Simulation of the automated workcenter for a part processing

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Introduction

The manufacturing enterprise consists of a number of shops and production lines. Ensuring rhythm of their work taking into account their interrelation providing effective use of the available resources (machines and the equipment; human resources; raw materials and the completing materials and products, etc.), are the most important task of machine-building enterprise.

Application of mathematical methods is an important condition in the analysis and optimization of work of production structures. The special place among these methods is taken by the device of imitating modeling which allows to build adequate models of the studied objects that, often not in forces to analytical methods because of their big complexity of logical interrelation between elements of system, dynamic and stochastic nature of these interrelations. Often these interrelations can be described only algorithmically. It means, the only way of modeling of such systems is the method of imitating modeling. Imitating models can be applied for:

* researches of borders and structures of system for the purpose of the solution of specific problems;

* definition and the analysis of critical elements, components and points in the studied systems and processes;

* synthesis and an assessment of the proposed solutions;

* forecasting and planning of future development of the studied systems.

Process of imitating modeling begins with definition of the problems which are subject to the decision that in turn defines structure and borders of the studied system. Creation of imitating model of the studied system, though depends on specifics of the solved problem, demands a certain methodological scheme. Imitating language provides the researcher with such scheme, and also carries out broadcast of model in a form, available to the computing system. The computer on which the imitating model is investigated, issues information on behavior of model which then can be analyzed in the course of a solution. There is a set of languages (GPSS, SLAM, GASP, Q-GERT) and systems (TESS, P-Spice, MatLab) imitating modeling which are focused for wide use or concrete subject domain.

Now for world practice of development of technological projects of an assessment of efficiency of technological lines of the enterprises application of methods of imitating modeling for the purpose of optimization of schemes of material streams, structure and characteristics of processing equipment, production layout schemes is characteristic. It is caused by need of ensuring high competitiveness of the enterprises in the market that, in turn, it is possible only at introduction of the modern technologies allowing to reduce considerably terms and to reduce labor input of construction of technological lines.

Application of methodology of imitating modeling allows to make the qualitative analysis and an assessment of efficiency of functioning of the enterprise, to carry out the reasonable technical and economic analysis of options of realization of difficult production systems. The mathematical apparatus of imitating models allows, setting probabilistic characteristics of events and productions, with necessary degree of reliability to model functioning of production systems in various intervals of time.

Process of modeling begins with definition of the purpose of development of model on the basis of which then borders systems and necessary level of specification of the modeled processes are installed. The chosen level of specification has to allow to abstract from is inexact the aspects of functioning of real system defined because of a lack of information. The description of system has to besides include criteria of efficiency of functioning of system and the estimated alternative decisions which can be considered as part of model or as its entrances. Estimates of alternative decisions on the set criteria of efficiency are considered as model exits. Usually the assessment of alternatives demands modification of the description of system and, therefore, reorganization of model. Therefore in practice process of creation of model is iterative. After on the basis of the received estimates of alternatives recommendations can be developed, it is possible to start introduction of results of modeling.

After the end of development of imitating model with it machine experiments which allow to drawing a conclusion on behavior of system are made:

* without its construction if it is the designed system;

* without intervention in its functioning if it is the operating system experimenting with which too expensive, or is unsafe;

* without its destruction if the purpose of experiment consists in definition of limits of impact on system.

Thus, imitating models can be used for design, the analysis and an assessment of functioning of systems. Now imitating modeling is used for research of various systems.

Relevance of the diploma project is characterized by that in many problems of practice direct studying of objects (technical systems or technological processes) is complicated because of complexity of object, high cost or duration of research, absence of object (at a development stage the object still is absent in the nature), difficulties of a task of necessary operating conditions of object (for example, definition of characteristics of processes of transportations in emergency situations) and other reasons.

In such cases for studying of objects modeling - the method of scientific research consisting in replacement of initial object with its model, studying of model and synthesis of the characteristics received in the analysis on object is used.

