CN106257470A - In battle-damaged equipment queuing system, computational methods and the system of element number managed by upper finishing - Google Patents

Abstract

The present invention discloses computational methods and the system of upper finishing reason element number in a kind of battle-damaged equipment queuing system, it is possible in calculating battle-damaged equipment queuing system, upper finishing reason element number most preferably allocates.Method includes: S1, c the upper finishing reason unit calculating crawler belt break upper finishing reason during waiting repair averagely equip quantity, wherein, c is integer, and initial value is 1, and each on, to manage the average service rate of unit the most equal for finishing；S2, judge that whether the average equipment quantity of the waiting repair that latest computed obtains is less than the first numerical value, if the average equipment quantity of the waiting repair that latest computed obtains is less than described first numerical value, then the value of c is defined as in target finishing reason element number, otherwise, update the value of c be initial value with 1 and, and return step S1.

Description

In battle-damaged equipment queuing system, computational methods and the system of element number managed by upper finishing

Technical field

The present invention relates to equipment repahs technical field, be specifically related to upper finishing reason unit in a kind of battle-damaged equipment queuing system The computational methods of quantity and system.

Background technology

The most at ordinary times during equipment scheduled repair, or during War Equipment repairing, time and efficiency are had Certain requirement.In especially wartime, owing in Campaign Process, change between attack and defend is frequent, operation is fast, and the persistent period is shorter, permissible The time implementing Maintenance for Equipment is shorter, thus has higher requirement the ageing of equipment repair.Therefore in wartime The target of equipment Safeguard mechanism is reparation battle-damaged equipment as much as possible so that it is go into battle rapidly.Battle-damaged equipment wants to Entering repair organ and can be instantly available repairing, and the time stayed in systems is the shortest more good, this just requires to put into maintenance The number some to be reached of the upper finishing reason unit ensured, has higher efficiency of service, reduces the time of maintenance support. From equipment Safeguard mechanism one side consider, increase repair element number, can reach improve maintenance ability purpose, but this Sample can increase support organization battlefield tissue undoubtedly, command, manages and the difficulty of the work such as safety guard, and when repair organ is empty Idle can cause again the waste of equipment Support Resource.Therefore the quantity repairing unit is increased to reach to improve Maintenance for Equipment Efficiency is also conditional on.How to calculate the optimal encoding of upper finishing reason element number in battle-damaged equipment queuing system to be made into as one Problem demanding prompt solution.

Summary of the invention

It is an object of the invention to, it is provided that the computational methods of upper finishing reason element number in a kind of battle-damaged equipment queuing system And system, it is possible to calculate upper finishing in battle-damaged equipment queuing system and manage most preferably allocating of element number.

For this purpose, on the one hand, the present invention proposes the meter of upper finishing reason element number in a kind of battle-damaged equipment queuing system Calculation method, including:

S1, c the upper finishing reason unit calculating crawler belt break upper finishing reason during waiting repair averagely equip number Amount, wherein, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

S2, judge the average equipment quantity of the waiting repair that latest computed obtains whether less than the first numerical value, if up-to-date meter The value of c less than described first numerical value, then is defined as in target filling repair order by the average equipment quantity of the waiting repair obtained Unit's quantity, otherwise, update the value of c be initial value with 1 and, and return step S1.

On the other hand, the present invention proposes the calculating system of upper finishing reason element number in a kind of battle-damaged equipment queuing system, Including:

Computing unit, waiting repair during c the upper upper finishing reason fitting up reason unit calculating crawler belt break Averagely equipping quantity, wherein, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

Judging unit, for judging that the average of waiting repair that latest computed obtains equips whether quantity counts less than first Value, if the average equipment quantity of the waiting repair that obtains of latest computed is less than described first numerical value, is then defined as target by the value of c Upper finishing reason element number, otherwise, update the value of c be initial value with 1 and, and notify that described computing unit is operated.

In battle-damaged equipment queuing system described in the embodiment of the present invention, computational methods and the system of element number managed by upper finishing, Using team leader as the index optimized, by increasing the quantity of upper finishing reason unit, draw the operating index of system, by optimizing index With operating index relative analysis, finally determine the upper finishing reason element number needing to put into such that it is able to provide one to calculate war Damage the method most preferably allocated of upper finishing reason element number in equipment queuing system, it is simple to scientific dispatch, rationalization ensures single Unit.

Accompanying drawing explanation

Fig. 1 is computational methods one embodiment of upper finishing reason element number in the present invention a kind of battle-damaged equipment queuing system Schematic flow sheet；

Fig. 2 is single " client " many " information desk " model schematic；

Fig. 3 is calculating system one embodiment of upper finishing reason element number in the present invention a kind of battle-damaged equipment queuing system Structural representation；

Fig. 4 is the Petri network schematic diagram of tri-layer；

Fig. 5 is the multi-level Petri network model Establishing process schematic diagram of equipment repahs flow process.

