Augmented timed Petri nets for modeling, simulation, and analysis of robotic systems with breakdowns

Augmented timed Petri nets for modeling, simulation, and analysis of robotic systems with breakdowns

Venkatesh, Kurapati

INTRODUCTION Over the last few years, industry has been constantly increasing its efforts to combine flexibility and automation to meet dynamically changing market needs. To this end, flexible factories capable of flexible and agile manufacturing and assembly have to be designed to achieve higher productivity with labor savings. This paper focuses on modeling and analysis issues related to flexible assembly systems (FASs) in such factories.

An FAS often consists of a number of robots, automated guided vehicles (AGVs), part feeders, and magazines. An FAS is capable of agile production of small and medium-sized components and avoids many disadvantages encountered with fixed assembly systems.(1) An FAS increases resource utilization and maximizes production rate by avoiding unnecessary job transfers within the factory; however, to realize the full benefits of FASs, one has to consider their modeling and simulation to investigate problems relating to design, performance optimization, and control. An important issues in modeling an FAS is breakdown handling, which takes into account many design and control issue. Considering the importance of breakdowns in production control, Gershwin and Berman(2) presented the analysis of transfer lines consisting of two unreliable machines with random failures. Groenevelt et al.(3) investigated issues related to estimation of economic lot size and safety stock levels for an unreliable manufacturing system with a constant failure rate. Glassey and Hong(4) presented a model for the analysis of behavior of an unreliable n-stage transfer line with finite size buffers.

Most of the above researchers studied conventional manufacturing systems by estimating economic safety stocks to handle breakdown situations; however, to implement just-in-time manufacturing and to increase automation, there is a need to handle breakdowns by reducing safety stock levels and implementing efficient breakdown handling procedures. Breakdowns and other production interruptions stop a system’s operation and pose difficulties for shop floor control in ensuring uninterrupted production. Furthermore, breakdowns increase system downtime and degrade performance. Due to breakdowns, the optimal system operational parameters that are designed for the system without considering breakdowns have to be changed. Furthermore, these parameters may differ as the component breakdown rates vary. Issues to be specifically addressed when considering a system with breakdowns are (1) detailed breakdown handling to ensure uninterrupted production and (2) estimation of new optimum design parameters for different breakdown rates. Detailed breakdown handling helps implement the real-time shop-floor controller as reported in Zhou and DiCesare.(5) Estimation of new optimum design parameters for various breakdown rates aids system designers and production managers in achieving optimal system performance.

Tools such as queuing networks, integrated computer-aided manufacturing definition (IDEF), perturbation analysis, mathematical programming and simulation packages such as SIMAN, SLAM, and XCELL can offer solutions for problems related to manufacturing system design. This paper instead presents a Petri net (PN) based graphical and mathematical tool to address the issues. Detailed advantages of PN modeling over other tools are discussed in Kaighobadi and Venkatesh;(6) Narahari and Viswanadham;(7) Stecke;(8) Zhou, DiCesare, and Rudolph;(9) Zhou, DiCesare, and Desrochers;(1O) and Zhou and DiCesare.(11) Important ones include hierarchical graphical modeling, direct generation of control code from models, validation of control code with either analytical or simulation methods, qualitative property analysis, performance analysis, and real-time control and monitoring.

Although PNs are proven as a tool to solve a variety of problems relating to manufacturing systems, their full application to address design and analysis issues of FASs with breakdowns remains to be explored. PN modeling of breakdowns was considered in Barad and Sipper(12) and Sheng and Black.(13) Barad and Sipper presented a PN model considering a machine breakdown while illustrating the flexibility of modeling a flexible manufacturing systen (FMS) with PNs. Sheng and Black modeled a PN For machine breakdown while demonstrating the application of PN in a cellular manufacturing system. Performance of a transfer line was analyzed by considering the breakdown of machines using stochastic PNs.(14) Stochastic PNs are also used for performance analysis of a flexible assembly system considering various robot failure rates.(15) None of the above presented detailed breakdown handling procedures and performance optimization issues for various machine/robot breakdown rates. Furthermore, they considered only breakdowns that arrive before starting of an activity; however, in real-life situations, breakdowns may arrive when an activity is in progress. In the above models, transition time delays either follow exponential distribution or are instantaneous. This restricts the accuracy of analysis of a realistic assembly system.

