CN108090720B

CN108090720B - Process analysis method based on type petri net

Info

Publication number: CN108090720B
Application number: CN201711282464.6A
Authority: CN
Inventors: 刘伟; 冯新; 杜玉越
Original assignee: Shandong University of Science and Technology
Current assignee: Shandong University of Science and Technology
Priority date: 2017-12-07
Filing date: 2017-12-07
Publication date: 2021-09-21
Anticipated expiration: 2037-12-07
Also published as: CN108090720A

Abstract

The invention discloses a process analysis method based on a type petri net, which belongs to the field of process analysis of the type petri net and specifically comprises the following steps: putting forward a type petri net theory; defining a type library in a network, defining a classification function on a transition output arc, and classifying the Token; defining a transformation function on the transition to solve the problem that the types of an input library and an output library of the transition are different; adding a constant enabling expression and a counting function on the transition to define a transition triggering rule; and (4) jointly defining a time function and a manpower function, and solving the actual problem. Analyzing two schemes of a distribution system, establishing a distribution system model by utilizing a type petri net theory, setting a time and manpower parameter table according to actual conditions, carrying out state conversion analysis on the two distribution schemes, constructing a process conversion diagram, analyzing time resource consumption and manpower resource consumption under different distribution schemes by utilizing the type petri net theory, and finding out a better solution.

Description

Process analysis method based on type petri net

Technical Field

The invention belongs to the field of process analysis of a type petri net, and particularly relates to a process analysis method based on the type petri net.

Background

A petri net is a model used to describe distributed systems. The system can describe the structure of the system and simulate the operation of the system. The part describing the structure of the system is called the net (net), and the part describing the state of the system is represented by identification. One of the salient advantages of petri nets compared to other net system models is that it is more convenient to describe concurrency and conflicts. With the increasingly wide application of petri nets in various systems and processes, the petri nets are expanded, and at present, several more mature advanced petri nets include color petri nets, time petri nets, logic petri nets and the like.

The essence of the color petri nets is to sort the tokens to enable folding of the nets. Compared to PT-net, the color petri net defines a color for each torr, and a representation method that defines a set of colors for each bin may use fewer bins. The color petri nets are very versatile and can be applied to describe a wide variety of different types of systems.^[2]The classification is added into the Petri net, so that the modeling capability of the Petri net can be remarkably improved, the types defined by the library are further specified, and the classification function classification method defined on the output arc of the transition is more concise and universal.

The logistics terminology (GB/T18354-2006), the national standard of the people's republic of China, gives the following definition to the distribution center (distribution center): a distribution center is a "place or organization that engages in distribution traffic and has a sophisticated information network. The following requirements should be met basically: a) primarily to provide service to specific users or end customers; b) the distribution function is sound; c) the radiation range is small; d) providing high frequency, small batch, multi-batch delivery services. "

The delivery system discussed herein is based on campus meal ordering services, and meets the above 4-point requirement. In the system, a user provides order requirements, a merchant processes the requirements and then delivers the requirements, different delivery schemes are selected according to actual conditions, and the optimal solution of the delivery process in terms of manpower and time is compared. In the process of using the color petri network, the usage of the arc expression has certain limitation and redundancy, the established model cannot be generally used for order requirements under each condition, the specific content on the arc expression needs to be changed again in each modeling, if a guard function is added into the network, more color sets of different types need to be defined, and the layering is slightly complicated in logic.

The type of petri nets proposed herein considers the problem of how classification can be implemented more simply and universally. A distribution system model based on the type petri net is established, the problems of time resource consumption and human resource consumption in the distribution process are analyzed aiming at the two schemes, and a more optimized scheme is found.

Disclosure of Invention

Aiming at the technical problems in the prior art, the invention provides a process analysis method based on a type petri net, which is reasonable in design, overcomes the defects of the prior art and has a good effect.

In order to achieve the purpose, the invention adopts the following technical scheme:

a process analysis method based on a type petri net comprises the following steps:

step 1: analyzing a specific flow of a distribution system;

step 2: establishing a distribution system model based on the type petri net by using a type petri net theory;

and step 3: according to the actual situation, a time parameter table and a manpower parameter table of the distribution system are given;

and 4, step 4: performing state conversion analysis on two distribution schemes of a distribution system, and constructing a type petri net process conversion diagram;

and 5: and analyzing time resource consumption and human resource consumption under different distribution schemes by utilizing a type petri net theory to find out a better solution.

Preferably, in step 1, the distribution system comprises a distribution system scheme a and a distribution system scheme B; wherein:

flow of distribution system scheme a: order demand → { order processing } → production → delivery → { confirmation delivery } → order delivery completion;

flow of the distribution system scheme B: order demand → { order processing } → production → { sort order by address } → delivery → { confirm delivery } → order delivery completion.

Preferably, in step 2, the theory of type petri nets is as follows:

definition 1.1 a triplet N ═ (P, T; F) satisfying the following conditions is referred to as a net;

1)

2)

3)

definition 1.2 let N ═ (P, T; F) be a net, remembering that for x ∈ PU! T

^·x＝{y|y∈P∪T∧(y,x)∈F}；

x^·＝{y|y∈P∪T∧(y,x)∈F}；

Balance^·x is a preceding or input set of x, x^·X postset and output set;

definition 1.3N ═ (P, T; F) is a net; mapping M: S → {0,1,2 … } into an identity (marking) of the net; the doublet (N, M) (i.e. the quadruplet (P, T; F, M)) is called an identification net (marked net);

definition 1.4 a network system (net system) is an identification net ∑ (P, T; F, M) and has the following transition occurrence rule (transition probability function):

1) for a transition T ∈ T, if

i.

ii, indicating that the transition t has an occurrence right (enabled) in the mark M, and marking as M [ t >;

2) if M [ t >, (fire) can occur in the mark M, and a new mark M '(denoted as M [ t > M') is obtained from the transition t occurring in the mark M

Concurrence of

Definitions 1.5 in the P/T system ∑ (P, T; F, K, W, M), if specified

The resulting system is called the basic network system (elementary net system);

definitions 1.6 ∑ ═ (B, E; F, c)₀) For an EN system, B represents a condition set, E represents an event set, E₁,e₂E belongs to the E, and c is an aspect of sigma; if it is not

