petri net based modeling of fms and its deadlock

PETRI NET BASED MODELING OF FMS AND ITS DEADLOCK PREVENTION MURALI M. AMBEKAR1 & S. G. BHATWADEKAR2 1

M.E (CAD/CAM/CAE) K.I.T’s College Of Engineering, Kolhapur, India 2 Dept of Prod. Engg. K.I.T’s College Of Engineering, Kolhapur, India

Abstract- This paper illustrates the Petri net modeling of a conceptual model of flexible manufacturing system (FMS) and addresses the problem of deadlock by establishing deadlock prevention policy. The first part introduces the problem of deadlock in FMS, deadlock handling strategies and basic concepts of etri net modeling. Literature review is presented in the second part and third part shows an illustration of Petri net modeling of a conceptual model of FMS processing two part types, consisting of four machines, a load/unload station and two robots. It is assumed that each of the part has four machining operations to be performed. Reachability graph is then generated for this model and is used to detect the possible deadlock states. Finally deadlock prevention policy is established for this conceptual FMS model based on reachability graph analysis. Keywords- Deadlock, FMS, Petri net, deadlock prevention.

I. INTRODUCTION In the modern age of globalized market, the customer requires diversified products customized to their specific requirements. Also the needs of the customer are changing rapidly and hence the product life cycles are becoming shorter. This has forced the conventional single product, mass producing manufacturing systems to become more flexible to sustain in the competitive world. Figure 1. A typical deadlock scenario.

This has made the modern manufacturing industries adopt the concept of flexible manufacturing systems (FMS). FMS are having characteristics of concurrency [6] which enable them to process multiple products at the same time and can deal with varying product mix. The FMS typically processes a variety of components from a part family with variable routings with versatile work centers. Hence multiple resource – sharing is a common situation in FMS. i.e. the same resource (Machines, AGV’s, robots etc.) is requested by many jobs (process) simultaneously. Hence appropriate allocation of shared resources to the process becomes more important, failing which leads to a situation called as deadlocks in FMS.

Figure1 shows an example of a typical deadlock scenario. The deadlock situation can disrupt the entire system and makes the automated system stop working. To recover from deadlock one has to shutdown the system where deadlock has occurred and forcibly remove the part which is being processed and then restart the system in order to return to normalcy. Thus occurrence of deadlock causes unpredictably long down-time and causes under utilization of resources and may also lead to catastrophic results in safety-critical systems. Deadlocks in a FMS are in general considered to be a result of: [15] 1. Deficiency of system resources (Excessive sharing of resources). 2. An inappropriate order of process execution and 3. Improper resource allocation logic.

1.1 DEADLOCKS IN FMS Deadlock is a state where a set of parts are in “Circular waiting” situation, i.e., a situation where a set of two or more processes keep waiting indefinitely for other processes in the same set to release resources. Deadlocks have been discussed extensively in the computer science literature [23]. But in context of FMS resources refer to machines, buffers, AGVs, robots, fixtures etc. and process refer to operations to be performed on the raw material at the work centers.

There are four necessary conditions for a deadlock to occur [16], known as the Coffman conditions: 1. Mutual exclusion condition: a resource can only get involved in one process at a time. 2. Hold and wait condition: processes (operation) already holding resources may request new resources;

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Petri Net Based Modeling of FMS and Its Deadlock Prevention

3. No preemption condition: no resource can be forcibly released from a process holding it, when processing is under progress and resources can be released only by the explicit action of the process; 4. Circular wait condition: two or more processes form a circular chain where each process waits for a resource that the next process in the chain holds.

for modeling, analysis and design of discrete event systems [6]. It is their simplicity and ability to model sequential execution, concurrency, conflict, synchronization and merging like situations which makes them suitable to model FMS. Detailed discussion of Petri nets is beyond the scope of this paper and more on basics of Petri nets can be found in [6], [5], [18], [16].

A deadlock will never occur if one of these conditions is not satisfied[4]. The physical characteristics and technical background of an FMS which is a discrete event system, show that the first three deadlock conditions always hold and any method which guarantees that the fourth condition (the circular wait) does not hold, is a valid solution to tackle problem of deadlock in FMS.