The goal of this paper is to graphically Formulate models that clearly capture the details of breakdown handling in FASs to address issues related to their design, performance, and control. Objectives of this paper are to:

1. Introduce a new class of PNs called augmented timed Petri nets (ATPNs) aimed to conveniently model breakdown handling. in manufacturing systems, 2. Illustrate a methodology to formulate ATPN models for breakdown handling, and 3. Model, simulate, and analyze an FAS using ATPNs for estimating the optimum number of assembly fixtures for various robot breakdown rates.


Petri nets are a powerful graphical and mathematical modeling tool to solve many problems related to asynchronous concurrent systems.(16) They have gained popularity as a versatile tool for addressing design issues related to FMSs.(17) Typical applications of PNs in manufacturing include performance evaluation;(14) modeling, validation, and analysis;(7,18) specification and implementation;(19) discrete event control design;(9-11,28) and simulation and scheduling. (18,20-22) PNs were used to address tool management issues,(23) model automated storage/ retrieval systems,(24) design of automated guided vehicle systems,(25) and to determine the optimal number of kanbans in just-in-time manufacturing systems.(26)

CONCEPTS AND TERMINOLOGY OF PETRI NETS A PN is defined as a bipartite graph containing places (pictured by circles) and transitions (pictured by bars). Places and transitions are connected by directed arcs (pictured by arcs with arrows). Places contain tokens (pictured by black dots). Distribution of tokens in the places of a PN is called its marking. Sometimes, weights (pictured as labels on the arcs) may also be used to facilitate modeling. If there is no weight on an arc, unit weight is assumed. Places can model different entities comprising the system, such as robots, machines, and AGVs, and different intermediate system states, such as Robot_i_is_ ready_to_load_part_j. Transitions can model activities involved in the system, such as Robot_i_ loads_part_j. Directed arcs model information, material, and control flow. A token in a place represents the true value of the condition modeled by the place.

All places that have arcs leading into (out of) a transition are said to be that transition’s input (output) places. A transition is said to be enabled if each of its input places has at least a number of tokens equal to the weight of the arc leading from that place to the transition. An enabled transition fires by removing a number of tokens equal to the weight of the corresponding input arc from each of its input places and depositing a number of tokens equal to the weight of the corresponding output arc in each of its output places. Hence, firing a transition changes the token distribution over some places, which in turn changes the marking of the PN. Each marking models a unique state of the system. Hence, as each transition in the PN fires, each unique state of the system can be easily determined by observing its PN. For example, if there are 40 tokens in a place modeling the buffer _between_machines_i_and_j , the work-in -process inventory between these two machines is said to be 40. Formally, a PN Z is a five-tuple, Z = (P, T,I, O, m) where:

1. P is a finite set of places.

2. T i. a finite set of transitions with PUTfZi and PnT = M.

3. : ‘ x T-N is an input function that defines the set of directed arcs from P to T where N =

4. O: P x T-N is an output function that defines the set of directed arcs from T to P.

5. m: P-)N is a marking whose ith component reresents the number of tokens in the ith place.

An initial marking is denoted by m,. Execution rules of a PN include the following enabling and firing rules:

