International Journal of Computer Engineering and Applications, Volume XII, Issue I, Jan. 18, ISSN

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1 A PRIORITY AND REQUEST BASED MUTUAL EXCLUSION ALGORITHM FOR DISTRIBUTED SYSTEM Soumik Guha Roy 1, Sowvik Dey 2, Joy Samadder 3 1, 2, 3 Assistant Professor, Department of Computer Science & Engineering Brainware University Kolkata, India ABSTRACT: This paper aims towards designing a new token based mutual exclusion algorithm for distributed systems that addresses both fairness and priority of each process. One major limitation of the token based mutual exclusion algorithm in the distributed environment like Raymond's well known work is the absence of fairness property. In the proposed algorithm both priority as well as number of token request sent by a process are taken into consideration. Keywords: Distributed System, Mutual Exclusion, Critical Section, Priority [1] INTRODUCTION In order to secure integrity of the shared resources, concurrent access to a shared resources by several uncoordinated user requests are serialized. The problem of mutual exclusion frequently arises in distributed systems whenever concurrent access to shared resources by several site is involved. For correctness, it is necessary that the shared resource be accessed by a single site (process) at a time. Mutual exclusion is a fundamental issue in the design of distributed systems and an efficient and robust technique for mutual exclusion is essential to the viable design of distributed systems. In single computer-computer systems, the status of a shared resource and the status of the users is readily available in the shared memory, and the solutions to the mutual exclusion problem can be Soumik Guha Roy, Sowvik Dey and Joy Samadder 319

2 A PRIORITY AND REQUEST BASED MUTUAL EXCLUSION ALGORITHM FOR DISTRIBUTED SYSTEM easily implemented using shared variables (e.g. semaphores). However, in distributed systems, both the shared resources and the users may be distributed and shared memory does not exists. Consequently, approaches based on shared variables are not applicable to distributed systems and approaches based on message passing must be used. Solutions to the mutual exclusion problem in distributed systems tend to differ in their communication topology and in the amount of information maintained by each site about other sites. These algorithms can be classified into two groups-token based and non-token based algorithms. All the algorithms described in [1, 2, 3, 4, 5] are token based algorithms. In tokenbased algorithms, a unique token is shared among all sites. The site which holds the token is allowed to enter its critical section. Non token based algorithms [6, 7, 8, 9, 10] need two or more rounds of message exchanges among the nodes. Apart from Token and non-token based algorithm, there is also Hybrid based algorithm [11, 12, 13, 14]. Best of both token and non-token based algorithms are combined to form hybrid approach. In this paper, we have proposed a new token based prioritized algorithm which avoids starvation by taking care of both priority and critical section entry request. [2] OVERVIEW OF THE PROPOSED ALGORITHM We assume that the system contains N nodes which are uniquely numbered from 1 to N. Each node is assigned a priority. In the proposed algorithm, we have assumed that highest number indicates highest priority. At any point of time, each node can have any number of token requests. Nodes do not need to keep information about all other nodes. Each node has to keep information about the outgoing and incoming links. Each node Ni holds a token request holder queue (RQN i) and a variable RC i which contains total number of token holding request received by the node N i and a variable named HIGHPRIO i which holds the largest priority of a token request. Request queue (RQN i): Each node N i maintains a queue to store all the requests. Each tuple of the request queue has the following form: <N j, P j, RC j> where N j is address of the Node N j, P j is priority of the node N j and RC j is the total request message sent via N j. In general, the content of the RQN i is {...,<N i, P i, RC i>, <N j, P j, RC j>, <N k, P k, RCk>,...} where N i, N j, N k are the address of the nodes which want to enter its critical section and P i, P j, P k are the largest priorities of token requests that came from the nodes N i, N j, N k respectively and RC i, RC j, RC k are the request counter send by the nodes N i, N j, N k. Types of Nodes: All the nodes can be partitioned into two sets: Token Holder Node set and Non Token Holder set. Types of messages: Non token holder nodes can sent three different types of messages. They are New Token Request Message, High Priority Request and Request Counter Increase Message. New Token Request Message: This message is sent by a node N j which wants to access the critical section. This message is sent by node N j only for one time. This message contains <N j, P j, 1> High Priority Request Message: This message is send by Node Ni whose request queue is not empty and got a New Token Request message from node N j and priority of node N j is highest among all the nodes currently in the Request Queue of N i. Request Counter Message: This message is sent by the node N i whose request queue is not empty and got a New Token Request from a Node N j which already exists in the Token Request Holder Queue RQ of N i. This message contains <N i, RC> [3] THE PROPOSED ALGORITHM Soumik Guha Roy, Sowvik Dey and Joy Samadder 320

