Extension of N-schemes. - Modeling of systems

Extension of N-schemes.

Possible extensions of N-schemes , defined in the form of Petri nets, discussed in Section 2.6, will be considered from the point of view of their application, ie, with an orientation toward increasing the modeling capabilities of this apparatus. To model the processes in information systems, the most interesting are N-schemes in the form of temporary networks and E-networks, being the most powerful extension of Petri nets [28].

Set the time network, t. With. Nr-scheme, includes seven sets

where B, D /, O Y M have the same meaning as the one (see § 2.6); ...

... Y, ...) is an increasing sequence of real numbers, called the time base; v: Bxv => v is a function of time delays.

The time factor is taken into account in H $ schemes by introducing the passive state of the label in the position. When the label arrives at the position bI , it remains in the passive state (can not participate in the excitation of transitions) for a time V (6 , * 5 ) -/ 5 and only then goes into the active state.

The subclass of the time network is the Merlin network, where the time of the passive state of the label is defined as a random variable that is in the range between/* and/** 0 * ^ * 5 ^ ***) which are specified in the description of the A ^ -scheme.

Example 8.11. We will construct the model of the microprocessor subscriber station (AP) of the information network (30, 54,] in the form of the scheme .The structure of this AP is shown in Figure 8.25, where: MP - a macro processor, RAM - random access memory PA - peripheral adapter; EPM - electrified typewriter; KS 2 and KS 3 - - input and output communication channels.

The task N s in the form of a time network includes the specification of the structure I, O}, of the vector markings M 0 and the delay vector b.

The structure of the Ns-scheme is given graphically, since it is the graphical representation that has the greatest visibility, and the simplicity of the relationship with the structure of the object, i.e. in this example with the structure of the AP. At the cassock. 8.26 for the sake of clarity, the elements N r of the scheme relating to specific elements of the structure of the AP are highlighted for the sake of clarity (figure 8.25).

The markup vector has the form

and the delay vector

Using the N-schemes , a structural approach to the construction of the simulation model is implemented, which provides visibility of the model, the modular principle of its development (assembly), the possibility of transition to an automated interactive design procedure.

Even greater possibilities for modeling complex systems are provided by such extensions No Schemes, as setyy which we denote as M E schemes. Unlike time networks in E-networks , four types of transitions are defined: branching, union, managed branching and priority association. An important feature of the 1 E -scheme is also the detailed presentation of the label representation. With each label in the No E -circuit is related -

Fig. 8.25. AP Structure

Fig. 8.26. Structure cxemy

would be n descriptors. Each of the label descriptors carries a certain quantitative information about the modeled object, i.e., the system 5.

The structural assignment of the model of the elements of the system A * in the form N ^ of the scheme makes it possible to use the modular principle of developing the simulation model using the library of ^ -net modules and their parametric adjustment. In this case E - the network model is the basis for assembling the simulation program from the modules implemented in some programming language [30, 54].

The basis for building program modules is a generalized algorithm for the functioning of the ^ -net module, which we will consider in the following example.

Example 8.12. The arrival of a label in the input position of the transition i t (Figure 8.27) initiates the procedure for checking the readiness for the trigger (Fig. 8.28). The conditions checked include the analysis of the layout of the deciding position M {bk}, where 6 * eH d , as well as checking marking of the output positions M {0 (& lt;/ t )} and conjugate positions A/{/ (4 *)}. In the case when bieB p , in this phase, also the calculation of the deciding transition procedure is performed when the required conditions are reached, the transition enters the active phase, the content of which is determined by the transition description elements/(& lt; ;/*,) and p (& lt;/ t ), where the element/(& lt;/*,) can be specified either directly or as a function. In the latter case, it is necessary to pre-clean this function, and then simulate the required time

The procedure for the transition p (& lt;/*,) is performed in two stages: first the predicates P1 are computed, and then the required subset of operations on the label descriptors p p ) is realized. Then the transition < t enters the completion phase, the content of which

Fig. 8.27.

The generalized structure of the network transition is the change in the size of the input and output positions of the transition A/{/ (4 ,)} and A/(0 <& pound ;,}}. Layout of the position b { changes to zero: A/(b |): - 0. When marking, the deciding position becomes undefined: A/(b *): e °. Then, the labels are moved to a number of output positions 0 (to t ) according to the type of this transition. This operation completes the transition to processing the incoming label.

One of the main questions to be solved by the developer of the simulation process model, formalized on the basis of No Schemes, is the choice of the programming language. The implementation of the N E • cxeem modules in machine-oriented languages ​​or general-purpose languages ​​can reduce the costs of computer time and memory in system modeling, but you should take into account the high complexity of development libraries of modeling subroutines. This disadvantage is eliminated when using the modeling of the system & pound ;, formalized on the basis of No Schemes, of simulation languages.

Using the YAM. The software implementation of models of systems 5 based on extended H-schemes (N3-, N E -cxem) is more complex than programming models based on conventional Petri nets. To simplify the transition to a modeling program, it is rational to use the languages ​​of simulation modeling (NIM). Let's consider the peculiarities of the use of NIM for simulation based on the No E -scheme using the simulation system (7P55, which was considered in detail earlier.

Fig. 8.28. The algorithm of the E -main transition

Example 8.13. We will analyze the correspondence between the elements 7Я г -schemes and objects of the modeling language (see § 5.3). As a result of the comparative

analysis, the following 37 can be formulated.

1. The H l schema tag can be represented by a dynamic object OR55, that is, a transaction.

2. Label tags are similar to the parameters of the RNC transactions.

3. The Ng-scheme position is identical to the object belonging to the GPSS hardware category of the single-capacity storage type.

4. The decisive positions of the Ng-scheme , depending on whether they belong to the multiplier

The In p are implemented in two ways: a) if bc In p , then bk is equivalent to a set of objects of type Boolean variables of the computational category GPSS; b) if bk 6 B/Bp, then bk can be represented by a storage unit of the hardware category GPSS.

5. The time parameters of the transitions t (d m ) are implemented by the ADVANCE object of the operating category GPSS.

6. The operations of calculating the predicates Pu, j - I, S, for p (d m ) corresponds to the use of the TESTE block, which changes the routes of transients, in combination with Boolean variables of the computational category GPSS.

7. The operations {lj p } for p {d m ) are performed using ASSIGN blocks of the dynamic category GPSS in combination with arithmetic variables.

8. You can simulate the values ​​of label descriptors by storing the values ​​of the transaction parameters in the cells of the stored values ​​(X, XH) using the SAVEVALVE block of the storage category GPSS.

9. The processes of synchronizing the movement of labels through the transition d m and removing the labels from the deciding position/b * e & pound; d can be provided with the logical switches LOGIC S and LOGIC R of the hardware category GPSS.

10. The generator's macro is similar to the GENERATE block of the dynamic category GPSS.

11. The absorption macro-function is functionally identical to the TERMINATE block of the dynamic category GPSS.

12. The queue macro can be interpreted in GPSS by writing a transaction to the user's circuit.

Thus, the considered representation of models of information system elements in the form N E -cxeM allows to simplify the stage of determining their basic structure. Specifying the model as N E -cxeM allows a fairly simple software implementation of the simulation model for YON or YAM.

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