1. A transition t ET is enabled if and only if m(p) r I(p,t), t) p EP 2. Enabled in a marking m, t fires and yieldis a new marking m’ following the rule: m’ )= m(p)+ O(p,t)-Co,t), pEp Marking m’ is said to be reachable from nl. Given Z and its initial marking m,, the reachability set is the set of all markings reachable from m, through various sequences of transition firings. Irnportant PN properties related to stability, repetil:iveness, and absence of deadlocks can be defined, ;md their implications for system behavior are reported in Narahari and Viswanadham,7 Zhou and Di(:esare,” and Association of time with transitions in the PN described above results in a timed PN. Fol-mally, a timed PN (TPN) is a net Z in which each lransition is associated with either a deterministic ol. random firing delay time. Note that the random tinle delays may follow standard probabilistic distributions. There are two events for a transition firing, that is, stcrrt_firing and endiring. Between therr, the firing is active. Removal of tokens from a tr;nsition’s input place(s) occurs at start_firing. Thejr deposition to a transition’s output place(s) (ccurs at endiring. While a transition’s firing is active, the time to end firing, called the remainingfii-ing time, decreases from firing duration to 0, at which its firing is completed. Instantaneous description (ID) defining a state of a TPN is a four-tup:le, ID = (m,F,e,A) where:

1. m is a marking 2. F is a binary selector function, F: T -f0,11. If F(t) = 1, t is enabled, otherwise disenabled. 3. e: T R+ is remaining firing time function. If e(l) ‘ q, there is q amount of time to complete firing t. e is a cumulatively decreasing time function .

4. A: T j R’ is active time function. If A(r) = q’, r is said to be active for q’ amount of time. A is a cumulatively increasing time functin.

ID is useful for the quantitative and behavioral analysis of the system. Figure I shos a TPN

modelin a machining operation. In Figure la, before nlachining is started, machine, part, and tool availability are modeled by depositing tokens in places nlachine_ready, partready, and tool_ready. This triggers machining by absorbing the input tokens and firing the transition modeling the activity machinjrzg. During machining, machine and tool are bus4 and there is no processed part available, as modelel in Figure lb. Once machining is completed, l:he part is processed and machine and tool are ready to process another part. This is modeled in Figure Ic by depositing each token in the places proces;;edqart_read4′, machine4eady, and toolrea dy .

Augmellted Timed Petri Nets The ]’N and TPN described above cannot easily model breakdowns in manufacturing systems. There exists ar extension of PNs with inhibitor arcs that can model l:he breakdowns; however, they can only model treakdowns that arrive before the start of an activity. In real-life situations, breakdowns may come at any time. Unlike previous classes of PNs, ATPNs ;re proposed to model breakdowns that may occur tlefore an activity starts and/or during an activity. Breakdowns may result not only because of power cr inteace failure but also due to subcomponent failure in a component. For example, a machine breakdown may result due to a fault in cutting fluid lubricatjon or tool handling system, and a robot may break down because of an error in its gripper. To model reakdowns, the following new constructs are added t> TPNs, leading to ATPNs: 1. Deal-tivation place. This is used to model the mest;age that is sent from cell controller to stop the (,peration of the breakdown component and start the standby component. Deactivation placl:s are pictured by two concentric circles. 2. Dea7tivation transitions. Two kinds of deactivation transitions are introduced. The former models the activity changeover from the breakdown component to standby one and vice versa. The latter models an activity that is being executed by the component and immediately stopped at the time of breakdown. These transitions are pictured as shaded ones.

3. Inpt and output deactivation arcs. These are used to model the control and information flow

among component and cell controllers. Input arc models control flow from cell controller to the breakdown component’s controller (to stop its operation). Output arc models control flow from cell controller to the standby component’s controller (to start the operations of blakdown component) .

4. Secandary arc. This is used to model the conditions that exist before and after change(ver from one component to another. It is pictued by a dotted arc.

Formally, an ATPN Z’ is an eleven-tuple, Z’ = (P, T,I, O,m,D,Pd,Td,P,Od,l’) , where the last five tuples are the new tuples proposed in thi paper as an addition to TPN. They are defined as lollows: 1. pd C P is a finite set of deactivation places. pd E pd connects the two transitions in the transition pair defined in 7d, which is described next.