3 There are 5 major procedures as described from section 3.1 to 3.5 which describes the proposed token based mutual exclusion algorithm in distributed systems. Table.1. shows various events and actions which are used in phase 1 and phase 2 in tabular format. Table. 1. Various events and actions EVENT NAME DESCRIPTION ACTION DESCRIPTION Critical Section(CS) P i wants to enter CS Send Token Request message to P j P i want to enter CS. So P i sends a Token request message to P j Token Request message from P j P i receives a token request message from P j Send Request Counter Increase message to P j P i receives a message and its Request counter increases. So P i sends this message to node P j Request Count Increment message from P j HIGHPRIO &Token Increment message from P j P i receives a Request Counter Increment message from P j P i receives a Priority and token counter increment message from P j Send HIGHPRIO and Token Increment message to P j P i receives a message and increases both high priority and request counter. So P i sends this message to node P j [3.1] TOKEN REQUEST MESSAGE GENERATION BY NON TOKEN HOLDER SITE WHICH WANTS TO ENTER CRITICAL SECTION When a node N i (non-token holder site) wants to enter its critical section then the following sets are being executed. Step 1: if ( RQN i=null) then set RQN i=<n i, P i, 1>, RC i=1, HIGHPRIO i=p i Step 2: if (RQN i!=null) then node N i does not want to enter its critical section but other child nodes of node N i want to enter critical section. Other conditions will not occur. [3.2] TOKEN REQUEST MESSAGE RECEIVE [3.2.1] TOKEN REQUEST MESSAGE RECEIVED BY NON TOKEN HOLDER SITE When a node N i (non-token holder site) receives a token holding request from a node N j, then the following steps are being executed Step 1: if (RQN i=null) then Set Request Counter Variable for node N i to 1. and Set RQN i= (N j, P j, RC) and sent a token request message to the holder node. Step 2: if ((N j RQN i) and (RQN i!=null)) then increment RCi by one and update Request Queue of the node N i, RQNi=RQNi (N j, P j, RC j). Step 3: For all nodes N l RQN i and N j is parent of N l, if P l * RC l < P j * RC j then increment priority of node N l P l by one. Find the highest priority from RQN i and update HIGHPRIO i with the new high priority in the Request Queue of RQN i. Send the modified priority token request message <P i, HIGHPRIO i, RC i > to the holder node. Step 4: if ((N j RQN j) and (RQN i!= NULL) ) then increment RC i and RC j by one. Now send a token request counter message <N j, RC i> to holder. [3.2.2] TOKEN REQUEST MESSAGE RECEIVED BY TOKEN HOLDER SITE Soumik Guha Roy, Sowvik Dey and Joy Samadder 321

4 A PRIORITY AND REQUEST BASED MUTUAL EXCLUSION ALGORITHM FOR DISTRIBUTED SYSTEM When a node Ni (non-token holder site) receives a token holding request from a node N j, then the following steps are being executed Step 1: if (RQN i = NULL) then Set Request Counter Variable for node N i to 1. and Set RQN i=(n j, P j, RC) and sent a token request message to the holder node. Step 2: if ((Nj RQN i) and (RQN i!=null)) then increment RC i by one and update Request Queue of the node N i, RQNi=RQNi (N j, P j, RC j) Step 3: Now for all nodes N l RQN i and N j is parent of N l, if P l * RC l < P j * RC j then increment priority of node N l, P l by one. Now find the highest priority from RQN i and update HIGHPRIO i with the new high priority in the Request Queue of RQN i. Now send the modified priority token request message <P i, HIGHPRIO i, RC i> to the holder node. Step 4: if ( ( Nj RQN i ) and (RQN i!= NULL) ) then increment RC i and RC j by one. Now send a token request counter message <N j, RC i> to holder. [3.2.3] TOKEN REQUEST MESSAGE RECEIVED BY TOKEN HOLDER SITE When a token holder site N i receives a Token Request Message and N i has not finished its execution in critical section, it takes the following actions: Step 1: if (RQN i=null) then Set Request Counter Variable for node N i to 1. and Set RQN i=(n j, P j, RC j) Step 2: if ((N j RQN i) and (RQN i! =NULL)) then increment RC i by one and update Request Queue of the node Ni, RQNi=RQNi (N j, P j, RC j). Now for all nodes N l, N l RQN i, if P l * RC l < P j * RC j then increment P l by one. Now find the highest priority from RQN i and update HIGHPRIO i with the new high priority in the Request Queue of RQN i. [3.3] PRIVILEGE MESSAGE GENERATED BY THE TOKEN HOLDER SITE When a token holder site N i finishes its execution in critical section, it takes the following actions to generate the Privilege message: Step 1: Send a Privilege message to node N k such that N l RQN i N k RQN i and N k! =N l and P l*rc l< P k*rc k /* Send Privilege message to a node N k such that for all nodes N l in the Request Queue of the node N i if there exists another node N k in Request Queue of N i and P l*rc l< P k*rc k */ Step 2: Then node N i delete its entry from its Request Queue and set holder variable to point N k. Step 3: If RQN i! =NULL then send a Token Request Message <N i, HIGHPRIO i, RC i>to the node N k. [3.4] PRIVILEGE MESSAGE RECEIVED BY THE NON TOKEN HOLDER SITE WHICH WANTS TO ENTER CRITICAL SECTION When a non-token holder site N i receives a Privilege message, it takes the following actions: Step 1: if N i RQN i then delete the entry N i from RQN i. Step 2: Decrease RC i by 1. Step 3: Now N i will enter its critical section. [3.5] PRIVILEGE MESSAGE RECEIVED BY THE NON TOKEN HOLDER SITE WHICH DOES NOT WANT TO ENTER ITS CRITICAL SECTION Soumik Guha Roy, Sowvik Dey and Joy Samadder 322