1)c[e₁＞∧c[e₂＞

2)c[e₁＞c₁→c₁[e₂＞∧c[e₂＞c₂→c₂[e₁＞

Scale e₁And e₂Concurrent in the situation c, or e₁And e₂In scenario c, there is a further right to occur, denoted c [ { e [ ]₁,e₂}>；

Generally speaking, two events are said to be concurrent in a certain situation if both events have rights to occur in the situation and the occurrence of either event does not deprive the other;

type petri net

Definition 1.7 Type Petri nets (Type Petri nets, TPNs) are six-membered groups TPN ═ Type, P_KK, T, a, M), satisfies:

1)Type：Type＝(ty_1,ty₂,...,ty_n) A vector composed of types for tokens;

2)P_Kis a finite set of type libraries;

3) k is a type function and is defined on a type library;

4) t is a finite set of transition constituents;

5) a is a finite set of directed arcs connecting libraries to transitions or transitions to libraries;

6) m is a finite set of type identifiers for the net;

defining a 1.8 type function K on a type library set, wherein the type function K is used for specifying a token type which can be only accommodated in the type library;

1) when we mark the Type library as Type _ i, it means that the Type library can only accommodate token with Type i;

2) when we mark a Type library as Type _ i: ty1 ═ x, it means that the Type library can only accommodate tokens of Type i, and ty1 is x;

3) when we mark the Type library as ty1 ═ x, it means that the Type library can only accommodate tokens whose ty1 is x Type and no requirement is made on Type;

defining a 1.9 classification function CL on an output arc of the transition, and classifying all tokens in the transition input library by specified types;

1) the classification function expression If Type _ i indicates that when the Type of token in the front collection library of the transition is Type _ i, the transition is enabled, after the transition is triggered, the corresponding Type of token in the front collection library of the transition is consumed, the Type of token is generated in the output library corresponding to the output arc of the transition, and the number of the tokens is equal;

2) ty is a classification function expression of If Type i₁X represents when the Type of the pre-set library of the transition is Type _ i and ty₁When the number of the tokens is x, enabling the transition, and after the transition is triggered, consuming the tokens of the corresponding type in the front collection library of the transition, and generating the tokens of the type in the output library corresponding to the output arc of the transition in equal quantity;

3) classification function expression If ty₁X represents when the type ty is contained in the pre-set library of the transition₁When the number of the tokens is x, enabling the transition, and after the transition is triggered, consuming the tokens of the corresponding type in the front collection library of the transition, and generating the tokens of the type in the output library corresponding to the output arc of the transition in equal quantity;

defining a 1.10 transformation function TR on the transition set, and performing specified type transformation on all tokens in the transition input library;

1) the transfer function expression Trans (Type _ i) ═ Type _ j represents: the Type _ i has n Type components, the Type _ j has n +1 Type components, the first n Type components of the Type _ j correspond to the Type _ i, n is larger than or equal to 1, the Type _ i is called as a subtype of the Type _ j, and the Type _ j is called as a parent Type of the Type _ i; or the Type _ i has n +1 Type components, the Type _ j has n Type components, the first n Type components of the Type _ i correspond to the same Type _ j, n is greater than or equal to 1, the Type _ j is called as a subtype of the Type _ i, and the Type _ i is a parent Type of the Type _ j; when the Type of token in the pre-set library of the transition is Type _ i, enabling the transition, consuming the Type of token in the pre-set library of the transition after the transition is triggered, and generating a corresponding number of types of tokens in Type _ j in the post-set library of the transition;

2) the transfer function expression Trans (Type _1| Type _2| Type _3|. | >) Type _ j indicates: all types from Type _1 to Type _ n have n same Type components, Type _ j has n +1 Type components, the first n Type components of Type _ j are corresponding to the n Type components from Type _1 to Type _ n, n is not less than 1, and the types from Type _1 to Type _ n form a parallel relation; when the Type of the token from Type _1 to Type _ n is contained in the pre-set library of the transition, enabling the transition, after the transition is triggered, consuming the token from Type _1 to Type _ n in the pre-set library of the transition, and generating a corresponding number of tokens with Type _ j in the post-set library of the transition;

defining 1.11 constant enabling expressions via on a transition set, enabling the transition when an input base place of the transition is not empty and the type of a front set base place of the transition is the same as that of a rear set base place of the transition, wherein after the transition is triggered, all tokens in the input base place of the transition disappear and all tokens are generated in an output base place of the transition;

defining 1.12 counting function Ntoken (p), defined on the transition set, for limiting the triggering of the transition by calculating the total number of tokens in the library;

1)Ntoken(p_i)＝n₁,n₁is a depot p_iTotal number of all tokens in;

2)Ntoken(·t_i)＝n₂,Ntoken(t_i·)＝n₃,n₂and n₃Respectively denoted as transition t_iThe total number of tokens in the front and back libraries;

3)

sub(P_k) Is all P_kSet of subsets, p_KBelong to P_KP belongs to P_KAny subset of, n₄Representing the number of tokens of a certain subset of the type library;

4)

n₅representing the total number of tokens of a certain library subset p of the input library set of transitions t;

5)

n₆representing the total number of tokens of a certain library subset p of the output library set of the transition t;

6)If Ntoken(·t_i)＝n₂indicating only when the transition t is_iIn the preceding library of (2) is n₂Token time, t_iEnabling;

7)If

n₅the total number of tokens for a subset p of input libraries representing transitions t is n₅When, transition t is enabled;

defining a 1.13 time function TM (T, ctoken), wherein T belongs to T, the ctoken is an expression related to the type of token, and the TM is jointly defined on triggered transitions and the token which changes after the triggered transitions;

1) TM (t, ctoken) ═ m indicates that after the transition t triggers, the token satisfying the condition ctoken is consumed from the front-end repository of t, and is generated in the rear-end repository of t, and the consumed time is m;

2)TM(t₁,ctoken₁)＝m₁，TM(t₁,ctoken₂)＝m₂if m is₂>m₁Then TM (t)₁,ctoken₁|ctoken₂)＝m₂Indicating that the condition ctoken is satisfied after the transition t1 is triggered₁And token of ctoken2 are both from t₁The front library section of (1), the rear library section of (t 1)M is generated₂Maximum of the time consumed for two tokens;

