Deadlock avoid

Graduate Seminar - Deadlock Avoidance in FMS, June 2002

Deadlock Avoidance Methods

in Flexible Manufacturing Systems

Jacob Rubinovitz
Technion - Israel Institute of Technology
Faculty of Industrial Engineering & Mgmt.

Dr. Jacob Rubinovitz


Introduction: Flexible Manufacturing Systems
An automatic, programmable manufacturing system
Volume
Transfer
Lines

Dedicated CIM
Systems
Flexible
Systems
Automated
Cells
Job
Shops

Variety



Components of the System
•Programmable machines (CNC, Robots)
•Flexible tools and fixtures
• Flexible MH systems (AGV’s, Robots)
•Automated Storage and Retrieval System
•Computer control



Deadlock-free operation is crucial
to the operation of an FMS
Research of Deadlock Avoidance Methods:
• Evaluation of different policies.
• Integration of avoidance policies into the control
software of Flexible Manufacturing Cells.
• A joint work with Jean-David Salama.



Deadlock - background
Parts in FMS compete for a finite number of
resources (like robots, tools, pallets, fixtures, etc),
and share buffers or queues having limited
capacities.
A deadlock state occurs when each process in a
set of processes is blocked indefinitely from
access to resources held by other processes
within the set.
A good FMS control method must resolve or avoid
all the potential deadlocks during operation,
without seriously degrading the system
performance


Necessary conditions for deadlocks
Mutual exclusion: resources can be allocated to
only one process at a time.
No preemption: resources held by one process
cannot be allocated to another process until they
are released by the process holding them.
Hold and wait: processes hold their resources
when waiting for the next required resources.

Circular wait: closed chain of processes, where
each process waits for a resource held by the next
process in the chain.



Part Flow Deadlock
Machine M1 Machine M2
P1: M1→M2
(No Buffer ) (No Buffer ) P2: M2→M1
Part P1 Part P2 M1 M2
‫) טובורובוט‬MHD(

M2 M1
M2
P1: M1→M2
M1
P2: M2→M3
P3: M3→M1
M3 P1: M1→M2 M3
P2: M2→M3
P3: M3→M1



Methods for handling Deadlocks
Detection/Recovery (Wysk et al., 1994)

Prevention – System design, such that
deadlocks are impossible
(Epzeleta et al., 1995;Minoura and Ding, 1991;
Viswanadham et al., 1990)
Avoidance – a control policy that
examines each request for resource
allocation prior to its execution
(Banaszak and Krogh,1990; Ferrarini and Maroni,1998;
Hsieh and Chang,1994; Lee and Lin, 1995; Revelotis
and Ferreira,1996; Xing et al.,1996;Yim et al.,1990)


(Capacity-Designated Graph (CDG

Mi Ni

3
IBi

A machine and its CDG node.

Yim, D.S., Kim, J.I. and Woo, H.S. (1997) Avoidance of deadlocks
in flexible manufacturing systems using a capacity-designated
directed graph. International Journal of Production Research, 35
(9), 2459-2475.


(Capacity-Designated Graph (CDG

N2
|N|=4, N1
A12=A21=A24=A43=A32=A14=A41=1 2 2
A42=A13=A31=A34=A23=0
N4
X={1,2,0,1} N3
C={2,2,1,3} 3 1
Fully detailed CDG graph G=(N,A,X,C).

Yim, D.S., Kim, J.I. and Woo, H.S. (1997) Avoidance of deadlocks
in flexible manufacturing systems using a capacity-designated
directed graph. International Journal of Production Research, 35
(9), 2459-2475.


Loops in a Capacity-Designated Graph
N2
N1
Cycle S1: N1→N2→N1
N1 N2 N3
Cycle S2: N1→N2→N4→N1
Cycle S3: N2→N4→N3→N2
N4 CDG
A G=(N,A) Cycle S : N →N →N
N3
containing 57 cycles. 4 1 4 1

Cycle S : N1→N →N3→N2→N1
A CDG G=(N,A) containingN5 cycles. 4
5
5
N4

N
N!
Smax = [Σ i =1 (N -i) !·i
] -N


Loops in a Capacity-Designated Graph
N2
N1
N3

A CDG G=(N,A)
containing 57 cycles.
N5
N4

Routing Intensity Index
N N

ΣΣA
i = 1 j =1,j = i
ij
RII = ; 0<RII<1
N (N - )
1


Necessary Condition for a Deadlock
There is a loop S i
such that : ΣX(N ) = ΣC(N )
Nj ∈ Sj
j
Nj ∈ Sj
j

Macro N1 N2 S1: N1→N2→N1

Nodes S2: N2→N3→N2
S3: N1→N3→N1
MN1={N1,N2}
MN2={N2,N3}
S4: N1→N2→N3→N1 MN3={N1,N3}
N3 S5: N1→N3→N2→N1 MN4={N1,N2,N3}
A CDG G=(N,A)
with 5 cycles and 4 macro nodes.

