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Simulation Modelling Practice and Theory 63 (2016) 133–148
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory
journal homepage: www.elsevier.com/locate/simpat
Colored ACD and its application
Hyeonsik Kim , Byoung-Kyu Choi ∗
Department of Industrial and Systems Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea
a r t i c l e i n f o
Article history:
Received 25 August 2015
Revised 27 December 2015
Accepted 24 February 2016
Keywords:
Colored activity cycle diagram (C-ACD)
Model tractability
Online simulation
Initialization of simulation model
Hierarchical modeling
Electronics Fab
a b s t r a c t
The classical ACD invented by KD Tocher about 60 years ago was recently enhanced to the
extended ACD by allowing each edge to have a guard and multiplicity, and then to the pa-
rameterized ACD (P-ACD) by adding parameters and variables. This paper presents a colored
ACD (C-ACD) formalism which extends the P-ACD formalism by (1) introducing colors to
increase model tractability and (2) adding hierarchical modeling features to reduce model
complexity . As a result, C-ACD models are easier to construct and validate and is suitable
for online simulation. In order to quantify the tractability of ACD models, two kinds of
measures are introduced: model tractability index (MTI) and initialization tractability index
(ITI) . Also presented is a systematic method of initializing C-ACD models required for on-
line simulation. It is shown that the C-ACD formalism provides more tractable models in
terms of both MTI and ITI. The applicability of the C-ACD formalism is demonstrated via
an illustrative simulation example for a hypothetical electronics Fab.
134 H. Kim, B.-K. Choi / Simulation Modelling Practice and Theory 63 (2016) 133–148
Fig. 1. Single server system: (a) Reference model. (b) Classical ACD.
simulation was used in an operation management system , which is also referred to as a manufacturing execution system , for
die and mold manufacturing in the 1990s [10] . More recently, online simulation is gaining popularity in simulation-based
operation management of electronics fabrication lines [11,12] . Online simulation is also used in other application areas such
as road networks traffic simulation [13] , wildfire spread simulation [14] , and resource failure management in production
lines [15] . Initialization issues in online simulation were investigated recently [16,17] , but to the best of our knowledge,
this paper is the first one to provide a systematic solution to the initialization problem in discrete-event simulation. The
possibility of using the CMSD standard in online simulation was investigated in [16] , and [17] dealt with initialization issues
in tracking simulation where the communication between the real plant and the continuous simulation system can be used
for initialization purposes.
The rest of the paper is organized as follows. Section 2 presents a brief review of classical, extended and parameterized
ACD formalisms. Formal definitions, executions, tractability, systematic initialization, and hierarchical modeling of the col-
ored ACD are presented in Section 3 . Section 4 presents an illustrative example of constructing and executing a colored ACD
model of an electronics Fab. Conclusions and discussions are given in the final section.
2. Brief review of ACD formalisms
This section gives a brief review of ACD formalisms: classical, extended, and parameterized ACD formalisms. The classical
ACD invented by Tocher in 1957 [4] is a bipartite directed graph consisting of a set of activities (rectangular nodes), queues
(circular nodes), and edges (directed arcs). It can be algebraically specified as follows:
A classical ACD is a six tuple N C = 〈 A , Q , E , τ, μ, μ0 〉 (1)
• A = {a 1 , a 2 , …, a n } is a finite, non-empty set of activity nodes.
• Q = {q 1 , q 2 , …, q m
} is a finite, non-empty set of queue nodes.
• E = {e 1 , e 2 , …, e e } is a finite, non-empty set of edges, e i ∈ (A ×Q) ∪ (Q ×A).
• τ: A → R 0 + is a time delay function associated with activities.
• μ= { μq ∈ N 0 + | ∀ q ∈ Q} is the number of tokens associated with queues.
• μ0 : Q → N 0 + is the initial value of μ (initial marking).