Detailed description of the invention

For making the purpose of the embodiment of the present invention, technical scheme and advantage clearer, below in conjunction with the embodiment of the present invention In accompanying drawing, the technical scheme in the embodiment of the present invention is explicitly described, it is clear that described embodiment is the present invention A part of embodiment rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art are not having Make the every other embodiment obtained under creative work premise, broadly fall into the scope of protection of the invention.

Referring to Fig. 1, the present embodiment discloses the computational methods of upper finishing reason element number in a kind of battle-damaged equipment queuing system, Including:

S1, c the upper finishing reason unit calculating crawler belt break upper finishing reason during waiting repair averagely equip number Amount, wherein, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

S2, judge the average equipment quantity of the waiting repair that latest computed obtains whether less than the first numerical value, if up-to-date meter The value of c less than described first numerical value, then is defined as in target filling repair order by the average equipment quantity of the waiting repair obtained Unit's quantity, otherwise, update the value of c be initial value with 1 and, and return step S1.

After equipment Support Resource integrated suppliers, according to repairing technology demand marshalling upper finishing reason unit.Each upper dress unit There are 4 mechanics, the repairing of the upper dress part of the equipments such as self-propelled gun, tank, panzer, tracked construction equipment can be completed.

The present invention to equipment arrival situation to be repaired in system, upper finishing reason unit hold the ability of repairing, the row to equipment to be repaired Team's situation makees following hypothesis:

A () produces repair assignment according to equipment and obeys Poisson distribution, it will be assumed that equipment was delivered between finishing reason district's time Every also obeying Poisson distribution；

B the repairing time of () each equipment upper dress part obeys quantum condition entropy；

C () upper dress region can be with the multiple upper finishing reason unit of centralized configuration, multiple stage equipment launches to repair simultaneously, meets flat war In conjunction with needs, belong to centralized configuration model, many " information desk " model.

Meanwhile, following restrictive condition is also met:

A the utilization rate of () each support Unit has minimum and maximum requirement；

The quantity of b equipment that () is waited in line is not to be exceeded certain quantity；

C the average time of () equipment waiting repair is not to be exceeded the regular hour.

Assume that the upper dress part of equipment to be repaired can be queued up when needing to place under repair in time, and repair the use process of unit Meet following four condition:

A is in certain section of time interval t, and the probability of maintenance items quantity k is unrelated with initial time during this period of time, substantially The most relevant with the length of this time interval, according to army at ordinary times to equipment war preparedness situation and the analysis of monitoring situation, for certain One specific task, the maintenance items quantity occurred in a period of time all controls within the scope of certain, and probability is substantially certain,

K maintenance items is produced } in P{ [0, t]

K maintenance items is produced } in=P{ [a, a+t]

=P_k(t)

That is: stationarity requirement is met；

The maintenance items quantity that b produced within disjoint time is clearly separate.That is: markov property is met；

C assumes occur that the situation of plural maintenance items does not exists or probability in the least time Δ t simultaneously The least (this situation reality is set up substantially).

That is: universality is met:

In formula:

--the probability that two or more maintenance items occurs simultaneously；

D has the probability of k item maintenance items to be 1 within any a period of time,

I.e. meet finiteness:Wherein, m is the quantity of the equipment to be repaired that crawler belt workshop accommodates up to.

If upper finishing reason unit in use meets above four conditions analyzed, according to Eugéne Balme-glad limit Theorem is asserted: the summation of a large amount of separate small intensity streams is similar to a simple stream (Poisson input), if the most each stream It is steady and common.Therefore in a subtask, occur maintenance items meet Poisson flow input, have within the t time k item need into It is λ Poisson distribution that the probability of the project (client of arrival) of row maintenance obeys intensity:

$P_k\left(t\right)=\frac{{\left(\mathrm{\λ}t\right)}^k}{k!}{e}^{-\mathrm{\λ}t},t>0,k=0,1,2,\mathrm{....}$

After determining the probability of the project that k item in the t time needs to carry out to keep in repair, it is thus necessary to determine that the average utilization of system, We use quantum condition entropy to determine the average utilization of system.

Assume that MT=1/ λ average time of two maintenance items occurs in equipment, because the function that is evenly distributed of MT is:

F_T(t)=P (T≤t),

This probability probability of at least 1 maintenance items appearance in [0, t] interval is:

p₀(t)=e^-λt,

F_T(t)=1-p₀(t)=1-e^-λt, t > 0,

Probability density is:

$P_T\left(t\right)=\frac{{\mathrm{dF}}_T\left(t\right)}{dt}={\mathrm{\λe}}^{-\mathrm{\λ}t},t>0,$

The making time interval obedience parameter repairing unit is the exponential of λ；Put in the time [0, t] is interval and ensure The probability of basic guarantee unit (client's arrival) be:

F (t)=1-e^-λt, t > 0.

