ORIGINAL ARTICLE

Comments on “Efficient deadlock prevention policy in automatedmanufacturing systems using exhausted resources”

Murat Uzam & Gökhan Gelen

Received: 19 September 2013 /Accepted: 7 January 2014# Springer-Verlag London 2014

Abstract As reported by Hu and Li (International Journal ofAdvanced Manufacturing Technology 40:566-571, 2009), inorder to design liveness-enforcing supervisors for automatedmanufacturing systems (AMS), a deadlock prevention policywas proposed based on the exhausted resources. The proposedpolicy exploits a special structure of Petri nets for the livenessof a specific system. In order to show the applicability of thismethod, two examples were considered. One of the examplesinvolves an AMS with a large-state space. Unfortunately, theliveness-enforcing supervisor containing seven monitors (con-trol places) computed as reported by Hu and Li (InternationalJournal of Advanced Manufacturing Technology 40:566-571,2009) to enforce liveness on this system does not provide a livebehaviour. This paper reports this fact.

Keywords Automatedmanufacturing systems . Petri nets .

Deadlock . Exhausted resources

1 Introduction

A deadlock prevention policy based on the exhausted re-sources was proposed in [1] to design liveness-enforcingsupervisors for automated manufacturing systems (AMS),by using their Petri net models (PNM). Two examples were

considered to show the applicability of the proposed approach.Figure 1 depicts the S3PR PNM of a manufacturing cellconsidered in [1]. The PNM shown in Fig. 1 suffers fromdeadlock problems and therefore, to enforce the liveness onthis PNM, it is necessary to introduce a liveness-enforcingmechanism. Therefore, by using the approach proposed in [1],seven monitors (control places) given in Table 1 were com-puted to enforce liveness on the PNM shown in Fig. 1.However, as it is shown in the next section, the controlled(closed-loop) system containing the PNM shown in Fig. 1 andseven monitors given in Table 1 do not provide a live system.

2 Analysis of the controlled model

The controlled PNM consists of the uncontrolled PNM shownin Fig. 1 and of seven monitors given in Table 1. In order to

Fig. 1 The S3PR Petri net model (PNM) of a manufacturing cell takenfrom [1]

M. Uzam (*)Elektrik-Elektronik Mühendisliği Bölümü, Meliksah UniversitesiMuhendislik-Mimarlik Fakultesi, 38280, Talas Kayseri, Turkeye-mail: murat_uzam@meliksah.edu.tr

M. Uzame-mail: murat_uzam@hotmail.com

G. GelenMuhendislik ve Doga Bilimleri Fakultesi, Mekatronik MühendisliğiBölümü, Gaziosmanpasa Universitesi, Tokat, Turkeye-mail: gokhan.gelen@gop.edu.tr

Int J Adv Manuf TechnolDOI 10.1007/s00170-014-5615-z

analyse the controlled PNM, a Petri net analysis software toolcalled INA (http://www.informatik.hu-berlin.de/∼starke/ina.html) was used. The controlled PNM is obtained as an INAfile as shown in Fig. 2. Analysis results for the controlledPNM by using INA is obtained as shown in Fig. 3. It can beseen from Fig. 3 that the controlled PNM is not live.

In addition to the above comment, let us consider anotherfact related to these seven monitors. Based on the further

studies carried out on the controlled PNM with these sevenmonitors, it can be concluded that six of these monitors areredundant. Let us now consider the uncontrolled PNM shownin Fig. 1 together with only one monitor related to resource R2from Table 1. Figure 4 shows an INA file representing thecontrolled PNM consisting of the PNM shown in Fig. 1 andonly one monitor related to resource R2. Figure 5 provides theanalysis results obtained from INA for the controlled PNMshown in Fig. 4.When these analysis results are compared withthe ones in Fig. 3 related with controlled PNM consisting of thePNM shown in Fig. 1 and seven monitors given in Table 1, itcan easily be seen that both the controlled PNM with sevenmonitors andwith only onemonitor related to resource R2 havethe same analysis results. This means that six monitors exceptfor the monitor related to resource R2 are all redundant.