Deadlock
Avoidance Policy: C(MNi ) < Σ C(Nj)-1
Nj ∈ Si


Impending (Policy-Induced) Deadlocks
N2
MN1={N1,N2,N4,N5} N1 N3
MN2={N2,N3,N4}
1

2 constraints: 1 1
X(MN1) ≤ 3
X(MN2) ≤ 2 N5 1
N4
1

In order to avoid the impending deadlocks,
CDG graph (cycle) reduction is needed



Cycle reduction in a CDG graph
Cycle Reduction Algorithm output
N2
N1 N3 Macro Node elements Macro node capacity
Level 0 1 node
1
1
N5
MN1 {N1,N2,N4,N5} C(MN1)=C(N1)+C(N2)
1 N4 1 G1 +C(N4)+C(N5)-1=3
Level 1
N
N11 MN2 2
MN
MN1 N3 MN2 {N2,N3,N4} C(MN2)=C(N2)+C(N3)
1 +C(N4)-1=2
1 2
2
3 1 N5 5
11
G2 G3 {MN1,N3}= C(MN3)=C(MN1)
MN3
{N1,N2,N3,N4,N5} +C(N3)-1=3
MN3 MN4
Level 2

G4 3 3 G5 MN4 {MN2,N1,N5}= C(MN4)=C(MN2)
{N1,N2,N3,N4,N5} +C(N1)+C(N5)-1=3



Objective- Deadlock Avoidance Policies
To propose various control solutions for part flow
regulation in FMCs, all structured around four
different deadlock avoidance policies (DAPs).

The DAPs will be evaluated by their
properties of:
 correctness,
 scalability,
 configurability,
 efficiency.



DAP properties
Correctness
Guarantees always a deadlock-free operation

Scalability
Computational complexity for the control system
is independent of the FMC complexity

Configurability
Can be applied to various FMC configurations

Efficiency
FMC operation is not restricted by policies that
degrade its performance



The Deadlock Avoidance Method

Request for movement Compute the current number of parts in
of a part to a node in a each relevant macro node assuming that
given CDG graph G the requesting part was transported

Yes Condition No
Allow the X(RMNi)≤C(RMNi) Refuse the
movement satisfied for all i ? movement



Part Flow Management
Operation on part completed... The robot completed a delivery...

Is the robot idle and is there some open
Checking if the transfer of each
space in the downstream station ?
waiting part is unfeasible,
No Yes feasible but refused, or feasible
and accepted
Transfer Transfer feasible:
unfeasible: DAP applied to 2 or
more
Part waiting for allow or refuse the A part
Number
future transfer transfer selection
of accepted
0 transfers ? rule is used
Transfer Transfer to pick a
1
refused: allowed: Parts requesting part
Part waiting for Part actually movement remain The requesting
future transfer moved by the at their locations. part picked by
robot the robot



Four Different Deadlock Avoidance Policies

Static (SDAP) M1 M2
Dynamic (DDAP)
FIFO Loading Discipline M3
applied to parts in the Entry Buffer
Input Buffer
Selective Static (SSDAP)
Selective Dynamic (SDDAP) Step-by-step
M1 M2

Selection from all the backward search

different part types waiting M3

in the input buffer Entry Buffer


Static Strategy
Off-line Movement of a waiting
On-line
Create a CDG from the static part feasible
information on machines, machine
capacities and complete part type Determine the resulting number of parts
routes in each relevant macro node X(RMN)

Compute the relevant macro nodes
RMNs and their capacities C(RMNs) Apply the deadlock
avoidance method

Dynamic Strategy
On-line Movement of a waiting part feasible

Create a CDG considering remaining machine sequences of each part
in the system, and assuming that the requesting part was transported.

Determine the current number of parts in
Compute the relevant macro each relevant macro node X(RMN)
nodes RMNs and their assuming that the requesting part was
capacities C(RMNs). transported.

Apply the deadlock
avoidance method


R1 : M1→M2→M3 M1 M2 M3
Illustrative R2 : M3→M2→M1
|N|=3
Example A12=A23=A21=A32=1 Entry Buffer
C={1,1,1}
Gantt chart, schedule under a static strategy - SDAP or SSDAP
M1
M2
M3
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
WIP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time
Gantt chart, schedule under a dynamic strategy - DDAP
M1
M2
M3
1 2 3 2 1 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1
WIP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time
Gantt chart, schedule under a dynamic strategy - SDDAP
M1
M2
M3
1 2 3 3 2 1 2 2 3 3 2 1 1 2 2 1 1 1 1 1 1 1 1 1
WIP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time



Experimental Setup
CENTRAL STATION 2 # Processed Parts
WAREHOUSE Initial
State 0
EXIT STATION

0
0
STARVED
STATION 1 STATION 3

CENTRAL
BUFFER

IDLE STARVED
0 STARVED 0
0
0 STATION 4

STATION 5
INSPECTION

ENTRY STATION # Parts in System
0
Replication
Number
0 STARVED
Current Time 0 STARVED
08:00:00 0



System Structure
BP Static Deadlock Dynamic Deadlock External
Avoidance Module Avoidance Module Module
SBP SDAP SSDAP DDAP SDDAP

Deadlock
Cycle Reduction Algorithm Detection
Module
Part Flow Cycle Search
Control Module Part Selection Rules Module
Algorithm
PSR1 PSR2 PSR3 PSR4