5 When a non-token holder site N i which does not want to enter critical section receives a Privilege message, it takes the following actions: Step 1: Send a Privilege message to node N k which is children of N i, such that N l RQN i N k RQN i and N k! =N l and P l*rc l< P k*rc k /* Send Privilege message to a node N k such that for all nodes N l in the Request Queue of the node Ni if there exists another node N k in Request Queue of Ni and P l*rc l < P k*rc k */ Step 2: Set the holder variable to point N k. Step 3: if RQN i! = NULL then send a Token Request Message <N i, HIGHPRIO i, RC i> to the node N k. Step 4: Update the RC i by (RC i RC k) [4] ILLUSTRATING THE PROPOSED ALGORITHM We have taken 8 processes with the priority values has been listed in [Figure-1]. We assume that highest number in the priority values indicates highest priority. Process P8 is currently in its critical section and token requests are made by other processes in the distributed system in the order P1, P3, P2, P4, P5, P7. Figure: 1. A directed tree with eight nodes along with its priority list. According to the proposed algorithm the token request message (P1, 2, 1) generated by node P1 is stored in the request queue RQN1 and also stored in the request queue RQN8 of node P8. Then the token request message (P3, 1, 1) generated by Node P3 is stored into the request queue RQN3 and RQN8 of node P3 and P8 respectively. Then node P2 generated the token request message (P2, 2, 1) which is stored into RQN2 and sent to the node P3.Now the content of RQN3 is (P3, 1, 1) (P2, 2, 1). As the newly arrived token request message satisfies the property P2*RC2 > P3*RC3, the priority in the token request message (P3, 1, 1) in RQN3 is incremented and the content of RQN3 becomes (P3, 2, 1) (P2, 2, 1). Now P4 generates token request message and RQN4 becomes (P4, 1, 1). The token request message is sent to node P3 and the RQN3 becomes (P2, 2, 1) (P3, 2, 1) (P4, 1, 1). Now the request counter value RC3 increased to 3. According to the proposed algorithm, Node P3 send a Request Counter increment message <P3, 3> to node P8. Now the content of RQN8 becomes (P1, 3, 1) (P3, 2, 2) (P3, 3). The RQN8 becomes (P1, 3, 1) (P3, 2, 3). According to the proposed algorithm RQN8 becomes (P3, 2, 3) (P1, 4, 1).Now P5 generates a token request message (P5, 2, 1) to node P2. The request queue RQN2 of node P2 becomes (P2, 2, 1) (P5, 2, 1). The request counter value RC2 changed to 2.Hence the node P2 sends a request counter increment message (P2, 2) to node P3.The Request Queue RQN3 becomes (P2, 2, 1) (P3, 2, 1) (P4, 1, 1) (P2, 2). After receiving the request increment message, RQN3 becomes (P2, 2, 2) (P3, 2, 1) (P4, 1, 1). According to the proposed algorithm, RQN3 becomes (P2, 2, 2) (P3, 3, 1) (P4, 2, 1). Now both the priority and request counter increment of node P8 value becomes 3 and 4 respectively. According to the proposed algorithm node P3 send Priority and Request counter increment message (P3, 3, 4) to node P8. Now RQN8 becomes (P3, 2, 3) (P1, 4, 1) <P3, 3, 4>. Hence the RQN8 has been modified to (P3, 3, 4) (P1, 4, 1). According to the proposed algorithm, RQN8 becomes (P3, 3, 4) (P1, 5, 1). Now node P7 sends a token Soumik Guha Roy, Sowvik Dey and Joy Samadder 323