Statistics shows that general actual average repair rate obeys exponential, it is assumed that respectively repair unit (information desk) work mutually Independence and the identical μ of average service rate₁=μ₂=...=μ_l=μ, has a single MTTR:

MTTR=1/ μ,

The probability (completing the probability of service) repaired in [0, t] is interval is:

M (t)=1-e^-μt, t > 0.

First hypothesis below is made: the work of (1) each information desk is separate, and the identical μ of average service rate₁=μ₂= μ₃=...=μ_c=μ；(2) each information desk works simultaneously.

For the convenience analyzed, it is assumed that the average arrival rate of n item task is λ, and c helpdesk organizes work simultaneously.By vacation If understanding, the average service rate of whole service organization is c μ (as n>=c), and as n,<during c, service rate is n μ, theoretical according to queueing theory Understand and work asTime, flow process will increase over time, and not have unlimited team leader, its model as shown in Figure 2:

Understanding according to assumed above, during upper finishing reason, queuing rate model is M/M/C model, in the feelings considering steady state solution Under condition, main operating index is:

(a) average number of tasks (team leader)

$L_s=L_q+\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}},$

B number of tasks (queue length) that () etc. are to be serviced

$L_q=\frac{{\left(c\mathrm{\&rho;}\right)}^c\mathrm{\&rho;}}{c!{(1-\mathrm{\&rho;})}^2}{P}_0,$

(c) task residence time

$W_s=\frac{L_s}{\mathrm{\&lambda;}},$

(d) task waiting time

$W_q=\frac{L_q}{\mathrm{\&lambda;}},$

Wherein, P₀Represent that whole information desk does not process the probability of task

$P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1},$

In formula:

λ--need maintenance rate (arrival rate of customers)；

C--basic guarantee element number (service number of units)；

μ--mean repair rate (service rate).

The computational methods of upper finishing reason element number in battle-damaged equipment queuing system described in the embodiment of the present invention, by team leader As the index optimized, by increasing the quantity of upper finishing reason unit, draw the operating index of system, by optimizing index and operation Comparativeanalysis, finally determines the upper finishing reason element number needing to put into such that it is able to provide one to calculate battle-damaged equipment The method most preferably allocated of upper finishing reason element number in queuing system, it is simple to scientific dispatch, rationalization's support Unit.

Congestion lengths L_qWith waiting time W_qIt is reaction 2 important indicators of queuing system efficiency of service, by it is increased by one The method of fixed constraints determines the number of helpdesk.

Analyze according to the M/M/C model theory in queueing theory system, can try to achieve state probability:

$P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1},$

In formula:

λ--need maintenance rate (arrival rate of customers)；

μ--mean repair rate (service rate)；

C--repair element number (service number of units)；

For system service intensity.

System performance measure is tried to achieve as follows:

$L=\underset{n=1}{\overset{c}{\&Sigma;}}{\mathrm{nP}}_n=L_q+\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}},$

$L_q=\underset{n=c+1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}(n-c)P_n=\frac{{\left(c\mathrm{\&rho;}\right)}^c\mathrm{\&rho;}}{c!{(1-\mathrm{\&rho;})}^2}{p}_0,$

In formula:

L_p--waiting repair averagely equip quantity；

L--(the equipment quantity+etc. accepting maintenance is to be repaired to need the quantity of averagely equipping of maintenance in system Equipment quantity).

Average latency and residence time are tried to achieve by Little formula,

$W_q=\frac{L_q}{\mathrm{\&lambda;}},$

$W=\frac{L}{\mathrm{\&lambda;}},$

In formula:

W--the down time of every equipment；

W_q--the time that every equipment etc. are to be repaired.

By the computing formula of above-mentioned parameters, if inputting several known conditions, it is easy in a computer push away Calculate required upper finishing reason element number.Such as:

Average maintenance item number in unit interval in known equipment mean repair rate (μ), execution taskRequirement Maximum fault item number (L) or the W maximum residence time of the upper finishing reason unit that requires, these conditions are substituted into above formula, Utilize computer can calculate the upper finishing reason element number of minimum demand.