Fig. 1 shows a reference model and a classical ACD model of the ‘famous’ single server system [1] . A single server system
physically consists of a machine (M) and a buffer (B), but in order to make the system a closed one, the job-arrival process
is regarded as an active resource named Job Creator (C) and the outside world as a passive resource (Jobs) containing an
unlimited number of jobs. From Specification ( 1 ), the classical ACD model in Fig. 1 (b) may be algebraically specified as
follows:
Algebraic definition of the classical ACD in Fig. 1 (b)
• A = {a 1 = Create, a 2 = Process}
• Q = {q 1 = Jobs, q 2 = C, q 3 = B, q 4 = M}
• E = {e 1 = (q 1 , a 1 ), e 2 = (q 2 , a 1 ), e 3 = (a 1 , q 2 ), e 4 = (a 1 , q 3 ), e 5 = (q 3 , a 2 ), e 6 = (q 4 , a 2 ), e 7 = (a 2 , q 4 ), e 8 = (a 2 , q 1 )}
• τ (a 1 ) = t a , τ (a 2 ) = t p • μ = { μq1 , μq2 , μq3 , μq4 }
• E = {e 1 = (q 1 , a 1 ), e 2 = (q 2 , a 1 ), e 3 = (a 1 , q 2 ), e 4 = (a 1 , q 3 ), e 5 = (q 3 , a 2 ), e 6 = (q 3 , a 3 ), e 7 = (q 4 , a 2 ), e 8 = (q 5 , a 3 ), e 9= (a 2 , q 4 ), e 10 = (a 3 , q 5 ), e 11 = (a 2 , q 1 ), e 12 = (a 3 , q 1 )}
• τ (a 1 ) = t a , τ (a 2 ) = t 1 , τ (a 3 ) = t 2 • μ = { μq1 , μq2 , μq3 , μq4 , μq5 }
• E = {e 1 = (q 1 , a 1 ), e 2 = (q 2 , a 1 ), e 3 = (a 1 , q 2 ), e 4 = (a 1 , q 3 ), e 5 = (q 3 , a 2 ), e 6 = (a 2 , q 1 ), e 7 = (a 2 , q 4 ), e 8 = (q 4 , a 3 ), e 9= (q 5 , a 3 ), e 10 = (a 3 , q 5 ), e 11 = (a 3 , q 3 )}
The buffer capacity queues in both C-ACD models are initialized as follows:
BP = c 0 – (|C 1 | + |L 2 | + |C 2 | + |L 3 | + |L 4 | + |C 3 |); // available space in the uni-inline port (P) BPI = c 0 – (|C 1 | + |L 2 | + |C 2 |); // available space in the bi-inline in-port (PI)
BF = c 1 – (|C 2 | + |L 3 | + |L 4 | + |C 3 |); // available space of the in-line facility (F)
Finally, the entity queues (Q, P, and F) in both models are initialized as follows:
For k = 1 ∼|L 1 | {(L 1 [k].j, L 1 [k].p) → Q;} // enqueue the record L 1 [k] into Q
For k = 1 ∼|L 2 | {(L 2 [k].j, L 2 [k].p) → P;} // enqueue the record L 2 [k] into P
For k = 1 ∼|L 4 | {(L 4 [k].j, L 4 [k].p) → F;} // enqueue the record L 4 [k] into F
As mentioned earlier in Section 3.5 , all the non-instant activities in the C-ACD models have to be initialized as well. That
is, their BTO events have to be by scheduled during the initialization phase. The BTO events to be scheduled are:
• Load-end(j,p): BTO event of the Load(j,p) activity
• TI-end(j,p): BTO event of the TrackIn(j,p) activity
• TO-end(j,p): BTO event of the TrackOut(j,p) activity
• Flow-end(j,p): BTO event of the Flow(j,p) activity
From the current status data in Table 3 , the BTO events can be scheduled as follows:
If (|C 1 | > 0) {Schedule-Event (Load-end (C 1 .j, C 1 .p), t 0 /2);} // expected remaining time = t 0 /2
If (|C 2 | > 0) {Schedule-Event (TI-end (C 2 .j, C 2 .p), r 2 );}
If (|C 3 | > 0) {Schedule-Event (TO-end (C 3 .j, C 3 .p), r 3 );}
If (|C 2 | > 0) {C 2 → L 3 ;} // append C 2 at the end of L 3 If (|L 3 | > 0) {d = t 2 / (|L 3 | + 1); For k = 1 ∼|L 3 | {Schedule-Event (Flow-end (L 3 [k].j, L 3 [k].p), k ∗d);}}
4.5. Colored ACD modeling of the entire Fab
Fig. 19 shows a C-ACD model of an electronics Fab with two types of inline cells connected by an AMHS. The uni-
inline cell model of Fig. 17 is parameterized with parameter ‘u’ and the bi-inline cell model of Fig. 18 is parameterized with
parameter ‘b’. The AMHS is represented by the parameterized delay activity Move (j,p,c,c n ) with a move-time delay of t m
[c,c n ],
where
• j : job type
