Distributed Transactions Modeling with the Use of Petri Nets
The attempt of using ordinary Petri Net to model and study Three-Phase Commit protocol (3PC) is presented. A brief overview of Petri Nets is introduced. The nature of typical and distributed transactions are explained. 3PC protocol actions are described. The Petri Net of 3PCprotocol followed by rea...
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| Cite this: | Distributed Transactions Modeling with the Use of Petri Nets / M. Iwaniak, W. Khadzhynov // Реєстрація, зберігання і оброб. даних. — 2012. — Т. 14, № 3. — С. 81-91. — Бібліогр.: 4 назв. — англ. |
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| citation_txt | Distributed Transactions Modeling with the Use of Petri Nets / M. Iwaniak, W. Khadzhynov // Реєстрація, зберігання і оброб. даних. — 2012. — Т. 14, № 3. — С. 81-91. — Бібліогр.: 4 назв. — англ. |
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| description | The attempt of using ordinary Petri Net to model and study Three-Phase Commit protocol (3PC) is presented. A brief overview of Petri Nets is introduced. The nature of typical and distributed transactions are explained. 3PC protocol actions are described. The Petri Net of 3PCprotocol followed by reachability analysis and study of the net properties is presented.
Зроблено спробу використання простої мережі Петрі для моделювання й дослідження трифазного протоколу фіксації (ЗРС). Наведено короткий огляд мереж Петрі. Пояснено сутність звичайних і розподілених транзакцій. Дано опис кроків протоколу ЗРС. Проаналізовано доступність мережі Петрі з протоколом ЗРС і досліджено властивості запропонованої мережі.
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| first_indexed | 2025-12-07T15:15:46Z |
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ISSN 1560-9189 , , 2012, . 14, 3 81
UDC 004.5:519.876.2
M. Iwaniak, W. Khadzhynov
Technical University of Koszalin
Department of Electronics & Informatics
ul. niadeckich 2, 75-453 Koszalin, Polska
hadginov@ie.tu.koszalin.pl
Distributed Transactions Modeling with the Use of Petri Nets
The attempt of using ordinary Petri Net to model and study Three-Phase
Commit protocol (3PC) is presented. A brief overview of Petri Nets is intro-
duced. The nature of typical and distributed transactions are explained.
3PC protocol actions are described. The Petri Net of 3PCprotocol followed
by reachability analysis and study of the net properties is presented.
Key words: Petri Net, distributed transactions, 3PC, Three-Phase Commit
protocol.
1. Introduction
The theory and the practice of distributed database is a very complex issue. During
many years of studies the standard that would be helpful in projecting and implementa-
tion of systems based on distributed database was not developed. There is especially a
lack of operative standard for heterogonous distributed database.
The theory of Petri Net is used in modeling and analyzing parallel processes. The
structure and function of Petri Net could described in algebraic form and processed with
the use of numerical methods.
The solution allowing projecting, modeling and verifying processes in distributed
database with the use of Petri Net is searched. Such a net might serve for supervising
the flow of data in distributed database nodes or for generating configurations that allow
the realization of projected processes.
This work presents the attempt of usage Petri Net for showing the function of 3PC
protocol. We try to answer the question: whether the ordinary Petri Net is an adequate
tool for modeling such a complex process as a commitment of distributed transaction is.
2. Petri Nets
The mathematical theory of Petri Nets was created by Carl Adam Petri. It has wide
field of usage in analysis and modeling.
© M. Iwaniak, W. Khadzhynov
mailto:hadginov@ie.tu.koszalin.pl
M. Iwaniak, W. Khadzhynov
82
Most commonly described is The Ordinary Petri Network, also named as network
of class position/transition. It’s graphical representation is bipartite graph which con-
tains two types of nodes connected by arcs. Nodes of the net are:
— places (positions) — represented by circles;
— transitions () — represented by rectangles.
