Abstract—Computational complexity is one of the most
important criteria in evaluating the performance of deadlock
control method. Based on Petri net models, a polynomial
deadlock avoidance method is addressed for a class of flexible
manufacturing systems (FMSs) with key resources. It is first
proved that there are three kinds of reachable markings in these
FMSs:safe ones, deadlock, and secondary deadlock. Second, an
algorithm to determine the safety of a new marking resulting
from a safe one is presented, which has polynomial complexity. It
adopts a (two) one -step look-ahead method to prohibit the firings
of transitions that result in (secondary) deadlocks. Thus, a
polynomial deadlock avoidance policy for a class of FMSs with
key resources is established. An illustrative example is provided
to demonstrate the efficiency of the proposed method.
I. INTRODUCTION
A flexible manufacturing system (FMS) is a
computer-controlled manufacturing system containing
multiple concurrent flows of job processes. The introduction
of heavy resource sharing can increase flexibility, but may lead
to deadlock when two or more jobs keep waiting indefinitely
for the other jobs in a production sequence to release resources.
Deadlocks can reduce productivity drastically or lead to the
entire stagnancy. Therefore, it is necessary to develop an
efficient deadlock control policy to guarantee that deadlocks
never happen in FMSs [3].
Petri nets are utilized as a formalism to describe FMSs and
develop appropriate deadlock resolution methods [8]-[9],
[14]-[15]. Based on Petri nets, three types of approaches are
developed for FMSs, i.e., deadlock detection and recovery [6],
deadlock prevention [1]-[2], [4], [7], [10]-[13], and deadlock
avoidance [16]-[18].
This work focuses on deadlock avoidance methods. The
development of efficient deadlock avoidance methods for
FMSs has received significant attention for a decade. However,
the computation of the optimal deadlock avoidance method is
NP-hard because it involves the problem of determining the
*Resrach was supported in part by the National Nature Science
Foundation of China under Grants 61304052, 61273152 and 61374066, in
part by China Post-Doctoral Science Foundation on the 55
th
Grant Program
under Grant 2014M551741, in part by the Doctoral Fund of Ludong
University under Grant LY2013008.
Huixia Liu is with School of Information and Electrical Engineering,
Ludong University, Yantai, 264025, China (corresponding author: huixialiu
@126.com).
Weimin Wu and Hongye Su are with State Key Laboratory of Industrial
Control Technology & Institute of Cyber-Systems and Control, Zhejiang
University, Hangzhou, 310027, China (e-mail: wmwu@iipc.zju.edu.cn,
hysu@iipc.zju.edu.cn).
Hongyong Yang are with School of Information and Electrical
Engineering, Ludong University, Yantai, 264025, China (e-mail:
hyyang@yeah.net).
safety of a given resource allocation state, which is NP-hard.
Thus, many researchers have focused on designing optimal
policies for some special classes of FMSs or suboptimal
policies that are computationally tractable.
For sequential resource allocation systems with non-unit
capacity, Reveliotis et al [16] prove that the systems contain
only two kinds of states: safe one and deadlock, and present
polynomial complexity deadlock avoidance methods. For
systems of simple sequential processes with resources (S
3
PRs)
without -resources, Xing et al [18] also prove that there are
only two kinds of reachable markings: safe one and deadlock.
They utilize maximal perfect resource transition circuits
(MPRT-circuits), a special circuit that only contains resource
places and transitions, to characterize deadlock in S
3
PRs. For a
marked S
3
PR without -resources, Xing et al derive an optimal
Petri-net-based polynomial complexity deadlock avoidance
policy. For a marked S
3
PR with -resources, by reducing it and
applying the design of an optimal deadlock avoidance policy
to the reduced one, a suboptimal deadlock avoidance policy is
established, and its computation is of polynomial complexity.
For a marked S
3
PR with -resources, we narrow the concept of
-resources and illustrate that not all -resources can result in
secondary deadlock when each MPRT-circuit is maximally
permissive controlled (The obtained controller is called first
controller and deadlocks in them as secondary deadlock) in
our previous work [13]. The concepts of key resources and key
transitions are presented. It proves that key transitions can
bring FMSs with key resources into secondary deadlock. For a
class of S
3
PRs with key resources, secondary deadlock can be
characterized by maximal perfect control transition circuits
(MPCT-circuits) that are saturated at some reachable marking
of the first controlled Petri nets.
Based on the design of the Petri net controller [13],
deadlock is characterized by a saturated MPRT-circuit and
secondary deadlock by a saturated MPCT-circuit, and it is first
proved that there are three kinds of reachable markings: safe
ones, deadlock and secondary deadlock in this work. Second,
an algorithm for determining the safety of a new state resulting
from a safe one is presented and then proved to be with
polynomial complexity. Finally, a polynomial complexity
deadlock avoidance policy for a class of FMSs with key
resources is established.
The rest of the paper is organized as follows. Section II
reviews preliminaries, such as Petri nets, S
3
PRs, key resources,
and maximal perfect control transition circuits used
throughout this paper. For a class of FMSs with key resources,
three kinds of reachable markings are presented in Section III.
Based on it, an algorithm to determine the safety of a new
A Polynomial Deadlock Avoidance Method for a Class of Flexible
Manufacturing Systems*
Huixia Liu, Member, IEEE, Weimin Wu, Hongye Su, and Hongyong Yang