Alternatively, another enforcement of the computational methods of finishing reason element number in battle-damaged equipment queuing system of the present invention In example, described S1 also includes:

Averagely equipping quantity and (need to keeping in repair of maintenance is needed during calculating the upper finishing reason of described c upper finishing reason unit Equipment includes the equipment of waiting repair and the equipment repaired)；

Wherein, described S2, including:

Judge that the average of waiting repair that latest computed obtains equips whether quantity is less than described first numerical value, and up-to-date meter Whether the average equipment quantity that the need obtained keep in repair is less than second value, if the average of waiting repair that latest computed obtains fills Standby quantity is less than described first numerical value, and the average equipment quantity of need maintenance that latest computed obtains is less than described second value, Then the value of c is defined as in target finishing reason element number, otherwise, update the value of c be initial value with 1 and, and return step S1.

Alternatively, in battle-damaged equipment queuing system of the present invention on finishing reason element number computational methods another embodiment in, The computing formula of the average equipment quantity of described waiting repair is $\begin{array}{cc}{L}_q=\frac{{\left(c\mathrm{\&rho;}\right)}^c\mathrm{\&rho;}}{c!{(1-\mathrm{\&rho;})}^2}{p}_0,& P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1},\end{array}$ Wherein, L_qQuantity is averagely equipped for waiting repair,λ is the average arrival rate of task, and μ is upper finishing reason unit Average service rate.

Alternatively, another enforcement of the computational methods of finishing reason element number in battle-damaged equipment queuing system of the present invention In example, the computing formula of the described average equipment quantity that need to keep in repair isWherein, L is the average equipment that need to keep in repair Quantity, L_qQuantity is averagely equipped for waiting repair.

The calculating process of finishing reason element number is specifically described below in the present invention.

According to repairing group repair capability with send and repair rule and may determine that μ and λ, dress queuing model computing formula in substitutions, such as: If μ=0.1/day, λ=0.15/day, according to the M/M/C model in queueing theory system, according to following formula:

$\left(1\right)---P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1},$

$\left(2\right)---L_q=\underset{n=c+1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}(n-c)P_n=\frac{{\left(c\mathrm{\&rho;}\right)}^c\mathrm{\&rho;}}{c!{(1-\mathrm{\&rho;})}^2}{p}_0,$

$\left(3\right)---W_q=\frac{L_q}{\mathrm{\&lambda;}},$

$\left(4\right)---W=\frac{L}{\mathrm{\&lambda;}},$

Each index when being computed proper c=2,3,4,5,6 is as shown in the table:

In conjunction with constraints, it may be determined that the quantity of maintenance teams and groups, as required when constraints:

(1)L_q≤0.5；

(2)W_q≤0.1。

As above the result of calculation in table, it is known that meet requirement when repairing teams and groups' quantity c=4, therefore under this constraint Little upper finishing reason element number is 4.

Referring to Fig. 3, the present embodiment discloses the calculating system of upper finishing reason element number in a kind of battle-damaged equipment queuing system, Including:

Computing unit 1, waiting repair during c the upper upper finishing reason fitting up reason unit calculating crawler belt break Averagely equipping quantity, wherein, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

Judging unit 2, for judging that the average of waiting repair that latest computed obtains equips whether quantity counts less than first Value, if the average equipment quantity of the waiting repair that obtains of latest computed is less than described first numerical value, is then defined as target by the value of c Upper finishing reason element number, otherwise, update the value of c be initial value with 1 and, and notify that described computing unit 1 is operated.

The calculating system of upper finishing reason element number in battle-damaged equipment queuing system described in the embodiment of the present invention, by team leader As the index optimized, by increasing the quantity of upper finishing reason unit, draw the operating index of system, by optimizing index and operation Comparativeanalysis, finally determines the upper finishing reason element number needing to put into such that it is able to provide one to calculate battle-damaged equipment The method most preferably allocated of upper finishing reason element number in queuing system, it is simple to scientific dispatch, rationalization's support Unit.

Alternatively, another enforcement of the calculating system of finishing reason element number in battle-damaged equipment queuing system of the present invention In example, described computing unit needs the averagely dress of maintenance during being additionally operable to calculate described c the upper upper finishing reason fitting up reason unit Standby quantity；

Wherein, described judging unit is the least for judging the average equipment quantity of waiting repair that latest computed obtains In described first numerical value, and the average of need maintenance that latest computed obtains equips whether quantity is less than second value, if up-to-date meter The averagely equipment quantity of the waiting repair obtained is less than described first numerical value, and the average of need maintenance that latest computed obtains fills The value of c less than described second value, is then defined as in target finishing reason element number by standby quantity, and otherwise, the value updating c is former Value with 1 and, and notify that described computing unit is operated.

Alternatively, in battle-damaged equipment queuing system of the present invention on finishing reason element number calculating system another embodiment in, institute The computing formula of the average equipment quantity stating waiting repair is $\begin{array}{cc}{L}_q=\frac{{\left(c\mathrm{\&rho;}\right)}^c\mathrm{\&rho;}}{c!{(1-\mathrm{\&rho;})}^2}{p}_0,& P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1}\end{array},$ Wherein, L_qQuantity is averagely equipped for waiting repair,λ is the average arrival rate of task, and μ is upper finishing reason unit Average service rate.