2. 7d is a finite set of deactivation transition pairs. Each pair consists of two transitions: deactivating, tj’ (generating the deactivation command), and deactivated, t,” (the transition that gets


1 L i I k, and k = I pd I 3 P’ I x ‘jfO,1), input function defining a set of deactivation arcs from pd to T” 4. od. pd X 7d’fO,1), output function defining a set (>f deactivation arcs from Ti’ to pd 5. I’: P x TfO,1), secondary input function defining a set of secondary arcs from P to T. When a system is working normally, that is withom: breakdowns, the initial marking ofpd E pd is always O. The firing rule of tj’ is the same as a normal transition, while that of tj” is different. The firing rule of tj” is the same as a normal transition until tlle p’ contains a token. As soon as p’ contains a token, the firing of tj” is stopped (the activit4 modeled by tj” is stopped). When tj” is stoppe( because of l?d, it does not deposit the tokens in its output places in P. In other words, the tokens that tj” has taken from its input places for its normal firing are absorbed by tj”. When a place is connected to a transition by 1′, the enabling rule of the trallsition is same; however, the firing rule is differellt from the normal firing rule in updating the new marking. If place Pi is connected to tj by r, firing Ij does not take any token from Pi. In other words, during execution of tj, Pi contains a token. Summrizing the above concepts, the firing rules of ATPNs are given as follows: 1. (i) A transition t E T-il” is enabled if and only if m(p)r I(p,t) and m)r P(p,t), t/ p E P. (ii) A transition t E Ti” is enabled if and only if m(p) L I(p,t) and m(p) r P(p,t), p E P and ‘t/ pd E pd.

2. Transition t E T” immediately terminates its firillg, if 3 pd E pd, Idpd,t) 1 and md) = 1. 3. En.bled in a marking m, t fires and results in a nepl marking m’ following the rule: (i) m'(p)= m(p)+ O(p,t)-l7,t)t)p EP, and if during the firing process 3 pd E pd 3 Pdt) 1 and pd is not marked.

(ii) If t E Tdl, m’) = m) – l,t) + o(p’,t)-d (pd,t) p E P, and if during the firing process 3 pd E pd 3 dpd,t); 1 and pd is marked.

The ID of the ATPN is the same as that of the TPN descrit,ed above. Figure 2 shows an example of the

ATPN. Figure 2a models the machinin): activity before a breakdown occurs. The mechanism of breakdown generation is modeled by the place breakdown_generation . Assume that the breakdown occurs 4 minutes after machining is started. This is modeled by associating 4 minutes to the transition breakdown_of_tool_occurring . Figure 2A models the system when machining is in progress. Because the arc connecting the place signal_formachine _to_do_its_task and the transition machining is a secondary arc, there is a token present in this place during machining. Four minutes after machining is started, tool breakdown arrives and hence machining should be stopped. This is modeled in Figure 2c by removing a token from place breakdolvn_generation and depositing one in the place tc,ol_breakdown. The actions involved to stop machining are represented by firing of transition stop_machining, which removes tokens from places signalformachine_to _do_its_task and tool_breakdown and deposits a token in place message_tostol,machining. Once this place contains a token, it sends a message to immediately stop machining.

In the above example, breakdown time (4 minutes) is assumed; however, breakdowns lnay occur at random on the shop floor. To collsider the random occurrence of breakdowns in the: analysis, the breakdown times should be generated by assuming proper probability distributions. Also, strategies to minimize downtime during the period of breakdowns should be modeled during the analysis. These issues and other related breakdowrl handling issues are elaborately addressed and modeled in the PNMs that are presented in subsequent sec:tions. For analysis of the ATPN model, simply ref:rred to as the Petri net model (PNM), a software pakage was developed using the principles of ATPN3. It is an extension of previous worklS.21,22 and gives the following information with respect to reeil time:

Marking of each place in the PNM Active time of each transition

Remaining time of each transition Transitions that are enabled Conflicts between transitions (a conflict results when a single resource is required to serve more than one customer simultaneously)

Application Illustration An F’AS is investigated to show the application of ATPNs The system can be used for assembling a variety of products as show’n in Figure 3; however, to focc.s on the objective of the paper, only one produc’:, namely a plastic ratchet assembly, is consid:red .