6 A PRIORITY AND REQUEST BASED MUTUAL EXCLUSION ALGORITHM FOR DISTRIBUTED SYSTEM request message (P7, 1, 1) to node P5 and the RQN5 becomes (P5, 2, 1) (P7, 1, 1). According to the proposed algorithm the priority values of the entry (P5, 2, 1) will not increase. Now the request counter variable of the node P5 has been incremented and request counter message (P5, 2) has been sent to the node P2 and the RQN2 becomes (P2, 2, 1) (P5, 2, 1) (P5, 2). Now according to the proposed algorithm RQN2 becomes (P2, 2, 1) (P5, 2, 2). Now as PR5*RC5>PR2*RC1, the priority value in the entry (P2, 2, 1) becomes (P2, 3, 1). Now RQN2 becomes (P2, 3, 1) (P5, 2, 2). Request counter at node P2 updated to 3. So P2 sends request increment message (P5, 2) to node P2 and RQN2 becomes (P2, 2, 1) (P5, 2, 1) (P5, 2). RQN2 updated to (P2, 2, 1) (P5, 2, 2). Priority entry of the entry (P2, 2, 1) changed to (P2, 3, 1) and RQN2 becomes (P2, 3, 1) (P5, 2, 2). Node P2 sends a request increment message (P2, 3) to node P3 and RQN3 becomes (P2, 2, 2) (P3, 3, 1) (P4, 2, 1) (P2, 3). After that RQN3 becomes (P2, 2, 3) (P3, 3, 1) (P4, 2, 1). Finally RQN3 is modified to (P2, 2, 3) (P3, 4, 1) (P4, 3, 1). As a result, both the priority and request counter message of the node P3 has been increased by one and Priority and request counter increase message (P3, 4, 5) is sent to P8.The request queue RQN8 becomes (P3, 3, 4) (P1, 5, 1) <P3, 4, 5>. After receiving the priority and request counter increase message by P8, RQN8 becomes (P3, 4, 5) (P1, 5, 1). According to the proposed algorithm, priority entry of the entry (P1, 5, 1) has been changed to (P1, 6, 1). Finally RQN8 becomes (P3, 4, 5) (P1, 6, 1). From the RQN8 we can conclude that P8 has received token request messages from node P3 and P1 and P3 has sent total 5 token request message and according to the proposed algorithm the priority of node P1 and P3 has been increased to 6 and 4 respectively. The [Figure-2] illustrates the first phase of proposed algorithm. Figure: 2. A tabular illustration of the first phase of proposed algorithm. Assume that P8 has finished its execution in the critical section. Now the Privilege message transmission phase begins from node P8.Request Queue of P8 holds (P3, 4, 5) (P1, 6, 1) and children of P8 is P1 and P3.Now according to the proposed algorithm P3*RC3>P1*RC1. Hence,P8 sends the Privilege Message (P8, 6, 1) to node P3 and holder node of P8 is P3.Then the request counter of P8 reduces to 1.When the privileged message is received by the node P3, the content of the request queue becomes (P2, 2, 3) (P3, 4, 1) (P4, 3, 1) (P8, 6, 1). Now according to the proposed algorithm, largest priority node is P2 as P2*RC2>P3*RC3 and holder node of P3 is P2. After sending the privileged message (P3, 4, 2) the request counter of P2 reduces to 2. After receiving the privileged message, the content of request queue of P2 becomes (P5, 2, 2) (P2, 3, 1) (P3, 4, 2). The privileged message (P5, 4, 1) will be send to the node P5 as according to the proposed algorithm P5*RC5 > P6*RC6 and holder node of P2 now becomes P5. When P5 receives the privileged message the request queue becomes (P5, 2, 1) (P7, 1, 1). Now P5 is the node which has the highest weighted priority according to this proposed algorithm. So P5 now enters its critical section after setting holder node of P5 to self. The [Figure-3] illustrates the last phase of proposed algorithm and the final result is shown in [Figure-4]. Soumik Guha Roy, Sowvik Dey and Joy Samadder 324