3)TM(t₁,ctoken₁)＝m₁，TM(t₂,ctoken₂)＝m₂，…TM(t_n,ctoken_n)＝m_nif t is₁，t₂，…t_nIn a concurrent relationship c₀Denoted by c₀[{t₁，t₂，…t_n}>Timing the occurrence of multiple transitions in concurrency, selecting the longest time function value, TM (c)₀)＝max{TM(t_i，ctoken_i)|t_i∈{t₁，t₂，…t_n}}；

Defining 1.14 human function WF (T, ctoken), wherein T belongs to T, the ctoken is an expression related to the type of token, and the WF is jointly defined on triggered transitions and the tokens changed after the triggered transitions;

1) after WF (t, ctoken) ═ n indicates that after the transition t is triggered, the token satisfying the condition ctoken is consumed from the front-end repository of t, and is generated in the rear-end repository of t, and the consumed human resources are n;

2)WF(t₁,ctoken₁)＝n₁,WF(t₁,ctoken₂)＝n₂,...,WF(t₁,ctoken_i)＝n_iWF (t1, ctoken)₁|ctoken₂|...|ctoken_i)＝n₁+n₂+...+n_iDenotes a transition t₁After triggering, the condition ctoken is satisfied_1,ctoken_2,...,ctoken_iToken of are all from t₁Generated in the back library of t1, n₁+n₂+...+n_iA sum of human resources consumed for a plurality of tokens;

definition 1.15 transition initiation rules

1) When the front collection base of the transition is not empty and the transition has a via constant enabling expression, the transition is triggered if and only if the type of the front collection base of the transition is the same as that of the back collection base of the transition, the token in the front collection base of the transition is completely consumed, and the token of the type with the same quantity is generated in the back collection base of the transition;

2) when the Type of token in the front set library of the transition is Type _ i and the Type of classification function expression If _ i exists on the output arc of the transition, the transition is triggered If and only If the Type of the back set library corresponding to the output arc is Type _ i, the token of the Type of Type _ i in the front set library of the transition is completely consumed, and the same number of tokens of the Type are generated in the back set library corresponding to the output arc;

3) when the front collection library of the transition is not empty and the output arc of the transition is provided with a classification function expression If Type _ i: ty₁When x is obtained, the transition is triggered if and only if the Type of the front collection library of the transition and the Type of the rear collection library corresponding to the output arc are both Type _ i, the Type of the front collection library of the transition is Type _ i, and ty is₁Generating the same number of tokens of the type in a postlibrary corresponding to the output arc for the total consumption of the tokens of x;

4) type ty contained in the pre-library when it is migrated₁The token of x and the classification function expression If ty on the output arc of the transition₁When x, the transition enables the ty of the type of the back library to which the output arc corresponds and only if₁X, trigger a transition, type ty in the pool before the transition₁Generating the same number of tokens of the type in a postlibrary corresponding to the output arc for the total consumption of the tokens of x;

5) when the Type of a front collection base of the transition is Type _ i and the Type of a back collection base of the transition is Type _ j, enabling the transition to be triggered if and only if the Type _ i is a subtype of the Type _ j, the front collection base of the transition is not empty and the transition has a transition function expression Trans (Type _ i) ═ Type _ j, and generating the same number of Type _ j types of tokens in the back collection base of the transition, wherein the Type of the front collection base of the transition is Type _ i;

6) when the Type of the front collection library of the transition is Type _ i and the Type of the back collection library of the transition is Type _ j, enabling the transition to be triggered if and only if the Type _ i is the parent Type of the Type _ j, the front collection library of the transition is not empty and the transition has a transition function expression Trans (Type _ i) ═ Type _ j, and generating the same number of Type _ j types of tokens in the back collection library of the transition, wherein the Type of the front collection library of the transition is Type _ i;

7) when the types of the former collection libraries of the transition are Type _1, Type _2, and Type _ n, and the types of the later collection libraries of the transition are Type _ j, the transition enables that when and only when the types of the former collection libraries of the transition are Type _ j, the Type _1, Type _2, and Type _ n are all the parent types of Type _ j, the former collection libraries of the transition are not empty, and the transition is provided with a transition function expression Trans (Type _1| Type _2| Type _3| Type.. ere.. | Type _ n) | Type _ j), the transition is triggered, the types of the former collection libraries of the transition are Type _1, Type _2,. the Type _ n are all consumed, and the same number of types of Type _ j are generated in the later collection libraries of the transition;

8) when the transition has the counting function expression If Ntoken (& t)_i)＝n₂When, the transition enables the transition if and only if t_iIn the preceding library of (2) is n₂Token, trigger transition t_iThe tokens in the pre-transition library are all consumed, and the tokens of the type with the same quantity are generated in the post-transition library;

9) when there is a counting function expression If on the transition

When the transition enables the total number of tokens p in a subset p of the input library set of the transition t if and only if n is the total number of tokens₅Triggering transition, wherein the tokens in the front library of the transition are all consumed, and the tokens of the type with the same quantity are generated in the rear library of the transition;

defining 1.16 type petri net states (tps), in which a quadruple tps ═ (m, enable (m), ttm (m), twf (m)) is a type petri net state, wherein:

1) m is current type identification and represents the type of each token in each library, and the initial type identification is m₀；

2) enable (m) is the set of all enabled transitions under type identifier m;

3) TTM (m) is the time resource consumed under the current type identifier m, and represents the time resource from the initial state m₀Total time resources consumed to the current state, TTM (m)₀) When the time resource consumed in the initial state is 0;

4)TWF(m) is the human resources consumed under the current type identifier m, representing m from the initial state₀Total human resources consumed to the current state, TWF (m)₀) When the human resources consumed in the initial state are 0;

defining 1.17 type petri net state transition rules, in the type petri net, t ∈ enable (m), after transition t triggers, m [ t > m ', the type petri net state tps becomes tps' ═ m ', enable (m'), TTM (m '), TWF (m')), wherein:

1) m ' represents a new type identifier m ' obtained by the type identifier m ' under the triggering of the transition t;

2) enable (m ') is a set of all enabled transitions under type identifier m';

3) TTM (m ') is a time resource cumulative consumption value of the type identifier m', and is TTM (m ') + TM (m');

4) TWF (m ') is a cumulative consumption value of human resources under the type identifier m', and TWF (m ') + TWF (m');

defining 1.18 type petri net state graph (tpsg), in which a triplet tpsg ═ tps, ca, ct is a type petri net state transition graph, where:

1) tps is a non-empty finite set of all types of petri net states for a type petri net;

2) ca is a non-empty finite set of directed arcs;

3) ct is the set of transitions that cause a change in the state of the type petri net.