The system consists of three robots and an inspection station to do assembly and inspection and is controlled by a cell controller. Each robot is controlled by its own controller. The functions of the cell controller are to give signals to robots to do their intended tasks and to send signals to stop their functioning at the time of breakdown and changeover. [t is assumed that all parts required for assemtlling the product are always available in aUtOIlliltiC part feeders and that there always exists deman for the finished product. The system descrited here is similar to such industrial robot assem,ly systems as the Westinghouse robot assembly sy.tems reported in Nof.27

The assembly operation is split into l:asks performed by three robots as follows:

Robot 1 (R1): Picks up and places a shaft in the assembly fixture; picks up and presses a p:iastic gear on the shaft; and picks up and presses a ratchet gear on the shaft.

Robot 2 (R2): Picks up and transfers the l;ubassembly from position 1 to position 2. Picks up and keeps a lever in assembly fixture and inserts a rivet in lever and rivets lever to the gear.

Robot 3 (R3): Transfers assembly to rotary table and inspects position and operations oflever. After R3’s operation, assembly fixture returns to R1 to start assembly of a new product. Assembly time for R1, R2, and R3 are 13, 18, and 10 minutes, respectively.

Various robot breakdown rates are considered to analyze the FAS. The system is evaluated for four values of mean time between failure (MTBF).

Ranges of MTBFs are chosen randomly. Values of MTBFs are obtained by assuming that they follow uniforn distribution within the given range. These ranges ;nd values of MTBFs for Rl, R2, and R3 for differer;t cases are shown in Table 1. Table 2 shows the exact time and breakdown sequence of robots for four different cases with different breakdown rates. h each case, given the MTBF, actual breakdown time is assumed to follow a truncated normal distribution to avoid negative values for time. Based on our experience, data with coefficient of variations below 20% are usually reliable and, hence, we have a:jsumed the standard deviation in normal distribution to be 10% of the mean.

The following assumptions are made in this model f the FAS to focus the objectives of the paper. ‘rhere is a standby robot for each robot in the system that will come on line when the con esponding robt fails. With this planning approach, unexpected lnanual intervention and subsequent productivity lclss can be precluded; moreover, it helps for smooth control of system during breakdown situations. P/laintaining a standby robot for each robot may not be economically feasible; however, to demonstrate application of ATPNs in the case of breakdcwn handling, a standby robot is assumed for each rolot. Changeover time is the time required to transfer the programs concerned with the breakdown ylbot to the standby robot (to carry subsequent lssembly operations), and to remove the unfinisled part from the asembly area of the breakdcwn robot. It is same for all robots and is assume( to be 20 minutes. Repair time for all robots is assulned to be the same and is equal to 100 minutes. These time durations can be changed to random variables depending on the system under conside: ation .

ATPN System Modeling This section presents the ATPN models of the FAS to address issues related to modeling, simulation, and analysis of robotic systems with breakdowns .

ATPN b/Iodel for Breakdown Handling Brea;down handling involves many concurrent actions such as passing information to a standby

robot or an operator, scheduling the unfinihed part, repairing the breakdown robot, and so on. Figure 4 shows an ATPN model (PNM) for breakdown handling of R3. The modeling methodology f ATPNs is explained, and the activities modeled and controlled by the PNM are chronologically listed below. The initial state of the FAS is model:d by the initial marking shown in FigLlre 4. Time durations for activities in the system are modeled by associating times to the transitions modeling corresponding activities. These are shown on the left-hand side of each transition. At the start of the sysa:m, R3 is ready to do its task (modeled by depositing a token in place R3_read) and the cell controller gives the signal to R3 to do its task (modeled by de]ositing a token in place signal_forR3_to_do_its_lask) . R3 functions normally till a breakdown occurs. Breakdown occurs after a random time called blakdown time (BT, obtained from Table 2), which is associated to the transition breakdown_ofi3_occurring . When it occurs, a token will be depositecl in place byeakdowyl_of_R3. Then after a changeover time from R3 to R6 (standby for R3), the l’ollowing concurrent operations are executed by the cell controller:

1. Sending a signal to R3’s controller to stop the operation and to R6’s to start. This is modeled by depositing a token in place message_ tostart6_andstop3 and removing the token from the place signa l_forR3_t_do_its_

task. As soon as place message_tastop3 gets a tokl:n, it stops the functioning of R3 by deactivatinl: the transition assembly_by_R3.