Alternatively, another enforcement of the calculating system of finishing reason element number in battle-damaged equipment queuing system of the present invention In example, the computing formula of the described average equipment quantity that need to keep in repair isWherein, L is the average equipment that need to keep in repair Quantity, L_qQuantity is averagely equipped for waiting repair.

Additionally, when defining Petri network (PN), it is necessary to difference PN and mark PN (Marked Petri network).It Define the state of system, event and the relation between them thereof, this is equivalent to the state equation of continuous state variable system. In PN, by the state of mark descriptive system.The latter is also known as PN, and it refers to the PN with certain mark, describes and be in certain shape Equipment repahs under state, is equivalent to the continuous variable dynamical equation in certain moment value of the state variable given state equation.

The structure defining 1 PN is by 4 directed graphs wanting unit to describe:

PNS=(P, T, I, O) (3-1)

Herein:

(1) P={p₁..., p_nBe storehouse finite aggregate, the number that n > 0 is storehouse；

(2) T={t₁..., t_mIt is the finite aggregate changed, m > 0 is the number of transition；

P ∩ T=Φ (empty set),

(3) I:P × T → N is input function, it defines repeat number or the set of power, the N here of directed arc from P to T =0,1 ... } it is set of nonnegative integer；

(4) O:T × P → N is output function, it defines repeat number or the set of power of directed arc from T to P.

In the directed graph representing PN, storehouse is so circle represents；Transition are shown with rectangle or heavy line segment table；If from storehouse Institute p is nonnegative integer w to the input function value of transition t, and (p, t)=w, then by the directed arc from p to t sidenote w to be designated as I Represent；If from transition t to storehouse institute p output function value nonnegative integer w, be designated as O (p, t)=w, then oriented with from t to p Arc sidenote w represent.Especially, if w=1, then need not mark；If I (p, t)=0 or O (p, t)=0, then need not draw arc.I and O All being represented by the nonnegative integer matrix of n × m, difference C=O-I of O Yu I is referred to as incidence matrix.

Definition 2 mark PN be 1 want unit:

PN={PNS, m}={P, T, I, O, m₀} (3-2)

Herein:

(1) PNS={P, T, I, O} are PN, and it is determined by defining 1；

(2) m:P → N be mark PN mark, it is a column vector, its i-th element representation i-th storehouse in Tuo Ken Number.Especially, m₀For just knowing mark, represent the original state of equipment repahs process.

During equipment repahs, a certain event must be met the situation of (realization) in all preconditions (state) Under be only possible to occur.Sometimes, it is desirable to a certain precondition (state) must is fulfilled for repeatedly (realizing repeatedly).For example, it is assumed that carry out A certain operation needs 2 operators, if definition status " a bit manipulation person is idle " and event " start operation ", then and this event Require that this state realizes 2 times, show that 2 operators are idle." 2 bit manipulation persons are empty of course, it is possible to definition status Not busy ", then this event requires nothing more than and realizes 1 time.

In PN, we represent an event with transition t, represent that event occurs because of premise by the enable (enabling) of transition Condition is satisfied and can occur.We also use the premise local shape required for the generation of input magazine this event represented of t State, with by input magazine define the number of times that these requirements local premise state realizes to the input function of t, and the reality of local state Existing situation by storehouse included in torr to agree number relevant.Enable regular to this end, introduce following transition:

Defining 3 one transition t ∈ T to enable under mark m, and if only if: $\&ForAll;p\&Element;\&CenterDot;t:m\left(p\right)$ $\&GreaterEqual;I(p,t).$

The generation of the event that all preconditions are satisfied, by " consumption " these premise states, changes and this thing simultaneously The local state that part is relevant, i.e. makes these result phases realize certain number of times.In PN, we swash with the transition enabled Send out (fire) and describe the generation of event.The premise state and the number of times thereof that are consumed are determined by the input function of transition, and With output storehouse institute in increase torr agree represent.Due to input magazine in torr agree minimizing and output storehouse in hold in the palm willing increasing Add so that the mark of PN changes.Enable regular to this end, introduce following transition:

The transition t that definition 4 enables under mark m excites generation new logo m '

$\&ForAll;p\&Element;P:m^{\&prime;}\left(p\right)=m\left(p\right)-I(p,t)+O(p,t)---(3-3)$

If definition 5 is from initial marking m₀Start to excite a transition sequence to produce mark m_r, then m is claimed_rIt is from m₀Up to (reachable).If from m₀As long as starting to excite 1 transition can produce m_r, then m is claimed_rIt is from m₀Immediately up to.All from m₀ Up to the collection of mark be collectively referred to as set of reachable markings or reachable set, be designated as R (m₀)。

Accessibility is an important behavioral trait of PN.A given PN, it is desirable to know from initial marking m₀Permissible Arrive which mark, or a given mark, if a series of transition can be excited to arrive this mark from initial marking.