• p : processing step
• c : current cell number
• c n : next cell number
In the AMHS part of the C-ACD model, arriving cassettes are generated by the create activity Generate with an inter-
generation time of t G , and the next cell number c n is obtained from the route function Route(j,p). After each move activity
Move, the job is sent to either a uni-inline cell or a bi-inline cell depending on its type. If the cassette has completed all
the processing steps (i.e., c n ≡ Done), it leaves the system by the Sink queue. Methods of initializing the BTO event of the
move activity Move(j,p,c,c n ) may be found in [7] .
4.6. Illustrative implementation
Online simulation experiments were made with the colored ACD model given in Fig. 19 for a hypothetical LCD Fab de-
picted in Fig. 20 . Tables 5–8 show the Route data, Machine master data, Moving time data , and Layout master data , respectively,
for the hypothetical Fab. The value of the route function Route(j,p) is obtained from the Route data in Table 5 (a minimum
146 H. Kim, B.-K. Choi / Simulation Modelling Practice and Theory 63 (2016) 133–148
Fig. 19. Colored ACD model of an electronics Fab consisting of uni-inline cells and bi-inline cells.
148 H. Kim, B.-K. Choi / Simulation Modelling Practice and Theory 63 (2016) 133–148
sets may be extended or modified if necessary). The C-ACD formalism increases model tractability by the use of colors and
reduces model complexity via hierarchical modeling. As a result, C-ACD is easier to construct and validate and it allows a
systematic initialization procedure needed for online simulation.
In order to quantify the tractability of ACD models, two kinds of measures were introduced: model tractability index (MTI)
and initialization tractability index (ITI) . Compared with non-colored ACD models it was shown that the C-ACD formalism
provides more tractable models in terms of both MTI and ITI. Also presented was a systematic method of initializing C-ACD
models required for online simulation. The applicability of the C-ACD formalism was demonstrated via an illustrative online
simulation of a hypothetical electronics Fab. For this purpose, a dedicated simulator was implemented in C#.
C-ACD may be regarded as an ‘ultimate’ extension of the classical ACD the same way the colored Petri net formalism is
an ultimate extension of the classical Petri net formalism. Moreover, as mentioned above the C-ACD formalism may allow
systematic initialization of complex simulation model for online simulation. However, this may be just a beginning of online
simulation R&D effort s toward the ‘smart’ operation management in real-life manufacturing systems and service systems.
Also, it will make a promising research topic to apply the proposed initialization framework to other types of modeling
formalisms such as event graphs and timed automata.
A widely accepted definition of model validation [22] is “the substantiation that a model within its domain of applicability
possesses a satisfactory range of accuracy consistent with the intended application of the model”. This paper brought about
a more focused view of simulation model validation where the concepts of model tractability and reference model played a
key role. It is a very important issue in real-life simulation studies, and deserves further research effort s.
Acknowledgment
The research was supported by the NRF of Korea grant funded by the Korean Government (NRF-2013R1A1A2062607) to
which the authors are grateful.
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