2. Activating the working of R6 by depositing a token in place R6_ready. Changeover between R3 arld R6 is modeled by removing a token from place signal_for_R3_to_do_its_task and depositing it in place signal_for 6_to_do_its_task . 3. Sending a message to the controller at the higher level to repair R3. This is modeled by depositing a tok:n in place R3_in_repair.

Durin: the repair of R3, R6 performs assembly operatiors. After a certain time, R3 is repaired,

modeled by firing the transition repair_of,R3. This resumes R3’s operation, modeled by place R3_ready_to_resume. Now the cell controller has to send signals for changeover from R6 to R3. Its functions for the changeover from R6 to R3 are similar to previous changeover, and hence the modeling is also similar. Various breakdown rates can be modeled by associating various values of time duration to transition breakdown_of_ R3_occurring.

The above ATPN model for breakdown handling is exactly the same when a skilled operator is used to replace the functions of a standby robot. Furthermore, the same ATPN modeling approach can be

extendel for the breakdown handling of other robots, machin:s, AGVs, and cell controllers in a manufacturing s:stem or for other production interruptions.

ATPN Ivlodel for Designing the Optimum Number of.issembly Fixtures ATPrJ models can be used to address various design issues. As an example, this paper determines the optimal number of assembly fixtures for various robot b::eakdown rates. To this end, the FAS has to be moleled using ATPNs considering the breakdowns f all robots. Then the obtained model has to be quarltitatively analyzed to determine the effect of various MTBFs on system performance. The ATPN model of the FAS is shown in Figure 5 and is obtained by duplicating the model shown in Figure 4 for R1 and R2. Interpretation of places and transitions used in the PNM is listed in Table 3. In case cf a breakdown, the assembly fixture is remov:d from the FAS, the unfinished part is remov(:d from the assembly fixture, and the assembly prccess starts again from Rl. This is modeled by output arcs from six transitions that are modeling changovers to place AF (assembly_fixrLire_ ready_before_RI).

Once a finished product is transferred by R3 to a rotary table, the assembly fixture is to be sent back to R1 This is modeled by output arcs from two transitions, one from R3 and another from R6 to place 4F (assembly_fixture_read,_beforel),

Simulation and Analysis of the ATPN Model Sinulation is carried out using the software packae briefly described earlier. The system is simulated for 20,000 time units. Execution of the ATPN for one set of parameters takes approximately 2 minutes of CPU time on a VAX system. Tble 4 showr the performance of the assembly system with and yithout breakdown of robots for different valuel; of MTBFs and numbers of assembly fixtures. During simulation, the number of assembly fixtures is incl eased until the increase in production output is less than 1%. Figure 6 shows the effect of MTBF on production volume. FigLlre 7 shows the effect of MTBI; on the utilization of the FAS.

From simulation results, the following conclusions are drawn. When there is no breakdown in the syste!n, there is a significant increase in production outpllt when the number of assembly fixtures is

changed From one to two; however, after it increases to more than two, there is no increase either in producti,n output or average robot utilization due to the detelministic nature of the FAS. Hence the optimum number of assembly fixtures required without lny breakdown in the FAS is two. Figures 6 and 7;lso indicate the sensitivity of the production output and average robot utilization for different cases when there are robot breakdowns.

In the presence oC breakdowns, to achieve the maximunl production rate, more assembly fixtures are requjred than that without breakdowns. The number f assembly fixtures does not increase linearly ,ith the increasing value of the MTBF. This is the corclusion drawn by observing the values of optimum assembly fixtures for various cases of MTBFs ar; shown in Table 5.

From the results, it can be inferred that system performallce depends not only on the MTBF but also

on the exact breakdown sequence of robol:s. Even though the value of MTBF increases from (Jase #1 to Case #4, the number of assembly fixtures decreased from Case #1 as well as Case #2 to Case #3 and increased from Case #3 to Case #4.