1. Use of the device of imitating modeling for research of production systems

Improvement of methods of management of production in the conditions of the market is based on increase of efficiency of functioning and the organization of a control system, wide use of modern computer aids and the automated information systems for the analysis of the made decisions and forecasting of development of production, use of scientific approach and world experience to the solution of problems of management.

From the most important functions of management of production it is possible to allocate the following: formation of a portfolio of orders; planning of production in the group and specified nomenclature for various temporary periods; planning and regulation of product cost; analysis of an expense of raw materials and materials; definition of requirement and security with raw materials and materials; adjustment of volumes and product range; completing of parties of shipment of production taking into account a route; control over the implementation of the production program of the enterprise and product sales.

One of the most important and most difficult parts of the general enterprise management system is the system of operational management of production. The objects of its activity are shops of the main and auxiliary production.

Production management represents set of two processes: information and material. Information process is the basic and includes technical training of production, the operational account and control of the course of production and the analysis of performance of plan targets. Material process on an entrance has labor and production resources which in the course of production will be transformed to finished goods at the exit.

Operational management is exercised on the basis of realization of the main functions of management: operational planning, control (account, control, analysis) and dispatching regulation of production. From them functions of operational planning and dispatching regulation in the course of which realization decisions on production management are made are main.

Any operating plan represents some compromise in achievement of the following purposes:

- to execute all orders in time;

- to minimize expenses;

- to provide a production continuity;

- to achieve uniform loading of the equipment.

In the process of planning for each order is defined what equipment will be occupied with its performance in various timepoints. With branched technological process this stage of scheduling is most difficult for large production. Irrational distribution of resources can lead to long lines of works on separate sites, and at this time other equipment will stand idle that finally excludes possibility of implementation of some orders in time. It is most actual when releasing the difficult products consisting of a large number of details, knots, assemblies because of what it is impossible to plan precisely in time release of all components of a product and term of implementation of the order. Therefore quality of development of plans in modern conditions is possible only on the basis of use of the COMPUTER and economic-mathematical methods.

Application of computer facilities significantly changes nature of activity of the administrative personnel of the enterprise and changes a role of the person making the decision. Practice of decision-making shows that the majority of crucial decisions is made not according to the classical scheme, and as a result of dialogue. This purpose is served by the interactive procedures allowing the person making the decision to influence actively preparation and a choice of administrative decisions, and also to carry out imitation real economic and productions at various versions of decisions.

Information system of modeling of production is under construction on the basis of the principle of interactive dialogue of the user with system. Modeling represents interaction of the person, mediate through the interface, making the decision and imitating model of the course of production. It allows it to interfere with modeling process at any moment, to change modeling parameters, to add and exclude the used resources, to cancel carried out and to plan new orders, to estimate the current information on the course of modeling and a condition of system.

The initial stage in work of system is input of initial parameters of functioning of model and information receipt of packages of orders for production of these or those products. Further the structure of each product is defined, and technological routes for each detail, knot or the assembly entering a product with use of information and the structure of a product and stages of technological process which is stored in information base are formed.

The following stage is generation of dynamic objects (tranzakt) for imitating model. Every tranzakt represents a detail, assembly or a product and has the unique number used in model for identification of each component of a product. Tranzakta, belonging to a certain product, are in hierarchical subordination among themselves according to the principle of entry of details into assemblies, assemblies in knots, knots in a product. Therefore, completion of processing of the tranzakt representing a product is impossible, all tranzakta presenting to a detail, the assemblies and knots entering a product won't be processed yet. The logic of functioning of model - ascension from foundation of hierarchical structure of a product to its top is based on this principle. Search of a way, optimum from the point of view of production, and time of passing of this stage also makes the main objective of imitating modeling.

In model of a tranzakta start moving (are exposed to processing), promoting accumulation of information on modeling of the course of production. The received information is exposed to processing, group and generalization for the purpose of its representation in an available look for the person responsible for decision-making.

The model of production is developed according to the principles of event modeling according to which modeling represents continuous process of processing of the events coming in system. Dynamic processes in imitating model of the enterprise it is presented in the form of interaction of a number of components - devices, workers, turns, and events. Time in event imitating model changes jump upon transition from the current event to the subsequent.