Definition 6 gives PN=(P, T, I, O, m₀) and its reachable set R (m₀), for storehouse institute p ∈ P, ifThen claiming p is k bounded, and k is positive integer herein；If all storehouses of PN are all k bounded , then claiming PN is k bounded.

Especially, during k=1, i.e. when certain storehouse or PN be 1 bounded, we claim this storehouse or PN be safe.If for Arbitrary initial mark m₀, PN is k bounded, then PN is Structural boundedness.

Definition 7 is for a transition t ∈ T, under arbitrary mark m ∈ R, if there is a certain transition sequence s_r, this transition sequence Excite so that this transition t enable, then it is alive for claiming these transition.If all transition of a PN are all to live (live), then should PN is alive.

Dead transition (dead transition) and locked (deadlock) describe the activity of PN from the negative.If there is m ∈ R, There is not the transition sequence started from m, this sequence excite so that t enable, then transition t be dead transition.If there is m ∈ R, at this Enabling without any transition under m, then claim PN to comprise one locked, this is designated dead marking (dead marking).

If definition 8 is for each mark m ∈ R (m₀), m₀∈ R (m), then it is reversible for claiming this PN.

Reversibility means that model can initialize with self.Additionally, reversibility also assures that the cyclophysis of system.

The method introducing the time in PN can be divided into following 3 kinds:

(1) if represent event or the operation going through certain time with transition, then the time is associated with transition, obtain composing time-varying Move Petri network (Timed Transition Petri Net, TTPN).Once change enable, the most immediately each from these transition Input magazine institute removes a number of torr agree, but excite again after changing certain time to be postponed, and put in the institute of output storehouse A number of torr is agree.

(2) if with going through event or the operation of certain time represented by storehouse, then by associated by time and storehouse, storehouse when obtaining composing Institute's Petri network (Timed Place Petri Net, TPPN).Transition excite the most immediately once enable, each defeated from these transition Warehouse-in institute in remove a number of torr agree, and output storehouse institute in put into a number of torr agree.But these torr agree only prolong Just can use after certain time late.The most spendable torr agree to make transition enable.

(3) if with from be transitted towards storehouse output arc represent transportation or the Flow of Goods and Materials process of certain time gone through, Then the time is associated with output arc.The transition enabled excite immediately, but output torr arrives output after agreeing certain time to be postponed again Storehouse institute.

Define 9 Timed Petri nets

During tax, storehouse institute petri net (TPPN) is defined as following 6 and wants first:

TPPN={P, T, I, O, m₀, D} (3-4)

Herein, P, T, I, O, m₀Definition with basic PN is identical；

D={d₁, d₂..., d_nBe all storehouses time delay collection, wherein d_iFor p_iTime delay.

Define 10 timed transition Petri network

Timed transition petri net (TTPN) is defined as following 6 and wants first:

TTPN={P, T, I, O, m₀, D} (3-5)

Herein, P, T, I, O, m₀Definition with basic PN is identical；

D={d₁, d₂..., d_nIt is the time delay collection of all transition, wherein d_iFor t_iTime delay.

The transition of TTPN excite according to the firing rules identical with basic PN change input and output storehouse in Tuo Ken.But Being once to change enable, then remove a number of torr from each input magazine institute of these transition and agree, transition to postpone a timing Excite again after between, and it is willing to put into a number of torr in the institute of output storehouse.Therefore, leave input magazine institute from Tuo Ken to agree arrive to torr Output storehouse existing space, when by basic PN method for TTPN model analysis, it has to be noted that this space, do not ignore The Tuo Ken that will delay to reach.

The time of determination is changed into by the Time Petri Nets determined as stochastic variable or the time delay of obedience probability distribution, Stochastic Timed Petri Nets model will be obtained.The method generally acknowledged is to be associated with transition the time of stochastic variable.If time delay is for obeying General distribution variables or existing random have again determine, then be difficult to obtain being suitable for the analytic solutions of ordinary circumstance, have to borrow Help emulation or try to achieve approximate solution.Especially, in Stochastic Timed Petri Nets, all of time delay is obeys exponential Stochastic variable, then obtain stochastic Petri net (SPN).

Define 11 SPN be defined as 6 want unit (P, T, I, O, m₀, Λ), herein, P, T, I, O, m₀Identical with PN definition, and Λ: T → R+ (arithmetic number territory) is the excitation function associated with all transition by the firing rate of arithmetic number.Usually, λ is used_iRepresent transition t_iFiring rate.