Preferably, in step 4, the specific steps of performing the state transition analysis on the flow of the distribution system scheme a are as follows:

step 4.1: application case A model initial state tps₀The values of the following elements are:

m₀＝(((1,A,a1,x),(2,B,b1,x),(3,A,a2,y),(4,C,c1,z),(5,E,e1,y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₀)＝{T1,T2}，TTM(m₀)＝0，TWF(m₀)＝0；

step 4.2: set enable (m) according to enable transitions₀) Selecting a trigger transition T1 or T2; if selected, theTriggering a transition T2, and executing a step 4.3; if the trigger transition T1 is selected, executing the step 4.4;

step 4.3: transition T2 trigger to reach state tps₂The values of the elements are:

m₂＝(0,0,((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₂)＝{T4,T5,T6,T8}，TTM(m₂)＝0.1，TWF(m₂)＝0；

selecting the transition with the minimum number in the enabled transition set for triggering in sequence, and specifically comprising the following steps:

step 4.3.1: selecting transition T4 trigger, reaching state tps4, the values of the elements being:

m₄＝(0,0,0,(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),0,0,0,0,0,0,0,0,0,0,0)，enable(m₄)＝{T5,T6,T8,T9}，TTM(m₄)＝1.1，TWF(m₄)＝2；

step 4.3.2: selecting transition T5 trigger, reaching state tps5, the values of the elements being:

m₅＝(0,0,0,0,(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),0,0,0,0,0,0,0,0,0,0)，enable(m₅)＝{T6,T8,T9,T10}，TTM(m₅)＝1.1，TWF(m₅)＝3；

step 4.3.3: selecting transition T6 trigger, reaching state tps6, the values of the elements being:

m₆＝(0,0,0,0,0,0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,0,0,0,0,0,0,0,0)，enable(m₆)＝{T8,T9,T10,T11}，TTM(m₆)＝1.1，TWF(m₆)＝4；

step 4.3.4: selecting transition T8 trigger, reaching state tps7, the values of the elements being:

m₇＝(0,0,0,0,0,0,0,((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),0,0,0,0,0,0,0)，enable(m₇)＝{T9,T10,T11,T13}，TTM(m₇)＝1.1，TWF(m₇)＝5；

step 4.3.5: selecting transition T9 trigger, reaching state tps8, the values of the elements being:

m₈＝(0,0,0,0,0,0,0,0,(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),(1,A,a1,x),(3,A,a2,y),0,0,0,0,0)，enable(m₈)＝{T10,T11,T13,T14,T15}，TTM(m₈)＝3.1，TWF(m₈)＝6；

step 4.3.6: selecting transition T10 trigger, reaching state tps9, the values of the elements being:

m₉＝(0,0,0,0,0,0,0,0,0,(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(2,B,b1,x)),(3,A,a2,y),0,0,0,0,0)，enable(m₉)＝{T11,T13,T14,T15}，TTM(m₉)＝3.1，TWF(m₉＝7；

step 4.3.7: selecting transition T11 trigger, reaching state tps10, the values of the elements being:

m₁₀＝(0,0,0,0,0,0,0,0,0,0,0,(5,E,e1,y),((1,A,a1,x),(2,B,b1,x)),(3,A,a2,y),(4,C,c1,z),0,0,0,0)，enable(m₁₀)＝{T13,T14,T15,T16}，TTM(m₁₀)＝3.1，TWF(m₁₀)＝8；

step 4.3.8: selecting transition T13 trigger, reaching state tps11, the values of the elements being:

m₁₁＝(0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),0,0,0,0)，enable(m₁₁)＝{T14,T15,T16}，TTM(m₁₁)＝3.1，TWF(m₁₁)＝9；

step 4.3.9: selecting transition T14 trigger, reaching state tps12, the values of the elements being:

m₁₂＝(0,0,0,0,0,0,0,0,0,0,0,0,0,((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),0,0,0)，enable(m₁₂)＝{T15,T16}，TTM(m₁₂)＝4.1，TWF(m₁₂)＝9；

step 4.3.10: selecting transition T15 trigger, reaching state tps13, the values of the elements being:

m₁₃＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),0,0)，enable(m₁₃)＝{T16}，TTM(m₁₃)＝4.1，TWF(m₁₃)＝9；

step 4.3.11: transition T16 triggers a state tps14 to be reached, the values of the elements being:

m₁₄＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),0)，enable(m₁₄＝{T17}，TTM(m₁₄)＝4.1，TWF(m₁₄)＝9；

step 4.3.12: transition T17 triggers a state tps15 to be reached, the values of the elements being:

m₁₅＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x),(3,A,a2,y),(5,E,e1,y),(4,C,c1,z))，

TTM(m₁₅)＝4.2，TWF(m₁₅)＝9；

enabling the transition set to be empty, and completing the analysis of the path;

step 4.4: transition T1 trigger to reach identifier m₁；

m₁(0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, transition T3 enables; triggering the transition T3 to reach the state mark m₃；

m₃(0,0,0,0,0,0,0,0,0,0,0,0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y))), no enable transition, and the path analysis is completed;

the specific steps for performing state transition analysis on the process of the application case B are as follows:

step 4.5: the values of the elements under tps0 in the initial state of the application case B model are:

m₀＝(((1,A,a1,x),(2,B,b1,x),(3,A,a2,y),(4,C,c1,z),(5,E,e1,y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₀)＝{T1,T2}，TTM(m₀)＝0，TWF(m₀)＝0；

step 4.6: set enable (m) according to enable transitions₀) Selecting a trigger transition T1 or T2; if the trigger transition T2 is selected, executing the step 4.7; if the trigger transition T1 is selected, executing the step 4.8;

step 4.7: transition T2 trigger to reach state tps₂The values of the elements are:

m₂＝(0,0,((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₂)＝{T4,T5,T6,T8}，TTM(m₂)＝0.1，TWF(m₂)＝0；

step 4.7.1: selecting transition T4 trigger, reaching state tps4, the values of the elements being:

m₄＝(0,0,0,(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₄)＝{T5,T6,T8}，TTM(m₄)＝1.1，TWF(m₄)＝2；

step 4.7.2: selecting transition T5 trigger, reaching state tps5, the values of the elements being:

m₅＝(0,0,0,0,(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),0,0,0,0,0,0,0,0,0,0,0,-,0,0)，enable(m₅)＝{T6,T8}，TTM(m₅)＝1.1，TWF(m₅)＝3；

step 4.7.3: selecting transition T6 trigger, reaching state tps6, the value of each element:

m₆＝(0,0,0,0,0,0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,0,0,0,0,0,0,0,0,0,0,0)，enable(m₆)＝{T8}，TTM(m₆)＝1.1，TWF(m₆＝4；

step 4.7.4: selecting transition T8 trigger, reaching state tps7, the values of the elements being:

m₇＝(0,0,0,0,0,0,0,((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),(4,C,c1,z),0,(5,E,e1,y),0,0,0,0,0,0,0,0,0,0)，enable(m₇)＝{T9}，TTM(m₇)＝1.1，TWF(m₇)＝5；

step 4.7.5: selecting transition T9 trigger, reaching state tps8, the values of the elements being:

m₈＝(0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),0,0,0,0,0,0,0)，enable(m₈)＝{T10,T11,T12}，TTM(m₈)＝1.2，TWF(m₈)＝5；

step 4.7.6: selecting transition T10 trigger, reaching state tps9, the values of the elements being:

m₉＝(0,0,0,0,0,0,0,0,0,0,0,0,0,((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),0,0,0,0,0,0)，enable(m₉)＝{T11,T12,T13}，TTM(m₉)＝2.2，TWF(m₉)＝6；

step 4.7.7: selecting transition T11 trigger, reaching state tps10, the values of the elements being:

m₁₀＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),0,0,0,0,0)，enable(m₁₀)＝{T12,T13,T14}，TTM(m₁₀)＝2.2，TWF(m₁₀)＝7；

step 4.7.8: selecting transition T12 trigger, reaching state tps11, the values of the elements being:

m₁₁＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),0,0,0,0)，enable(m₁₁)＝{T13,T14,T15}，TTM(m₁₁)＝2.2，TWF(m₁₁)＝8；

step 4.7.9: selecting transition T13 trigger, reaching state tps12, the values of the elements being:

m₁₂＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),0,0,0)，enable(m₁₂)＝{T14,T15}，TTM(m₁₂)＝3.2，TWF(m₁₂)＝8；

step 4.7.10: selecting transition T14 trigger, reaching state tps13, the values of the elements being:

m₁₃＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,(4,C,c1,z),((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),0,0)，enable(m₁₃)＝{T15}，TTM(m₁₃)＝3.2，TWF(m₁₃)＝8；

step 4.7.11: selecting transition T15 trigger, reaching state tps14, the values of the elements being:

m₁₄＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x)),((3,A,a2,y),(5,E,e1,y)),(4,C,c1,z),0)，enable(m₁₄＝{T16}，TTM(m₁₄)＝3.2，TWF(m₁₄)＝8；

step 4.7.12: selecting transition T16 trigger, reaching state tps15, the values of the elements being:

m₁₅＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(2,B,b1,x),(3,A,a2,y),(5,E,e1,y),(4,C,c1,z)))，

TTM(m₁₅)＝3.3，TWF(m₁₅)＝8；

step 4.8: transition T1 trigger to reach identifier m₁；

m₁(0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0) transition T3; triggering the transition T3 to reach the mark m₃；

m₃No enable transition, and the path analysis is complete (0,0,0,0,0,0,0,0,0,0,0, ((1, a1, x), (2, B1, x), (3, a2, y), (5, E1, y), (4, C1, z))).

The invention has the following beneficial technical effects:

1) when the problem related to classification is solved, the method has good universality, and the model does not need to be subjected to large structural change or multi-range content modification according to different conditions every time.

2) Compared with the common petri net, the type petri net defines the type of the token, enriches the type of the token, has stronger expressive force and reduces the scale of the net system.

3) The complexity of modeling is reduced to a certain extent, and the reusability of the model is improved.

4) The net model looks simpler, clearer and easier to understand.

Drawings

Fig. 1 is a schematic diagram of a type a petri net model of a distribution system scheme.

Fig. 2 is a schematic diagram of a type B petri net model of a distribution system scheme.

Fig. 3 is a distribution system scheme a distribution process conversion diagram.

Fig. 4 is a distribution process conversion diagram of the distribution system scheme B.

Detailed Description

The invention is described in further detail below with reference to the following figures and detailed description:

1. basic knowledge

1.1 delivery System

With the continuous development of information technology, the life style of people is changed, the distribution system is operated due to the acceleration of the life rhythm, and the distribution of commodities is a more convenient, efficient, energy-saving and time-saving mode.

The distribution is a terminal link of commodity circulation, and the distribution system is an infrastructure and an organizer for commodity distribution. Many production enterprises and third-party logistics enterprises with strength establish distribution systems according to their own characteristics to distribute their products or operated commodities, so that the distribution systems are decisive for the development of enterprises.

The intellectualization of the distribution is based on the informatization of the distribution, and how to realize higher efficiency, lower cost, shorter distance and minimum time is the goal pursued by people.

1.2 basic introduction to petri nets

The definition for the petri nets is as follows:

1.2.1 basic concept

1)

2)

3)

definition 1.2 let N ═ (P, T; F) be a net, remembering that for x ∈ PU! T

^·x＝{y|y∈P∪T∧(y,x)∈F}

x^·＝{y|y∈P∪T∧(y,x)∈F}

Balance^·x is a preceding or input set of x, x^·The x postset and the output set.

Definition 1.3N ═ (P, T; F) is a net. S → {0,1,2 … } is mapped into an identity (marking) of the net. The doublet (N, M) (i.e., the quadruplet (P, T; F, M)) is called a marked net.

1) for a transition T ∈ T, if

i.