II. LITERATURE REVIEW Y. Narahari and N. Viswanadham (1990) [2] showed that prevention and avoidance of FMS deadlocks can be implemented using Petri net models. For deadlock prevention, they used the reachability graph of a Petri net model of FMS, and for deadlock avoidance, they proposed a Petri netbased on-line controller. Jie Wu (1995) [4] a Petri net based approach is employed in this paper to model, detect and avoid collisions and deadlocks in FMS’s. Approach uses the concept of critical states in the reachability graph to avoid the system from entering a state leading towards a deadlock state. A multirobot assembly example is used to illustrate the proposed scheme. Ezpeleta Joaquin et al.(1995) [5] illustrated a compositional method for modeling the concurrent execution of working processes in FMS through a special class of Petri nets called Sequential Processes Petri Nets. Richard Zurawski and MengChu Zhou (1995) [6] presented a tutorial paper on Petri Nets and Industrial Applications, an overview of applications of Petri nets in industry with a description of Petri nets properties, and analysis methods and further deals with modeling, formal analysis, and design of discrete event systems. Han Zandong et.al (2004) [9] presented a production Petri net (PPN) model for a given FMS.

1.2 DEADLOCKS HANDLING STRATEGIES There are three major approaches to manage a deadlock situation [16] namely deadlock prevention, deadlock avoidance, and deadlock detection and recovery. Deadlock prevention refers, to static resource allocation policies to eliminate completely the possibility of deadlock occurrence. This approach is too much conservative and leads to underutilization of system [20]. Deadlock avoidance involves dynamic resource allocation, so as to avoid deadlock just before it occurs. This approach is widely accepted because it leads to better utilization of resources than prevention policies. In deadlock detection and recovery, however, resources are granted to a process without any check. A deadlock detection algorithm determines whether a set of processes is deadlocked. If a deadlock is found, the system recovers from it by aborting one or more deadlocked processes. A good deadlock detection algorithm is the one, which detects all possible deadlocks and does not report nonexistent deadlocks.

Then for deadlock avoidance they constructed deadlock state equation that describes the intrinsic relationship between resources assignation and a deadlock state in PPN. Finally they proposed restrictive PN controller which can control the resources dispatching by excluding some enabled transitions from firing, consequently avoiding the deadlock. M.A. Shouman et.al (2005) [10] used Petri nets to analyze FMS to derive a theorem for checking the buffer overflows in an FMS and proposed a computer program to detect the deadlock phenomenon by use of P-invariant theory of Petri nets. Murat Uzam and MengChu Zhou (2007) [11] this paper proposes an iterative synthesis approach to Petri net (PN)-based deadlock prevention policy for FMS, by iterations the bad marking are prevented from being reached via a place invariant of the PN. W.M. Zuberek et.al (2007) [12] briefly discussed basic concepts of Petri nets and timed Petri nets, and then derived hierarchical Petri net models of manufacturing systems. Farooq Ahmad et.al (2010) [13] presented the method of modeling parallel

1.3 PETRI NETS AS A MODELING TOOL Petri nets are bipartite directed graphs, in which there are two types of vertices known as places and transitions. The places are represented by hollow circle and transitions are represented by vertical bar. Places usually represent a state of the system, conditions or a resource and transitions represent events. A token is a small solid dot (or solid circle), presence of token in a place means the condition represented by the place is satisfied or a resource represented by the place is available. Places are connected to transitions by directed arcs and they represents input and output function. A firing of transition indicate occurrence of an event represented by it and transition is said to be enabled for firing, if all the input places of a transition are having tokens in them, in other words an event can occur only if all the conditions are satisfied or all the resources required for an event are available. Petri nets, as graphical and mathematical tools, provide a uniform environment

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Petri Net Based Modeling of FMS and Its Deadlock Prevention

processing flows, sharing limited number of resources, in flexible manufacturing systems (FMSs). A new class of Petri net called parallel process net with resources (PPNRs) is introduced for modeling such FMSs. They proposed new technique for deadlock detection and recovery based on transition vectors which have the power of determining the structural aspects as well as the process flow condition in PPNRs.

each robot can handle one part at time. Also it is assumed that the raw materials are always available in the load/unload station but once a particular part type is under processing the system doesn’t start processing the same type of new part. For example when processing of part A is under progress till the completion of all four machining operation of part A. The system will not accept raw material of A to start machining new part A. The figure 2 shows the Petri net model of the concetual model of the manufacturing system. The Petri net model has been developed using PIPE v4.2.1 software [21]. The places are used to represents the resources (robots, machines) and state of process. Where as firing of transitions represents the occurrence of activities or events. The table 1 describes each of the places and transition.