If all states of equipment repahs process are defined as storehouse institute, all Support activities are defined as transition, according to Petri network method is had to set up model, it finds that: owing to equipment repahs process is uncertain random event, same activity (becomes Move) may to produce different states (storehouse institute), i.e. output function be uncertain (or claiming random).Therefore, set forth herein A kind of new Petri network modeling method timed transition, stochastic Petri net (TTSPN).

Define 12 TTSPN be defined as following 6 want unit:

TTSPN={P, T, I, O, m₀, D, S} (3-6)

Herein, P, T, I, O, m₀, the definition of D with TTPN is identical；

And S:O → [0,1] be output excite expectation function, (p t) is the real number between 0 to 1 to meet S.

With θ, (p t) represents that ((p, t) obeys [0,1] distribution to θ to O, and its mathematic expectaion is that (p t), and expires S for p, state t) Foot

$\underset{pi\&Element;\&CenterDot;t}{\&Sigma;}\mathrm{\&theta;}(p_i,t)\&GreaterEqual;1---(3-7)$

Equipment repahs flow simulation analysis is exactly on the basis of setting up guarantee flow simulation model, to ensureing that flow process is carried out Simulation analysis, to ensureing that flow process is comprehensively evaluated and provides prioritization scheme.Now provide the multi-level of equipment repahs flow process Petri network model modelling approach, and illustrate how the emulation mould applying multi-level Petri network model to set up equipment repahs flow process Type.

It is various that the concepts such as resource in Petri network, storehouse institute, transition can preferably describe in equipment repahs network system Equipment, resource and their dynamic cooperative relation.But, Petri network there is also that some are the most not enough, large-scale, In the model of complication system, the main difficulty of Petri network application is the complexity problem in model state space, will be with real system Scale increase and be exponentially increased.So, the flow process of complication system this for equipment repahs, utilize Petri network technology to build Vertical corresponding phantom, it is necessary to take measures to reduce the complexity of Petri network.

The theoretical basic thought of refinement is (activity of this simple Petri network, to be had by the simple net of known or easy analysis Criticality and reversibility etc. are easily verified that) start, replace the storehouse institute in initial simple net with subnet in further detail step by step or become Moving, the subnet newly added does not changes some character of original net.This " top-down " process may be repeated modeler The degree of refinement that member wants.

In order to reduce the complexity setting up complication system Petri network, in the Petri network set up complication system, application is thin Change theory, set up multi-level Petri network.In operation flow, some task is inseparable or perhaps can directly perform , it is known as atom.And some task can Further Division, be referred to as compound, it is the most also a business mistake Journey.In like manner, can also contain composite task in composite task, this situation is often sent out in inter-organization extensive business procedure Raw.Correspondingly, in Petri network describes, transition are divided into two kinds: basic transition and subnet transition.Basic transition represent atom Task, subnet transition tabel shows composite task, and it has its internal structure, internal act and internal state.

The multiple stratification modeling of Petri network can lead to the advantage that

1. hide subnet internal structure, concentrate on corresponding abstraction hierarchy when modeling.

2. for there being mutually isostructural subnet, it is not necessary to repeat modeling and analyze.

3. business process model is made to have good structure, it is simple to it is analyzed and processed.

For the ease of realizing the replacement of subnet transition, and specification sub-network structures sets up model library (for follow-up process modeling Identical structon pessimistic concurrency control is provided), on the basis of basic petri net, increase by two storehouse institutes of START and FINISH for subnet model Initially change t_inWith termination transition t_fTwo immediate transitions (the execution time is zero).The beginning of subnet represented by START storehouse, Subnet represented by FINISH storehouse terminates.When subnet being replaced to change with subnet, that only need to find subnet initially changes t_inAnd end Only change t_f, the Petri network between the two transition is (together with t_in、t_fJust can replace together) in last layer Petri network corresponding Wait refinement transition.If Fig. 4 is the Petri network of a tri-layer.

Equipment repahs process is a sequence of events dynamic, multistage, starts from the Trouble Report of software or software more Change request, carry out a series of management and maintenance until software comes back to normal condition (or the state improved).Set up The multi-level Petri network model of equipment repahs flow process is mainly being divided into the only of composition equipment repahs flow process whole process exactly On the basis of the sequence of vertical subevent, utilize multi-level Petri network clear model, express the maintenance task studied legibly.This Individual process is substantially attributed to: the upper of flow process description is repaired in event → foundation that analytical equipment repairing activity → division activity is independent Petri network model → the profit of the independent task process of layer Petri network model → analyze → obtain subprocess model → elementary event The conductive suggestion of equipment repahs is improved with the index parameter of the whole flow process of the simulation calculation of model → proposition.Equipment repahs flow process Multi-level Petri network model set up process as shown in Figure 5.