And ii, indicating that the transition t has an occurrence right (enabled) in the identifier M and is marked as M [ t >).

1.2.2 concurrence

Definitions 1.5 in the P/T system ∑ (P, T; F, K, W, M), if specified

The resulting system is called the elementary network system (elementary net system).

Definitions 1.6 ∑ ═ (B, E; F, c)₀) For an EN system, B represents a condition set, E represents an event set, E₁,e₂E, c is an aspect of Σ. If it is not

1)c[e₁＞∧c[e₂＞

2)c[e₁＞c₁→c₁[e₂＞∧c[e₂＞c₂→c₂[e₁＞

Scale e₁And e₂Concurrent in the situation c, or e₁And e₂In scenario c, there is a further right to occur, denoted c [ { e [ ]₁,e₂}>。

Generally, two events are said to be concurrent in a situation if both events have rights to occur in the situation and the occurrence of either event does not deprive the other.

1.3 type petri nets

1)Type：Type＝(ty_1,ty₂,...,ty_n) A vector composed of types for tokens;

2)P_Kis a finite set of type libraries;

3) k is a type function and is defined on a type library;

4) t is a finite set of transition constituents;

6) m is a finite set of type identifiers for the net.

Definition 1.8 type function K is defined on a set of type libraries for specifying the types of tokens that can only be accommodated in the type libraries.

1) When we mark a Type library as Type _ i, it means that the Type library can only accommodate tokens of Type i.

2) When we mark a Type library as Type _ i: ty1 ═ x, it means that the Type library can only accommodate tokens of Type i, and ty1 is x.

3) When we mark a Type library as ty1 ═ x, it means that the Type library can only accommodate tokens whose ty1 is the x Type, but does not require Type.

Definition 1.9 a classification function CL is defined on the output arc of the transition for classifying all tokens in the input library of the transition with a specified type.

1) The classification function expression If Type _ i indicates that when the Type of token in the front collection library of the transition is Type _ i, the transition is enabled, after the transition is triggered, the token of the corresponding Type in the front collection library of the transition is consumed, the token of the Type is generated in the output library corresponding to the output arc of the transition, and the number of the tokens is equal.

2) Ty is a classification function expression of If Type i₁X represents when the Type of the pre-set library of the transition is Type _ i and ty₁And when the number of the output libraries is x tokens, the transition is enabled, after the transition is triggered, the tokens of the corresponding type in the front set library of the transition are consumed, and the tokens of the type are generated in the output library corresponding to the output arc of the transition, and the number of the tokens is equal.

3) Classification function expression If ty₁X represents when the type ty is contained in the pre-set library of the transition₁And when the number of the output libraries is x tokens, the transition is enabled, after the transition is triggered, the tokens of the corresponding type in the front set library of the transition are consumed, and the tokens of the type are generated in the output library corresponding to the output arc of the transition, and the number of the tokens is equal.

Definition 1.10 transformation function TR is defined on the set of transitions for inputting all tokens in the library of transitions into a specified type of transformation.

1) The transfer function expression Trans (Type _ i) ═ Type _ j represents: the Type _ i has n Type components, the Type _ j has n +1 Type components, the first n Type components of the Type _ j correspond to the Type _ i, n is larger than or equal to 1, the Type _ i is called as a subtype of the Type _ j, and the Type _ j is called as a parent Type of the Type _ i; or Type _ i has n +1 Type components, Type _ j has n Type components, the first n Type components of Type _ i correspond to Type _ j, n is equal to or greater than 1, Type _ j is called as a subtype of Type _ i, and Type _ i is a parent Type of Type _ j. When the Type of token in the front library of the transition is Type _ i, the transition is enabled, after the transition is triggered, the Type of token in the front library of the transition is Type _ i is consumed, and the corresponding number of tokens with the Type of Type _ j are generated in the back library of the transition.

2) The transfer function expression Trans (Type _1| Type _2| Type _3|. | >) Type _ j indicates: all types from Type _1 to Type _ n have n identical Type components, Type _ j has n +1 Type components, the first n Type components of Type _ j correspond to the n Type components from Type _1 to Type _ n, n is not less than 1, and the types from Type _1 to Type _ n form a parallel relationship. When the Type of the token from Type _1 to Type _ n is contained in the pre-set library of the transition, the transition is enabled, after the transition is triggered, the token from Type _1 to Type _ n in the pre-set library of the transition is consumed, and the token with the Type of Type _ j is generated in the post-transition set library correspondingly.

Defining 1.11 constant enabling expressions via on the transition set, when the input base of the transition is not empty and the type of the front base of the transition is the same as that of the back base of the transition, enabling the transition, after the transition is triggered, all tokens in the input base disappear, and all tokens are generated in the output base.

Defining 1.12 counting function Ntoken (p), defining on the set of transitions, for limiting the triggering of the transition by calculating the total number of tokens in the library.

1)Ntoken(p_i)＝n₁,n₁Is a depot p_iTotal number of all tokens in;

3)

4)

5)

7)If

a1.13 time function TM (T, ctoken) is defined, T epsilon T, and ctoken is an expression related to the type of token, and TM is jointly defined on triggered transitions and the token of the change after the triggered transitions.

2)TM(t₁,ctoken₁)＝m₁，TM(t₁,ctoken₂)＝m₂if m is₂>m₁Then TM (t)₁,ctoken₁|ctoken₂)＝m₂Indicating that the condition ctoken is satisfied after the transition t1 is triggered₁And token of ctoken2 are both from t₁Front set ofConsumption in Bank, generated in the postpool of t1, m₂Maximum of the time consumed for two tokens;

3)TM(t₁,ctoken₁)＝m₁，TM(t₂,ctoken₂)＝m₂，…TM(t_n,ctoken_n)＝m_nif t is₁，t₂，…t_nIn a concurrent relationship c₀Denoted by c₀[{t₁，t₂，…t_n}>Timing the occurrence of multiple transitions in concurrency, selecting the longest time function value, TM (c)₀)＝max{TM(t_i，ctoken_i)|t_i∈{t₁，t₂，…t_n}}。

Defining 1.14 human function WF (T, ctoken), T epsilon T, wherein the ctoken is an expression related to the type of token, and the WF is jointly defined on the triggered transition and the token of the change after the triggered transition.