Petri Net can be expressed as the triplet N = (P, T, D) where:
— P is a collection of places |P| = m;
— T is a collection of transitions |T| = n;
— D is incidence matrix of dimension m×n. This matrix describes relations be-
tween collections of places and transitions;
— D– is pre-incidence matrix of dimension m×n, it contains elements ijd = w(i, j)
which describe the weight of transition j input arc, that is the arc directly connecting
place i with transition j (P × T N);
— D+ is post-incidence matrix of dimension m×n, it contains elements
( , )ijd w i j which describe the weight of transition j out arc, that is the arc directly
connecting transition j with place i with (P × T N);
— D = [D+ – D–] is incidence matrix of dimension m×n, this matrix is created by
subtracting pre-incidence matrix from post-incidence matrix, it contains elements
ij ij ijd d d . These elements come from subtracting weights of input arc from weights
of output arcs.
2.1. Marking of net and firing of transitions
Marked Petri Net can be described by four-tuple PN = (P, T, D, M0), where
M0: P {0,1,2,..} is an initial marking of the net that defines the token distribution in
the network places.
In Petri Net with given initial marking can occur dynamic events. If the input
places of given transition have an amount of tokens equal to input arc weight then the
transition can be fired. After firing of the transition from all input places the tokens are
taken away and new tokens are inserted into the output places. The amounts of tokens
taken away from each input place and inserted into output places are equal to weights of
given input and output arcs. The process is presented on Fig. 1.
) b)
Fig. 1. Transition: a) transition ready to be fired; b) transition after firing
Depending on the initial marking the reachability set for given Petri Net can differ.
The sets of reachable markings are created and presented with usage of a directed graph
Distributed Transactions Modeling with the Use of Petri Nets
ISSN 1560-9189 , , 2012, . 14, 3 83
called a reachability tree. A reachability tree represents one by another both firing of
transitions and marking changes. Each sequence of firings and marking changes is
called the execution of the net.
A reachability tree contains such elements as:
— the root — representing initial marking,
— nodes — representing each reachable marking,
— arcs — representing fired transition,
— leaves — representing final or repeated markings.
A reachability tree can be prepared by analysis of following transitions firings.
This analysis can be simplified by algebraic properties of Petri Net. Each column of
the incidence matrix describes a change in marking after a firing of given transition.
Each marking can be computed with usage of the following formula
Mk = Mk–1 + e[ jt ]D,
where k = 1,2,3,… and e[ jt ] a firing vector containing a digit 1 in position correspond-
ing j transition.
2.2. Properties of Petri Net
Boundness — the net is bounded, when for each place we can determine a finite
number of tokens appearing in given place. This means that collection of possible mark-
ings is finite and can be searched.
Safeness is a detailed property of boundness. The place is safe if for any given
marking the number of tokens in place is 0 or 1. If this condition is valid for every place
in the net then the net is safe. This property is important when Petri Net is projected for
hardware implementation, where place will be replaced by transistor capable of having 0
or 1 value.
Conflictuality — a conflict of transition firing can occur when for given marking
more than one transitions is enabled. It can also happen if firing of one transition dis-
ables other already enabled transition [2].
Conservativness — the net is conservative if sum of tokens in every marking is
constant. This can be proven only for simple nets.
2.3. Timed Petri Net
In the Timed Petri Net we can define some time delay. If given transition gets
ready (required number of tokens for each place is preset), the transition firing will hap-
pen only after the delay. For two timed transitions sharing the same input place a spe-
cific situation can occur. If one gets fired it can take away the shared tokens and the an-
other might not be able to be fired.
2.4. Coloured Petri Net
Coloured Petri Net is a graph containing places, transitions and arcs in which the
token stores value of given type. For tokens of given type specific colors are assigned.
M. Iwaniak, W. Khadzhynov
84
Places of Petri Net can store tokens of many colors. Given place however must allow
the specific color to be stored in it. Colours separately are assigned to arcs weight. For
example transition can be enabled after number of each tokens colours are equal to col-
ours weights defined for the arc.
3. Processing transactions in database
The digital collection of properly organized data is called database. The stored da-
ta usually model real objects. Database Management System in short DBMS is respon-
sible for accuracy, safety and effectiveness of the access to stored data. The structure of
database is too complex to work with it without the usage of DBMS. Typically DBMS
is responsible for providing data access service. Through local operating system the
DBMS cares of safe data storing and mediates in all operations executed by users.