Table 1 Seven monitors (control places) computed in [1] to enforceliveness on the PNM shown in Fig. 1

i Resource ●Pci Pci● M(Pci)

1 M2 t3, t7, t12 t1, t5 14

2 M1 t7, t8, t22 t5, t21 14

3 R2 t4, t10, t11, t17, t23 t1, t5, t20, t21 3

4 R1 t6, t7, t15 t5, t20 14

5 M3 t6, t9, t16 t5, t20 14

6 M4 t6, t13, t18, t24 t5, t20, t21 14

7 R3 t14, t19 t5, t20 14

p m pre,post1 2 4,12 0 1,23 0 2,34 0 3,45 0 5,6 76 0 6,87 0 7,98 0 8,109 0 9,1110 0 10,1211 0 11,1312 0 12 13,1413 2 14,514 0 16,1515 0 17,1616 0 18,1717 0 19,1818 0 20,1919 0 21,2220 0 22,2321 0 23,2422 2 24,2123 2 15,2024 2 3 12,2 1025 2 8 23,6 2226 2 2 4 10 11 17 22,1 3 8 9 18 2127 2 6 7 15,5 1628 2 9 16,7 1729 2 13 18,11 1930 2 14 19 24,12 13 20 2331 14 3 7 12,1 532 14 7 8 22,5 2133 3 4 10 11 17 23,1 5 20 2134 14 6 7 15,5 2035 14 6 9 16,5 2036 14 6 13 18 24,5 20 2137 14 14 19,5 20@

Fig. 2 The INA file representing the controlled PNM consisting of thePNM shown in Fig. 1 and seven monitors given in Table 1

Computation of the reachability graphStates generated: 15185Arcs generated: 74443Dead states: 5183,Number of dead states found: 1The net has dead reachable states.The net is not live.The net is not reversible (resetable).The net has no dead transitions at the initial marking.The net is bounded.

Fig. 3 Analysis results obtained from INA for the controlled PNMshown in Fig. 2

p m pre,post1 2 4,12 0 1,23 0 2,34 0 3,45 0 5,6 76 0 6,87 0 7,98 0 8,109 0 9,1110 0 10,1211 0 11,1312 0 12 13,1413 2 14,514 0 16,1515 0 17,1616 0 18,1717 0 19,1818 0 20,1919 0 21,2220 0 22,2321 0 23,2422 2 24,2123 2 15,2024 2 3 12,2 1025 2 8 23,6 2226 2 2 4 10 11 17 22,1 3 8 9 18 2127 2 6 7 15,5 1628 2 9 16,7 1729 2 13 18,11 1930 2 14 19 24,12 13 20 2333 3 4 10 11 17 23,1 5 20 21@

Fig. 4 The INA file representing the controlled PNM consisting of thePNM shown in Fig. 1 and only one monitor related to resource R2 fromTable 1

Int J Adv Manuf Technol

3 Conclusions

This paper has shown that the liveness-enforcing supervisorcontaining seven monitors computed in [1] does not provide a

live behaviour. In addition, it is also shown that six of thesemonitors are redundant.

Acknowledgments This work was supported by the research grant ofthe Scientific and Technological Research Council of Turkey (TürkiyeBilimsel ve Teknolojik Araştırma Kurumu - TÜBİTAK) under the projectnumber TÜBİTAK-112 M229.

Reference

1. Hu HS, Li ZW (2009) Efficient deadlock prevention policy in auto-mated manufacturing systems using exhausted resources. Int J AdvManuf Technol 40(5–6):566–571

Computation of the reachability graphStates generated: 15185Arcs generated: 74443Dead states: 5183,Number of dead states found: 1The net has dead reachable states.The net is not live.The net is not reversible (resetable).The net has no dead transitions at the initial marking.The net is bounded.

Fig. 5 Analysis results obtained from INA for the controlled PNMshown in Fig. 4

Int J Adv Manuf Technol