2)WF(t₁,ctoken₁)＝n₁,WF(t₁,ctoken₂)＝n₂,...,WF(t₁,ctoken_i)＝n_iWF (t1, ctoken)₁|ctoken₂|...|ctoken_i)＝n₁+n₂+...+n_iDenotes a transition t₁After triggering, the condition ctoken is satisfied_1,ctoken_2,...,ctoken_iToken of are all from t₁Generated in the back library of t1, n₁+n₂+...+n_iThe sum of the human resources consumed for the plurality of tokens.

Definition 1.15 transition initiation rules

9) when there is a counting function expression If on the transition

1.3.2 graphical representation of type petri nets

1.3.3 analysis method of type petri nets

2) enable (m) is the set of all enabled transitions under type identifier m;

4) TWF (m) is the human resources consumed under the current type identifier m, representing m from the initial state₀Total human resources consumed to the current state, TWF (m)₀) When the human resources consumed in the initial state are 0, the human resources consumed in the initial state are 0.

2) enable (m ') is a set of all enabled transitions under type identifier m';

4) TWF (m ') is a cumulative consumption value of human resources under the type identifier m', and TWF (m ') + TWF (m').

2) ca is a non-empty finite set of directed arcs;

1.3.4 modeling advantages of type petri nets

4) The net model looks simpler, clearer and easier to understand.

2. Flow analysis for distribution system

Use of type 2.1 petri nets in distribution systems

2.1.1 distribution System flow

Distribution scheme A flow is order requirement → { order processing } → making → distribution → { confirmation delivery } → order distribution completion

And (4) a distribution scheme B flow: order requirement → { order processing } → production → { order classification by address } → delivery → { confirmation delivery } → order delivery completion → order delivery

2.1.2 distribution System flow modeling

1. Distribution system scheme A process modeling

Table 3-1 schematic of the meaning of elements shown in type a petri net model according to the delivery system scenario of fig. 1

1. Distribution system scheme B process modeling

Table 3-2 element meaning schematic shown in type B petri net model according to the distribution system scenario of fig. 2

2.2 type petri nets model Performance analysis

Table 3-3 scheme a model given time parameter table

Table 3-4 scheme a model given human parameters table

Tables 3-5 schedule B model given time parameter Table

Table 3-6 scheme B model given human parameters table

2.2.1 delivery Process transition analysis

Because a plurality of transitions in a concurrent state exist in the process, a representative path is selected for analysis.

According to the distribution system flow scheme A type petri net model in the figure 1, the distribution process conversion analysis is carried out according to the definition 2.10 and the definition 2.11, and the corresponding distribution process conversion state is calculated, wherein the specific process is as follows:

1) tps at model initial state₀The values of the following elements are:

2) set enable (m) according to enable transitions₀) Selecting a trigger transition T1 or T2;

selecting transition T₂Triggered to reach state tps₂The values of the elements are:

to avoid process redundancy, the least numbered transition trigger is selected in the enabled transition set each time

a. Selecting transition T4 trigger, reaching state tps4, the values of the elements being:

b. selecting transition T5 trigger, reaching state tps5, the values of the elements being:

m₅＝(0,0,0,0,(4,C,c1,z),0,(5,E,e1,y),((1,A,a1,x),(3,A,a2,y)),(2,B,b1,x),,0,0,0,0,0,0,0,0,0,0)，enable(m₅)＝{T6,T8,T9,T10}，TTM(m₅)＝1.1，TWF(m₅)＝3；

c. selecting transition T6 trigger, reaching state tps6, the values of the elements being:

d. selecting transition T8 trigger, reaching state tps7, the values of the elements being:

e. selecting transition T9 trigger, reaching state tps8, the values of the elements being:

f. selecting transition T10 trigger, reaching state tps9, the values of the elements being:

g. selecting transition T11 trigger, reaching state tps10, the values of the elements being:

h. selecting transition T13 trigger, reaching state tps11, the values of the elements being:

i. selecting transition T14 trigger, reaching state tps12, the values of the elements being:

j. selecting transition T15 trigger, reaching state tps13, the values of the elements being:

k. transition T16 triggers a state tps14 to be reached, the values of the elements being:

transition T17 triggers, reaching state tps15, the values of the elements being:

TTM(m₁₅)＝4.2，TWF(m₁₅)＝9。

enabling the transition set to be empty, and completing the analysis of the path.

Selecting transition T1 trigger to reach mark m₁，

m₁(0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, transition T3 enables; triggering the transition T3 to reach the state mark m₃，

m₃No enable transition, and the present path analysis is complete (0,0,0,0,0,0,0,0,0,0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y))).

According to the distribution system flow scheme A type petri net model in FIG. 1, and definition 2.12, a distribution process conversion graph is constructed, as shown in FIG. 3 (the construction of the graph only shows the case that only one transition is caused at a time).

According to the distribution system flow scheme B type petri net model in FIG. 2, and the definition 2.10 and the definition 2.11, the distribution process conversion analysis is performed, and the corresponding distribution process conversion state is calculated, wherein the specific process is as follows:

1) the values of the elements under tps0 in the initial state of the model are:

2) as can be seen by the set of enabled transitions, we can now choose to trigger the transition T1 or T2.

Selecting transition T2 trigger, reaching state tps2, the values of each element being:

c. selecting transition T6 trigger, reaching state tps6, the value of each element:

h. selecting transition T12 trigger, reaching state tps11, the values of the elements being:

i. selecting transition T13 trigger, reaching state tps12, the values of the elements being:

j. selecting transition T14 trigger, reaching state tps13, the values of the elements being:

k. selecting transition T15 trigger, reaching state tps14, the values of the elements being:

select transition T16 trigger to reach state tps15, the values of the elements being:

TTM(m₁₅)＝3.3，TWF(m₁₅)＝8；

Selecting transition T1 trigger to reach mark m₁，

m₁(0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0) transition T3; triggering the transition T3 to reach the mark m₃，

According to the distribution system flow scheme B type petri net model in FIG. 2, and defining 2.12 to perform distribution process conversion analysis, a distribution process conversion diagram is constructed, as shown in FIG. 4 (the construction of the diagram only shows the case that only one transition is caused at a time).