Stored data are fully useful only if they are valid and consistent. Each data change
takes a whole database into entirely new database state. Many data changes can happen
in one unit of time and some of them are erroneous. The transaction mechanism cares
for validness and consistence of an actual database state.
A transaction is an operation that correctly executed guaranties database consis-
tence. Transactions can consist of many operations of reading and writing the data. The
changes made by the transaction must be done as a whole or none.
The ACID properties are the ones that guaranty proper transactions processing.
These properties are:
— Atomicity — states that each transaction must be executed as whole or not at
all;
— Consistency — states that after the transaction is finished the database system
will remain consistent. The changes made by the transaction will not be stored in data-
base if during the commitment occurs an error like integrity bounds violation or any
other that guaranties a data validation;
— Isolation — level of isolation determines the possibility of mutual data reading
by transactions proceeded concurrently. By the selected level of isolation we determine
types of possible anomalies that may occur during transactions execution;
— Durability — states that database system can startup after failure and provide
consistent, not damaged and actual data stored in bounds of committed transactions.
DBMS registers all stages of transaction processing in a transaction log. During
database recovery only committed transactions are recovered, because only those can
guaranty receiving the consistent state of database.
In a single database during processing of transactions many anomalies can occur,
like blocking, conflicts or deadlocks. A single DMBS upon its configuration and capa-
bilities tries to avoid or removes occurring anomalies.
4. Transactions processing in distributed database
Distributed database is a collection of many logically bounded databases con-
nected via computer network. Variety of distributed database types is summarized in
[1].
Distributed Transactions Modeling with the Use of Petri Nets
ISSN 1560-9189 , , 2012, . 14, 3 85
Short time transactions are advised by DBMS. From application or user points of
view execution of transaction in distributed system should not be different from tradi-
tional system.
Standalone database has implemented program called transaction manager shortly
TM, that cares for proper database state management and for communication with cli-
ents. In distributed environment the additional communication is happening between
TMs. One of TMs serves a role of Coordinator, the others take a role of Cohorts. A way
of communication between Coordinator and Cohorts are defined by distributed commit
protocol. The classical example of such protocol is the one named Two-Phase Commit.
This protocol has two phases: phase of voting and phase of committing. The voting
phase when Coordinator sends question to its Cohors, asking if they are ready to commit
distributed transaction. Returning communicates are called votes. These votes can be:
vote-commit or vote-abort. After collecting votes Coordinator makes its decision. If
there was any vote for aborting or any of Cohorts did not respond at all, the coordinator
will make the decision of global abort of distributed transaction. If all of the votes were
positive its decision will be global commit.
Making of the decision only when all of the votes are for commit is the main way
for assure atomicity into distributed database.
4.1. Three Phase Commit protocol for distributed transaction
On Fig. 2 the algorithm of 3PC protocol is presented. Fig. 2 was prepared upon
[1]. The circles represent states of Coordinator and Cohort processes. The rectangles
represent operations of logging received messages and made decisions into system log.
Arrows represent the flow of messages and control. Algorithm looks as follows.
1. The coordinator creates log entry with information <begin_commit> and sends
<prepare> message to Cohorts. Coordinator now waits for Chorts votes. Coordinator
state is <WAIT>.
2. The cohorts decide if they are ready to commit transaction. They store their de-
cision into log file and send <vote-commit> or <vote-abort> to Coordinator. Varing of
the decision new state of Cohort process can be READY or ABORT.
3. The coordinator checks received messages from all cohorts:
a) If there was any vote-abort or some cohort did send his vote, the Coordinator
makes the decision of aborting distributed transaction. Coordinator writes his decision
into log file and sends <global-abort> message. Coordinator state is <ABORT>;
b) If all cohorts have responded with <vote-commit> message then Coordinator
makes decision to begin second phase of commit. Coordinator writes <prepare-to-
commit> into log file. It sends <prepare-to-commit> message to Cohorts. Coordinator
state is <PRE-COMMIT>.