7 . Figure: 3. A tabular illustration of the last phase of proposed algorithm. Figure: 4. Final result of the proposed method. [4] PERFORMANCE ANALYSIS FOR THE PROPOSED ALGORITHM The performance of the proposed algorithm is measured by the following four metrics: the number of message per critical section invocation, synchronization delay, response time and the system throughput. [4.1] NUMBER OF MESSAGES PER CRITICAL SECTION INVOCATION All the messages which are exchanged between nodes to send critical section entry request, are divided into three parts: Token Request Message, High Priority Message and Request Counter Increment message. In order to estimate total number of messages needed to send critical section entry request, we need to take consideration of all three different messages. When a leaf node process wants to enter critical section, it will send only one Token request message to its parent and the parent node will sent either request counter increment message or high priority message to its parent. So total number of messages sent by a token requesting node will be bounded by (One Token request Message + m Request Counter Increment message + n High Priority Message) where m+n<= h (h is the height of the directed tree). [4.2] SYNCHRONIZATION DELAY The time needed after a site leaves the critical section and another site enters critical section is called the Synchronization Delay. The maximum Synchronization delay (d) is bounded by the height (h) of the directed tree i.e. d<=h. [4.3] RESPONSE TIME Soumik Guha Roy, Sowvik Dey and Joy Samadder 325

8 A PRIORITY AND REQUEST BASED MUTUAL EXCLUSION ALGORITHM FOR DISTRIBUTED SYSTEM The time interval between nodes sent Token request message and the node finishes its critical section execution is called the Response time (r). Now consider a directed tree which has maximum b branches. The response time (r) is related with the branching factor b and the height of the directed tree with the following inequality r<=kb h where k is constant. [4.4] SYSTEM THROUGHPUT If s is the synchronization delay and e is the average critical section execution time, then the throughput is given by the following equation: System throughput=1/(s + e). [5] CONCLUSION In this paper,we have proposed a mutual exclusion algorithm in distributed environment which uses priority of a process and as well as the number of token request received by that process to decide which process will enter critical section next. Hence starvation which may occur due to priority, can be avoided by using the request counter message information stored at each node. To achieve this, we have taken consideration of both priority and the number of token request message received by a process. We have taken consideration of three different types of control messages so that a process can indicate its parent that either it wishes to enter critical section or it has received a new token request or the highest priority of its queue has been increased. The size of the queue of each process P i has been increased monotonically towards the path from P i to the process which is currently in critical section. REFERENCES [1] Raymond, K. (1989). A tree-based algorithm for distributed mutual exclusion. ACM Transactions on Computer Systems (TOCS), 7(1), [2] Singhal, M. (1989). A heuristically-aided algorithm for mutual exclusion in distributed systems. IEEE transactions on computers, 38(5), [3] Suzuki, I., & Kasami, T. (1985). A distributed mutual exclusion algorithm. ACM Transactions on Computer Systems (TOCS), 3(4), [4] Van de Snepscheut, J. L. (1987). Fair mutual exclusion on a graph of processes. Distributed Computing, 2(2), [5] Kanrar, S., & Chaki, N. (2006, December). Modified Raymond s algorithm for priority (MRA-P) based mutual exclusion in distributed systems. In International Conference on Distributed Computing and Internet Technology (pp ). Springer, Berlin, Heidelberg. [6] Carvalho, O. S. (1983). An mutual exclusion in computer networks. Commun ACM, 26, [7] Lamport, L. (1978). Time, clocks and ordering of events in distributed systems. 21 (7): [8] Maekawa, M. (1985). An algorithm for mutual exclusion in decentralized systems. ACM Transactions on Computer Systems (TOCS), 3(2), [9] Yadav, N., Yadav, S., & Mandiratta, S. (2015). A review of various mutual exclusion algorithms in distributed environment. International Journal of Computer Applications, 129(14). [10] Ricart, G., & Agrawala, A. K. (1981). An optimal algorithm for mutual exclusion in computer networks. Communications of the ACM, 24(1), [11] Lodha, S., & Kshemkalyani, A. (2000). A fair distributed mutual exclusion algorithm. IEEE Transactions on Parallel and Distributed Systems, 11(6), Soumik Guha Roy, Sowvik Dey and Joy Samadder 326

9 [12] Kakugawa, H., Kamei, S., & Masuzawa, T. (2008). A token-based distributed group mutual exclusion algorithm with quorums. IEEE transactions on parallel and distributed systems, 19(9), [13] Taheri, H., Neamatollahi, P., & Naghibzadeh, M. (2011). A hybrid token-based distributed mutual exclusion algorithm using wraparound two-dimensional array logical topology. Information processing letters, 111(17), [14] Neamatollahi, P., Taheri, H., & Naghibzadeh, M. (2012). Info-based approach in distributed mutual exclusion algorithms. Journal of Parallel and Distributed Computing, 72(5), Soumik Guha Roy, Sowvik Dey and Joy Samadder 327