2.2.2 time resource consumption analysis

Table 3-5 scheme a time resource consumption table 3-6 scheme B type time resource consumption table

Scheme a has a final tag time consumption value TTM (m12) of 4.2> scheme B has a final tag time consumption value TTM (m13) of 3.3, so that, from a time point of view, scheme B takes less time than scheme a takes to deliver the same order, and scheme B is superior to scheme a.

2.2.3 human resource consumption analysis

Table 3-7 scheme a human resources consumption table

Triggering transition sequences	TWF(m)
		T2	0
T4	2
		T5	3
T6	4
		T8	5
T9	6
		T10	7
T11	8
		T13	9
T14	9
		T15	9
T16	9
		T17	9

Table 3-8 scheme B human resources consumption table

Through analysis, the method has the following steps:

the final identified human consumption value TWF (m12) ═ 9> the final identified human consumption value TWF (m13) ═ 8 for solution B, so from a human perspective analysis, solution B consumes less human labor than solution a does to deliver the same order, and solution B is superior to solution a.

3. Summary and prospect

3.1 summary of

The concept and the transition initiation rule and the analysis method of the type petri net are provided, a distribution system model based on the type petri net is established, a state diagram of the system model is established, time resource consumption and manpower resource consumption of two schemes are analyzed, and a better solution is found out.

3.2 further work

1. The type petri net can be combined with the ideas of other advanced nets to improve and perfect other attributes of the net system in different aspects, such as a time petri net and a logic petri net.

2. The performance of the distribution system can be analyzed from more angles, such as cost consumption, distribution balance degree among different addresses and the like.

3. The type petri net can be applied to other systems for modeling and analyzing, and the characteristic of universality of the type petri net is verified.

It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims

1. A process analysis method based on a type petri net is characterized in that: the method comprises the following steps:

step 1: analyzing a specific flow of a distribution system;

the distribution system comprises a distribution system scheme A and a distribution system scheme B; wherein:

flow of the distribution system scheme B: order demand → { order processing } → production → { sort order by address } → delivery → { confirm delivery } → delivery completion of the order;

the theory of type petri nets is as follows:

1)

2)

3)

definition 1.2 let N ═ (P, T; F) be a net, remembering that for x ∈ PU! T

·x＝{y|y∈P∪T∧(y,x)∈F}；

x·＝{y|y∈P∪T∧(y,x)∈F}；

X is called as an x front set or an input set, and x is called as an x rear set and an output set;

1) for a transition T ∈ T, if

i.

Concurrence of

Definitions 1.5 in the P/T system ∑ (P, T; F, K, W, M), if specified

1)c[e₁＞∧c[e₂＞

2)c[e₁＞c₁→c₁[e₂＞∧c[e₂＞c₂→c₂[e₁＞

type petri net

1)Type：Type＝(ty_1,ty₂,...,ty_n) A vector composed of types for tokens;

2)P_Kis a finite set of type libraries;

3) k is a type function and is defined on a type library;

4) t is a finite set of transition constituents;

6) m is a finite set of type identifiers for the net;

3) classification function expression If ty₁X represents when the type ty is contained in the pre-set library of the transition₁When the token of x is, the transition is enabled, and the trigger is changedAfter the migration, the token of the corresponding type in the front collection library of the migration is consumed, the token of the type is generated in the output library corresponding to the output arc of the migration, and the number of the token is equal;

1)Ntoken(p_i)＝n₁,n₁is a depot p_iTotal number of all tokens in;

3)

4)

5)

7)

2)TM(t₁,ctoken₁)＝m₁，TM(t₁,ctoken₂)＝m₂if m is₂>m₁Then TM (t)₁,ctoken₁|ctoken₂)＝m₂Indicating that the condition ctoken is satisfied after the transition t1 is triggered₁And token of ctoken2 are both from t₁Generated in the back library of t1, m₂Maximum of the time consumed for two tokens;

2)WF(t₁,ctoken₁)＝n₁,WF(t₁,ctoken₂)＝n₂,...,WF(t₁,ctoken_i)＝n_iWF (t1, ctoken)₁|ctoken₂|...|ctoken_i)＝n₁+n₂+...+n_iDenotes a transition t₁After triggering, the condition ctoken is satisfied₁,ctoken₂,...,ctoken_iToken of are all from t₁Generated in the back library of t1, n₁+n₂+...+n_iA sum of human resources consumed for a plurality of tokens;

definition 1.15 transition initiation rules

9) when there is a counting function expression on the transition

1) m is the identification of the current type,representing the type of each token in each library, and the initial type is marked as m₀；

2) enable (m) is the set of all enabled transitions under type identifier m;

4) TWF (m) is the human resources consumed under the current type identifier m, representing m from the initial state₀Total human resources consumed to the current state, TWF (m)₀) When the human resources consumed in the initial state are 0;

2) enable (m ') is a set of all enabled transitions under type identifier m';

2) ca is a non-empty finite set of directed arcs;

ct is the set of transitions that cause the state of the type petri net to change;

2. The type petri net based process analysis method of claim 1, wherein: in step 4, the specific steps of performing state transition analysis on the flow of the distribution system scheme a are as follows:

step 4.2: set enable (m) according to enable transitions₀) Selecting a trigger transition T1 or T2; if the trigger transition T2 is selected, executing the step 4.3; if the trigger transition T1 is selected, executing the step 4.4;

TTM(m₁₅)＝4.2，TWF(m₁₅)＝9；

step 4.4: transition T1 trigger to reach identifier m₁；

m₁＝(0,((1,A,a1,x),(3,A,a2,y),(2,B,b1,x),(4,C,c1,z),(5,E,e1,y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)，

Transition T3 is enabled; triggering the transition T3 to reach the state mark m₃；

m₃＝(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,((1,A,a1,x),(3,A,a2,y),(2,B,b1,x),(4,C,c1,z),(5,E,e1,y)))，

No enabling transition exists, and the path analysis is finished;

TTM(m₁₅)＝3.3，TWF(m₁₅)＝8；

step 4.8: transition T1 trigger to reach identifier m₁；

m₁(0, ((1, a1, x), (3, a2, y), (2, B1, x), (4, C1, z), (5, E1, y)),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) transition T3 enable(ii) a Triggering the transition T3 to reach the mark m₃；