4. The cohorts write received message into the log. In case of <global-abort> Co-
horts processes turn into <ABORT> state and acknowledge is send to Coordinator. In
case of <prepare-to-commit> Cohorts processes turn into <PRE-COMMIT> state and
sends <ready-to-commit> message to Coordinator.
5. After collecting Cohorts <ready-to-commit> messages Coordinator writes
<commit> into log. It sends <global-commit> message to all Cohorts. Coordinator state
is now <COMMIT>.
M. Iwaniak, W. Khadzhynov
86
6. The cohorts write received message into log and send back acknowledge mes-
sage. Cohorts are now in <COMMIT> state.
7. The coordinator writes <end_of_transaction> into log file.
Fig. 2. Three Phase Commit protocol algorithm with one participant
5. The ordinary Petri Net model of 3PC protocol
Described in point 4.1 the 3PC protocol was introduced as Petri Net model on
Fig. 3. The example was prepared for Coordinator and one Cohort. Places of Coordina-
tor (Tab. 1) are aligned to left edge of figure. Places of Cohort (Tab. 2) are aligned to
right edge of figure.
Distributed Transactions Modeling with the Use of Petri Nets
ISSN 1560-9189 , , 2012, . 14, 3 87
Fig. 3. Petri Net of 3PC protocol algorithm
Table 1. Places and transitions of Coordinator
Places Transitions
P0 INITIAL T0 1) write to log (begin_commit)
2) message to Cohorts (prepare)
P1 WAIT T4 1) write to log (abort)
2) message to Cohorts (global-abort)
P2 ABORT T3 1) write to log (prepare-to-commit)
2) message to Cohorts (prepare-to-commit)
P3 PRE-COMMIT T7 1) write to log (commit)
2) message to Cohorts (global-commit)
P4 COMMIT – –
Table 2. Places and transitions of Cohort
Places Transitions
P5 INITIAL T1 1) write to log (abort)
2) message to Coordinator (vote-abort)
P6 ABORT T2 1) write to log (ready)
2) message to Coordinator (vote-commit)
P7 READY T5 1) write to log (abort)
2) potwierdzenie do Coordinator
P8 PRE-COMMIT T6 1) write to log (prepare-to-commit)
2) message to Coordinator (ready-to-commit)
P9 COMMIT T8 1) write to log (commit)
2) potwierdzenie do Coordinator
M. Iwaniak, W. Khadzhynov
88
5.1. Incidence Matrixes for Petri Net
Rows of Tab. 3 contains places P0, P1, P2, P3, P4 which represent the states of Co-
ordinator and places P5, P6, P7, P8, P9 which represent states of the Cohort. Columns
t0 – t9 represent transitions. The pre-insidence matrix contains weights of input arcs of
given transition. In case of no arc between place i and transition j we enter digit 0. This
matrix is marked as [D–].
Tabel 3. Pre-Incidence Matrix
D–
0t 1t 2t 3t 4t 5t 6t 7t 8t
P0 INITIAL 1 0 0 0 0 0 0 0 0
P1 WAIT 0 0 0 2 2 0 0 0 0
P2 ABORT 0 0 0 0 0 0 0 0 0
P3 PRE-COMMIT 0 0 0 0 0 0 0 2 0
P4 COMMIT 0 0 0 0 0 0 0 0 0
P5 INITIAL 0 1 1 0 0 0 0 0 0
P6 ABORT 0 0 0 0 0 0 0 0 0
P7 READY 0 0 0 0 0 1 2 0 0
P8 PRE-COMMIT 0 0 0 0 0 0 0 0 2
P9 COMMIT 0 0 0 0 0 0 0 0 0
Rows of Tab. 4 contain places P0, P1, P2, P3, P4 which represent the states of Co-
ordinator and places P5, P6, P7, P8, P9 which represent states of Cohort. Columns
t0 – t9 represent transitions. The post-insidence matrix contains weights of output arc of
given transition. In case of no arc between transition j and place i we enter digit 0. This
matrix is marked as [D+].