Wensong Hu,Yuyuan Zhu (2011) [14] presented an article which provides basic knowledge of Petri net at first, then analyzes two methods about the detection of deadlock in Petri nets. One is based upon the net structure; the other is based upon reachability tree and the article describes the steps of the arithmetic about it. ZhiWu Li et.al (2012) [15] carried-out Literature review on Deadlock control of automated manufacturing systems based on Petri Nets. The study surveys the state-of the-art deadlock-control strategies for automated manufacturing systems by reviewing the principles and techniques that are involved in preventing, avoiding, and detecting deadlocks. From the literature review one can infer that most of the works addressing deadlock problem using Petri net are based on structural analysis of Petri nets and few works are based on reachability graph analysis and are restricted to very small systems. Structural methods eliminate the derivation of the state space, so they avoid the “state explosion” problem, but they cannot provide as much information as the reachability approach does [12]. III. PETRI NET MODELING OF CONCEPTUAL MODEL OF FMS

Table 1: Definition of Places and Transition in Petri Net mode

A

A conceptual model of FMS consisting of four machines, two robots processing two part types is considered for illustration using Petri net. The figure 1 shows the schematic layout of the conceptual FMS model.

Figure 1: Conceptual model of FMS processing two partts A and B. Part A having sequence M1,M2,M4,M3, Part B having sequence M4,M1,M3,M4.

Each of the four machines in the above FMS are assumed to process one part at a time. The two robots are meant to load/unload the parts on/from the machines and load/unload station; it is assumed that International Journal of Mechanical and Production Engineering (IJMPE) ISSN No.: 2315-4489, Vol-2, Iss-1, 2013 67

Petri Net Based Modeling of FMS and Its Deadlock Prevention

Similarly one can reach state S3 by firing T9 and then T10. A deadlock state is a state from which no other state can be reached or in other words when system reaches deadlock state no transition are enabled for firing. In the reachability graph shown in figure 3, one can easily detect six such deadlock states viz. S60, S61, S62, S63, S29 and S17. This is the significance of reachability graph analysis; by mere inspection one can detect deadlock state. The safe states which is just before deadlock state and which lead to deadlock states are known as critical states [2]. In our case S47, S49, S23, S57, S59 and S11 are critical states. Now when the system reaches critical state, our deadlock prevention policy would be, not to allow those transitions to fire which will lead to deadlock state. For example, if the system reaches critical state S11 our deadlock prevention policy would be to avoid firing of transition T11which leads to deadlock state S17, instead fire transition T2 which leads to state S16. The physical interpretation is, whenever the system reaches a state S11 where the robot 2 has to choose between two operations

3.1 ESTABLISHING DEADLOCK PREVENTION POLICY The first step in establishing deadlock prevention policy is to detect the possible deadlock states. The deadlock states can be identified by using reachability graph. In this work the reachability graph is produced by using PIPE v4.2.1 software and is as shown in figure 3. Reachability graph shows all possible reachable states that a system can reach by firing all possible transitions. A state in a reachability graph is represented by a vector having elements equal to number of places and the value of each element corresponds to the number of tokens held by respective places at that instant. For example the initial state S0 in the reachability graph can be represented by a vector also called as initial marking M0 as M0= {1,1,1,1,1,1,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,1,1} Where places are in the order {A, B, M1, M2, M3, M4, P0, P1, P10, P11, P12, P13, P14, P15, P2, P3, P4, P5, P6, P7, P8, P9, ROB1, ROB2} One can observe that in the initial state, raw material for A and B, all machines and robots are available and hence the corresponding places have token 1. A reachable state is one which can be reached by firing a transition or a sequence of transitions. For example in the figure 3, one can see that state S1 can be obtained from the state S0 by firing transition T9.

1. Unloading of machine M4 and loading it on machine 1. 2. Unloading of machine M1 and loading it on machine 2. Our deadlock prevention policy would be that, robot 2 should always choose operation 2. Table 2 shows the deadlock prevention policy for all

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Petri Net Based Modeling of FMS and Its Deadlock Prevention

possible deadlocks in the system. The first column in the table shows one possible sequence of transition firing for a particular deadlock state; however there

can be many possible paths or sequence of transition firing which will lead to the same deadlock state.

Figure 3: Reachability graph of the Petri net model.

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Automated Guided Vehicles IEEE Transactions On Systems, Man, And Cybernetics—Part B: Cybernetics, VOL. 35, NO. 6, December 2005.

IV. CONCLUSION The paper presented an overview of the deadlock problem in FMS and Petri net as a modeling tool. A conceptual model of FMS having four machines, two robots processing two product types was analyzed for deadlock using reachability graph of Petri net model. Finally deadlock prevention policy was established which gives deadlock free resource allocation method. This work illustrates that the reachability graph technique can be effectively used for analyzing and establishing a deadlock prevention policy for an FMS.

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Zandong Han et al., Application of Petri nets foer deadlock analysis and avoidance in flexible manufacturing systems, International Journal of Adv Manuf Technology, vol. 25 pp. 735-742. 3 November 2004.

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