Conclusions and Further Research A new class of modeling tools called augmented timed Petri nets were introduced to model breakdown handling in manufacturing systems. ATPNs can model their operations in detail considering the breakdowns of various components. The lnethodology for formulating the ATPN models is illustrated by considering a flexible assembly system. Plso, the application of ATPNs for optimization and design is shown by investigating the optimum nurnber of assembly fixtures for the system under variolls robot breakdown rates. The methodology propose( in this paper can be extended to deal with breakdowns of several machines, AGVs, and cell controllers and other production interruptions. ATPNs provide rapid, flexible, and realistic modeling.

ATPN models can be extended for rv:al-time control. In such cases, the transition modeling the occurrence of breakdown is not associateld with

randon breakdown times. Instead, the sensors/limit switch:s that recognize the breakdown in the system are modeled as input places for this transition. When there is a breakdown in the system, these places get tokens and thus immediately fire the transition, modeling the occurrence of breakdown. Wh:n the system contains several components, the sizl: of ATPN models may grow. In such cases, colorel PNs can be combined with the principles of ATPNs to formulate concise graphical models. This research can be extended to study some important issues such as robot scheduling during breakdowns when only a single robot exists as a standby to all three robots, system performance when several product varieties are produced simultaneously in the system with random routing of parts, and cost considlration for standby robots and breakdown handlillg. The effect of random distributions of repair and changeover times on the system performance can also be investigated by associating various time values to the transitions modeling repair and changeover activities.

Ackrrowledgment Thit; research is supported by the Center for ManufBcturing Systems, New Jersey Institute of Technllogy, Newark, and the Department of Decision lnd Information Systems, Florida Atlantic Univel_sity, Boca Raton, Florida.

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20. K.P. Valavanis, “On the Hierarchical Modelling Analysis and Simulation of FMSs with Extended Petri Nets,” IEEl: Transuctions on Svstems. Mn and C

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Authors’ Biographies Kurapati Venkatesh is a research student in the Department of Mechanical Engineering at New Jersey Institute of Technology. He received a BS in mechanical engineering from S.V. University, Tirupati, in 1988 and an MS in mechanical engineering from Indian Institute ol’ Technology in 1990 and an MS in manufacturing systems enyineering from Florida Atlantic University in 1992. For the past th;le years, he has been app]ying the concepts of Petri nets to investig;1te a variety of problems in flexible automation. His research in:erests include Petri oets, flexible automation, design of control scftware using object-oriented techniques, intelligent machining, and neural networks. He has more than 20 publications in several journals and conferences, including Comyurers and Industrial En8ineering, International Journal of’ Operations and Production Manugement, and Journal af’ Material Processing and Techno[og?. He is a student member of the Phi Kappa Phi honor society.

Mehdi faighobadi received his PhD in operations management from Geor::ia State University in 1988. He has taught courses in quantitativ( methods and operations management at Florida Atlantic University since then. His research interests include factory automation, qualit management, and inventory control.

MengChu Zhou received his BS From East-China Institute of Technology in 1983, his MS from Beijing Polytechnic Institute in 1986, and his PhD from Renssalear Polytechnic Institul:e in 1990.

Since 1990 he has been an assistant professor in the eloctrical and computer engineering department and the manufacturing :ngineering program at New Jersey Institute of Technology. His resealch interests are in discrete event systems, Petri nets, and computer-integrated manufacturing. He has more than 50 publications, including books, book chapters, journal articles, and conference papers.

Reggie Caudill is the executive director of the Centel for Manufacturing Systems and professor of mechanical engineering at New Jersey Institute of Technology. He received his undergladuate and master’s degrees from the University of Alabama and his PhD in mechanical engineering from the University of Minnesota in ]976. Dr.

Caudill’s primary research interests are in the integration of advanced machine and computer technologies with applications in ;1gile manufacturing and automation. He is the author of more than fiO technical publications and has received several million dollars in research funding from various govemmental agencies and private industry. He is cited in Who’s Who in Technolog Toda, Director), of World Researchers, and Americun Men and Women of Science.

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