Tabel 4. Post-Incidence Matrix
D+
0t 1t 2t 3t 4t 5t 6t 7t 8t
P0 INITIAL 0 0 0 0 0 0 0 0 0
P1 WAIT 1 1 1 0 0 0 0 0 0
P2 ABORT 0 0 0 0 1 1 0 0 0
P3 PRE-COMMIT 0 0 0 1 0 0 1 0 0
P4 COMMIT 0 0 0 0 0 0 0 1 1
P5 INITIAL 1 0 0 0 0 0 0 0 0
P6 ABORT 0 1 0 0 0 1 0 0 0
P7 READY 0 0 1 1 1 0 0 0 0
P8 PRE-COMMIT 0 0 0 0 0 0 1 1 0
P9 COMMIT 0 0 0 0 0 0 0 0 1
Distributed Transactions Modeling with the Use of Petri Nets
ISSN 1560-9189 , , 2012, . 14, 3 89
Combined insidence matrix (Tab. 5) is computed by subtracting pre-incidence ma-
trix from post-incidence matrix [D+ – D–]. It describes dynamic changes that occur in
given Petri Net. It contains information about amount of tokens added and removed in
every place after the jt transitions is fired.
Table 5. Combined Incidence Matrix
D
0t 1t 2t 3t 4t 5t 6t 7t 8t
P0 INITIAL –1 0 0 0 0 0 0 0 0
P1 WAIT 1 1 1 –2 -2 0 0 0 0
P2 ABORT 0 0 0 0 1 1 0 0 0
P3 PRE-COMMIT 0 0 0 1 0 0 1 –2 0
P4 COMMIT 0 0 0 0 0 0 0 1 1
P5 INITIAL 1 –1 –1 0 0 0 0 0 0
P6 ABORT 0 1 0 0 0 1 0 0 0
P7 READY 0 0 1 1 1 –1 –2 0 0
P8 PRE-COMMIT 0 0 0 0 0 0 1 1 –2
P9 COMMIT 0 0 0 0 0 0 0 0 1
6. Reachability analysis
Initial marking is represented in the form of vector M0 = [10000000000] (Fig. 4).
For given marking we check which transitions will became enabled. For instance token
in the place P1 will cause firing of transitions t0.
Algebraic pattern for designate markings after firing j transition is as follows:
Mk = Mk-1 + e[ jt ]D,
where Mk — new marking; Mk-1 — previous marking; for k = 1 it is initial marking;
e[ jt ] — column vector of size i with digit 1 on index that corresponds fired transition;
D — the incidence matrix.
For given marking M0 we want to designate marking M1 by firing of transition t0:
e[t0]*D = [–1 1 0 0 0 1 0 0 0 0].
M0 = [10000000000].
After addition of two vectors we will have following marking of Petri Net:
M1 = [0100010000].
M. Iwaniak, W. Khadzhynov
90
Fig. 4. Reachability tree for Petri net from Fig. 3
(undesirable states are shown without markings)
6.1. Properties of Petri Net model
Boundness — maximal amount of tokens in places is 2 therefore the net is bounded.
Safeness — there are markings with places where quantity of tokens is 2 therefore
the net is not safe.
Conflictuality — in the presented model the conflicts take place in the Petri Net
places where decision must be made. Accurate amount of tokens in places P1, P2 and
P4 make all output transitions enabled (P1(T1, T2), P5(T3, T4), P7(T5, T6)). In place
P5 Cohort process in case of error must send abort vote or in case of being ready it must
send vote for commit.
Conservativnes — presented model is complex, the property cannot be validated.
7. Resume
In this work Petri Net model of 3PC protocol was presented. With usage of inci-
dence matrixes the reachability tree was created. Undesireble but reachable states were
identified on reachability tree.
During studies of presented Petri Net model a number of limitations and problems
were pointed. Most of them come from the Ordinary Petri Network limitations. We
must use higher level Petri Net in further research. Applying Coloured Petri Net should
Distributed Transactions Modeling with the Use of Petri Nets
ISSN 1560-9189 , , 2012, . 14, 3 91
resolve the problem of decision making in certain markings. It would help reducing
number of undesirable states in the analysis of reachability.