FMC Simulation Model
(Arena)



Experimental Design
Four Different Deadlock Avoidance Policies
M1 M2
Static (SDAP)
Dynamic (DDAP) M3

Entry Buffer

FIFO Loading Discipline applied to parts in the Input Buffer

M1 M2
Selective Static (SSDAP) Step-by-step
backward search

M3
Selective Dynamic (SDDAP)
Entry Buffer

Selection from all the different part types waiting in the
input buffer



Experimental Design – 2 cell types
part types machines, 4 : Cell A 3
part types machines, 5 : Cell B 6
Buffer Capacities
Cell A Cell B
1 C(CB)=0, C(IB)={0}, CBS=4 C(CB)=0, C(IB)={0}, CBS=5







Experimental Design
(Part Selection Rules (PSR
PSR1 – priority to parts with minimum
remaining processes
PSR2 – priority to parts with
maximum remaining processes
PSR3 – priority based on part type
PSR4 – priority based on resource
(machine) type



Experimental Design
RII – Routing Intensity Index

High RII Low RII
Cell A RII = 1 RII = 2/3
Cell B RII = 0.9 RII = 0.6



Experimental Design
High Routing Intensity Low Routing Intensity
R1: M4→ M2→ M1→ M4→ M3→ M1 R1: M1→ M2→ M4→ M3 Cell
R2: M1→ M2→ M3→ M4 R2: M4→ M1→ M3→ M2
R3: M3→ M2→ M4→ M1→ M3
N 1 N2
R3: M3→ M4→ M2 N1 N2 A
N4 N3 N4 N3

R1: M1→ M5→ M3→ M4→ M2 R1: M1→ M2→ M3→ M4 Cell
R2: M2→ M3→ M1 R2: M2→ M1→ M4
R3: M4→ M5→ M2→ M4 R3: M4→ M5→ M1
B
R4: M1→ M4→ M3→ M5 R4: M5→ M4→ M2→ M1
R5: M5→ M4→ M3→ M2→ M1 N2 R5: M3→ M4→ M1 N2
N1 N
R6: M4→ M1→ M2→ M5
1
N3 R6: M4→ M3→ M1 N3

N5 N5 N4
N4



Experimental Design – Product Mix
Unbalanced mix Balanced mix
P1=0.65 P1=P2=P3=0.333 Cell
P2=0.25 A
P3=0.10
P1=0.55 P1=P2=P3=P4=P5=P6= 0. 1666 Cell
P2=0.20 B
P3=0.10
P4=0.5
P5=0.5
P6=0.5

4 * 2 * 5 * 2 * 2 = 160


Results : C(CB)=0, C(IB)={0}



Results : C(CB)=M, C(IB)={0}



Results : C(CB)=0, C(IB)={1}



Results : SDDAP performance for different buffer sizes



Results : SDDAP performance for different buffer sizes

. #Config Cell A Cell B
[87.8%,67.3%] [79.4%,69.7%]
2 [90.6%,82.3%] [92.4%,78.9%]
3 [92.4%,84.1%] [98.5%,80.9%]
4 [99.5%,92.2%] [98.7%,88.3%]
[96.2%,82.4%] [99.8%,81.8%]



Incorporating a Central Buffer

Operation on a part completed: if the transfer
is unfeasible or refused by the DAP, the part is
moved to the central buffer CB, provided that
there is some open space in it .

The robot completed a delivery: the control
system checks first all the parts currently in the CB.
Priority is given to these parts in order to reduce
the amount of average WIP in the CB.



Conclusions - Efficiency:
The static policies are inefficient and generate low
throughput rates in single capacity cells (SCCs(, even after
incorporating a central buffer. For this system configuration,
SDDAP is the most appropriate operating policy.
The DAPs have similar performance for double capacity cells
(DCCs( with no central buffer; Throughput is slightly higher
with SDDAP. The use of SDDAP is recommended for a high
routing intensity level.
High throughput rate is achieved for manufacturing cells of |
M| machines with attached input buffers of single capacity
and a |M| capacity central buffer.
The superiority in terms of throughput of a selective policy
(such as SSDAP or SDDAP( over a standard one (like
SDAP or DDAP( is, as expected, more apparent when the
part mix is balanced.


Conclusions - Computational Complexity

The computational complexity becomes higher in the
following order of DAPs application: SDAP, SSDAP, DDAP,
and SDDAP.

SDDAP is computationally more intensive when applied
respectively to Single, Double and Triple Capacity Cells.

As a result, a static strategy may represent the best
alternative for operating a system including machines with
buffers of capacity two or more. Under such conditions, a
static policy is not less efficient than a dynamic one,
generates less WIP, and is computationally much less
complex.



Potential Implementation: Cluster Tools
NEXUS 600
Six-port cluster tool that will
accommodate four process
modules and dual load-locks
and integrated wafer handler.
NEXUS 600

NEXUS 800
Eight-port cluster tool that
will accommodate six process
modules and dual load-locks
and integrated wafer handler.
NEXUS 800



Questions?


Results : Part Selection Rules


Deadlock avoid

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