, where (q 1) for requet the permiion, (q 1) for grant the permiion, (q 1) for releae the permiion. If it ha aociated: one proce, in total require 3 + 3(q 1); l procee, in total require 3l + 3(q 1). If in average, each group ha to yield once o, the number of meage require are 5(q 1), where (q 1) for yield the permiion, (q 1) for grant the permiion, with l aociated procee in total require3l+5(q 1). If each group ha to yield the permiion at mot p time, then require with l aociated procee 3l+3(q 1)+2p(q 1) meage. With the maximum concurrency,nrequet for the ame group imultaneouly, in total require 3n+3(q 1) meage. Although the number of meage for a requet that i unique in a group i larger than 3q+1 in [4], the propoed algorithm require le meage for l imultaneouly requet to the ame group. VI. CONCLUSION In thi paper we propoed a ditributed olution for group mutual excluion conidering that procee have an aociated time to hare the group. Thi hould be the duration they will cooperatively work in the group in each tage. The algorithm i baed on prioritie over the group with no prompt. The communication among the procee and group ue meage. The group have aigned a quorum, that i ue in the competition to get the permiion to acce the reource. The algorithm guarantee mutual excluion, progre, bounded delay and concurrency. In the bet cae, where the group doe not yield the permiion, with l procee linked, requiere 3l+3(q 1) meage. The maximum concurrency of the algorithm i n, which implie that all procee have linked to the ame group. REFERENCES [1] D. Barbara and H. García-Molina. Mutual excluion in partitioned ditributed ytem. Ditributed Computing, 1:119 132, 1986. [2] K. M. Cenci and J. Ardenghi. Modelo do actore para grupo de proceo. In XIV Congreo Argentino de Ciencia de la Computación (CACIC 2008), 2008. [3] Y. J. Joung. Aynchronou group mutual excluion (extended abtract). In Proceeding of the 17th Annual ACM Sympoium on Principle of Ditributed Computing (PODC 98), page 51 60, June 1998. [4] Y. J. Joung. Quorum-baed algorithm for group mutual excluion. IEEE Tranaction on Parallel and Ditributed Sytem, page 463 476, May 2003. [5] H. Kakugawa, S. Kamei, and T. Mauzawa. A token-baed group ditributed group mutual excluion algorithm with quorum. IEEE Tranaction on Parallel and Ditributed Sytem, 19(9):1153 1166, September 2008. [6] M. Maekawa. A N algorithm for mutual excluion in decentralized ytem. ACM Tranaction on Computer Sytem, 3(2):145 159, May 1985. [7] Y. Manabe and J. Park. A quorum-baed extended group mutual excluion algorithm without unneceary blocking. In Proceeding of th Tenth International Conference on Parallel and Ditributed Sytem, page 341 348, 2004. [8] J. F. Myoupo, M. Naimi, and O. Thiare. A clutering group mutual excluion algorithm for mobile ad hoc network. In IEEE Sympoium on Computer and Communication, 2009. ISCC 2009., page 693 696, 2009. [9] Gurdip Singh and Ye Su. Efficient ynchronization in meage paing ytem. In 22nd International Conference on Advanced Information Networking and Applicacione, page 219 226, 2008. [10] A. Swaroop and A. K. Singh. A token-baed group mutual excluion algorithm for cellular wirele network. In Annual IEEE India Conference (INDICON), page 1 4, 2009. [11] O. Thiare, M. Gueroui, and M. Naimi. Ditributed group mutual excluion baed on client/erver model. In Proceeding of the Seventh Internacional Conference on Parallel and Ditributed Computing, Application and Technologie, page 67 73, 2006. [12] M. Toyomura, S. Kamei, and H. Kakugawa. A quorumbaed ditributed algorithm for group mutual excluion. In Proceeding of the Fourth International Conference on Parallel and Ditributed Computing, Application and Technologie, page 742 746, 2003. [13] K. P. Wu and Y. J. Joung. Aynchronou group mutual excluion in ring network. In 13th International Parallel Proceing Sympoium / 10th Sympoium on Parallel and Ditributed Proceing (IPPS / SPDP 99). Proceeding. IEEE Computer Society, page 539 543, April 1999. 26