Set up multi-level Petri network model and use the method the most successively refined.Setting up upper strata Petri model During, after analyzing critical process therein, then set up bottom flow process by Petri network model, complete multi-level Petri network mould Type.For conventional basic service unit, Petri network model library can be set up, directly quote these model libraries and complete at many levels Petri network model.

Although being described in conjunction with the accompanying embodiments of the present invention, but those skilled in the art can be without departing from this Making various modifications and variations in the case of bright spirit and scope, such amendment and modification each fall within by claims Within limited range.

Claims (8)

1. the computational methods of upper finishing reason element number in a battle-damaged equipment queuing system, it is characterised in that including:

S1, c the upper finishing reason unit calculating crawler belt break upper finishing reason during waiting repair averagely equip quantity, its In, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

S2, judge the average equipment quantity of the waiting repair that latest computed obtains whether less than the first numerical value, if latest computed obtains The value of c less than described first numerical value, is then defined as in target finishing reason unit number by the average equipment quantity of the waiting repair arrived Amount, otherwise, update the value of c be initial value with 1 and, and return step S1.

The computational methods of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 1 Being, described S1 also includes:

Need maintenance during calculating the upper finishing reason of described c upper finishing reason unit averagely equips quantity；

Wherein, described S2, including:

Judge that the average of waiting repair that latest computed obtains equips whether quantity is less than described first numerical value, and latest computed obtains The average equipment quantity of the need maintenance arrived whether less than second value, if the waiting repair that obtains of latest computed averagely equip number Amount is less than described first numerical value, and the average equipment quantity of need maintenance that latest computed obtains is less than described second value, then by c Value be defined as in target finishing reason element number, otherwise, update the value of c be initial value with 1 and, and return step S1.

The computational methods of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 1 Being, the computing formula of the average equipment quantity of described waiting repair isWherein, L_qFor waiting repair Averagely equip quantity, $\mathrm{\&rho;}=\frac{\mathrm{\&lambda;}}{c\mathrm{\&mu;}},P_0={\&lsqb;\underset{k=0}{\overset{c-1}{\&Sigma;}}\frac{1}{k!}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^k+\frac{1}{c!}\frac{1}{1-\mathrm{\&rho;}}{\left(\frac{\mathrm{\&lambda;}}{\mathrm{\&mu;}}\right)}^c\&rsqb;}^{-1},$ λ is averagely arriving of task Reaching rate, μ is the average service rate of upper finishing reason unit.

The computational methods of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 2 Being, the computing formula of the described average equipment quantity that need to keep in repair isWherein, L is the average equipment that need to keep in repair Quantity, L_qQuantity is averagely equipped for waiting repair.

5. the calculating system of upper finishing reason element number in a battle-damaged equipment queuing system, it is characterised in that including:

Computing unit, during c the upper upper finishing reason fitting up reason unit calculating crawler belt break, waiting repair is average Equipment quantity, wherein, c is integer, and initial value is 1, and on each, the average service rate of finishing reason unit is the most equal；

Judging unit, for judging that the average of waiting repair that latest computed obtains equips whether quantity is less than the first numerical value, if The value of c less than described first numerical value, is then defined as in target dress by the average equipment quantity of the waiting repair that latest computed obtains Repair element number, otherwise, update the value of c be initial value with 1 and, and notify that described computing unit is operated.

The calculating system of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 5 Being, described computing unit needs the averagely dress of maintenance during being additionally operable to calculate described c the upper upper finishing reason fitting up reason unit Standby quantity；

Wherein, described judging unit, for judging that the average of waiting repair that latest computed obtains equips whether quantity is less than institute State the first numerical value, and the average of need maintenance that latest computed obtains equips whether quantity is less than second value, if latest computed obtains The average equipment quantity of the waiting repair arrived less than described first numerical value, and the need maintenance that obtains of latest computed averagely equip number The value of c less than described second value, is then defined as in target finishing reason element number by amount, otherwise, update the value of c be initial value with The sum of 1, and notify that described computing unit is operated.

The calculating system of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 5 Being, the computing formula of the average equipment quantity of described waiting repair isWherein, L_qFor waiting repair Averagely equip quantity,λ is the average arrival rate of task, and μ is the average service rate of upper finishing reason unit.

The calculating system of upper finishing reason element number, its feature in battle-damaged equipment queuing system the most according to claim 6 Being, the computing formula of the described average equipment quantity that need to keep in repair isWherein, L is the average equipment that need to keep in repair Quantity, L_qQuantity is averagely equipped for waiting repair.