1. M. Tamer Özsu. Principles of Distributed Database Systems / M. Tamer Özsu, Patrick Valduriez
// Springer. — III ed. — 2011.
2. Banaszak Z. Procesy Wspó bie ne: Modele Efektywno ci Funkcjonowania. Rozdzia 2 «Modele
sieci Petriego» / Z. Banaszak, P. Majdzik, R. Wójcik. — Politechnika Koszali ska, Koszalin 2011. —
Str. 93–143.
3. Bidyut Biman Sarkar. Transaction Management for Distributed Database using Petri Nets /
Bidyut Biman Sarkar, Nabendu Chaki // International Journal of Computer Information Systems and In-
dustrial Management Applications (IJCISIM). — 2010. — Vol. 2. — . 069–076. — ISSN: 2150-7988.
4. Bidyut Biman Sarkar. Virtual Data Warehouse Modeling Using Petri Nets for Distributed Deci-
sion Making. doi:10.4156/jcit / Bidyut Biman Sarkar, Nabendu Chaki. — 2011. — Vol. 5. — Is. 5.1.
Received 01.07.2012
|
| id | nasplib_isofts_kiev_ua-123456789-50587 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-9189 |
| language | English |
| last_indexed | 2025-12-07T15:15:46Z |
| publishDate | 2012 |
| publisher | Інститут проблем реєстрації інформації НАН України |
| record_format | dspace |
| spelling | Iwaniak, M. Khadzhynov, W. 2013-10-24T00:11:43Z 2013-10-24T00:11:43Z 2012 Distributed Transactions Modeling with the Use of Petri Nets / M. Iwaniak, W. Khadzhynov // Реєстрація, зберігання і оброб. даних. — 2012. — Т. 14, № 3. — С. 81-91. — Бібліогр.: 4 назв. — англ. 1560-9189 https://nasplib.isofts.kiev.ua/handle/123456789/50587 004.5:519.876.2 The attempt of using ordinary Petri Net to model and study Three-Phase Commit protocol (3PC) is presented. A brief overview of Petri Nets is introduced. The nature of typical and distributed transactions are explained. 3PC protocol actions are described. The Petri Net of 3PCprotocol followed by reachability analysis and study of the net properties is presented. Зроблено спробу використання простої мережі Петрі для моделювання й дослідження трифазного протоколу фіксації (ЗРС). Наведено короткий огляд мереж Петрі. Пояснено сутність звичайних і розподілених транзакцій. Дано опис кроків протоколу ЗРС. Проаналізовано доступність мережі Петрі з протоколом ЗРС і досліджено властивості запропонованої мережі. en Інститут проблем реєстрації інформації НАН України Реєстрація, зберігання і обробка даних Технічні засоби отримання і обробки даних Distributed Transactions Modeling with the Use of Petri Nets Моделювання розподілених транзакцій за допомогою мереж Петрі Моделирование распределенных транзакций с помощью сетей Петри Article published earlier |
| spellingShingle | Distributed Transactions Modeling with the Use of Petri Nets Iwaniak, M. Khadzhynov, W. Технічні засоби отримання і обробки даних |
| title | Distributed Transactions Modeling with the Use of Petri Nets |
| title_alt | Моделювання розподілених транзакцій за допомогою мереж Петрі Моделирование распределенных транзакций с помощью сетей Петри |
| title_full | Distributed Transactions Modeling with the Use of Petri Nets |
| title_fullStr | Distributed Transactions Modeling with the Use of Petri Nets |
| title_full_unstemmed | Distributed Transactions Modeling with the Use of Petri Nets |
| title_short | Distributed Transactions Modeling with the Use of Petri Nets |
| title_sort | distributed transactions modeling with the use of petri nets |
| topic | Технічні засоби отримання і обробки даних |
| topic_facet | Технічні засоби отримання і обробки даних |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/50587 |
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