The mechanism of action of imitating model consists in the following. Events are distributed in time and performance of one causes performance of the subsequent. Realization of events in time reminds chain reaction. Each event is carried out instantly in time, model time is spent only for transition from an event to an event. Replenishment of the list of future events is carried out during processing of the current event. The control system of model addresses to the list of the planned events ordered on approach time and chooses the first element. Model time becomes equal to time of approach of an event. After performance of the actions connected with the current event, the system carries out transition to the following event etc.

The algorithm described above allows to consider all major factors of production in the course of modeling:

- consumption of material resources;

- existence of a necessary manpower;

- structure of production;

- existence of the necessary equipment and failures in its work;

- emergence of a manufacturing defect;

- temporary delays on readjustment of the equipment;

- expenses of time for transportation of the processed details.

The main criterion of successful functioning of any information system is adequacy of information display in it the relevant real system: the elements entering it, their properties and relationship.

Imitating modeling, as well as any other approach to creation of models of production systems, has the conventions and the principles used for the formal description of real systems.

Usually at the enterprise some types of products are let in, each of which is characterized by the size of party of the order, intensity and dispersion of their receipt, and also the priority defining the importance of this or that product in the general production program of the enterprise. The let-out products consist of a set of the accessories having the following characteristics: a code of this knot or a detail, their total in a product, situation in hierarchical structure of a product and amount of the material used by its production.

In imitating model the enterprise is considered as set of shops - elementary production facilities, each of which is characterized: the production equipment of various types, the materials used in production and number of the working various professions.

Technological process of production of a product represents sequence of operations, for each of which the shop in which it is carried out, type of the necessary equipment, a code of a profession of the worker and his category, time of performance and cost of works is specified. The processing equipment has the following characteristics: accession number, a code of this equipment shop in which it is, the balance cost and percent of wear. Production workers are characterized by organic number, shop in which they work, the qualification determined by their category, and also the list of professions causing the works performed by them.

In the present diploma project proposed two simulation models production process, implemented using an object-oriented language simulation discerning type - GPSS. They are, first and foremost, on the discrete manufacturing systems. This type of production, in particular, is characteristic for the majority of enterprise engineering industry. Developed simulation models production processes is the basis for an information system supporting the decision-making process, which are implemented with the use of contemporary version GPSS - GPSS world.

A number of the input parameters defining features of its work have the developed imitating models. They can conditionally be broken into two groups:

1. the parameters defining receipt of orders for production of each type of products;

2. the parameters considering certain characteristics of production and defining features of functioning of model.

Use of imitating modeling in process of management of production allows to predict behavior and future condition of a production system that significantly increases the accuracy of the developed plans of production. On the other hand the imitating model gives the chance to estimate alternative options of administrative influences, thereby, increasing the qualitative level of the made administrative decisions. It becomes possible thanks to information received in the course of modeling by the person, the making decision on the production course, terms of implementation of orders, load of the equipment and production workers, time of production and necessary financial expenses, volume of a work in progress, prime cost of products, the volume of consumption of materials and accessories, labor costs by types of works etc. On this basis there is possible a detailed prediction and the analysis of consequences of the made administrative decisions.

2. Imitating modeling of the automated site with serial processing of details a detailed prediction and the analysis of consequences of the made administrative decisions

2.1 Problem definition

The automatic transfer production line consists of two machines with numerical program control. The stream of the processed preparations of details arriving to the line represents a Poisson stream. An average interval of receipt of preparations - 110 seconds. The arriving preparations consistently are processed on two machines. Movement of the processed details from the machine to the machine and from the last machine to finished goods warehouse is provided with the robot. It is required to the robot from 14 to 16 seconds on capture or release of the processed detail (time is distributed evenly). Also the robot will need 13 seconds for its movement from a site of arrival of preparations to the first machine. Its movement from the first machine to the second - will require 14 seconds. And at last, its movement from the second machine to finished goods warehouse will require 12 seconds.

Time of processing of details on the first and second machines casual also submits to the normal law. The average time of processing of a detail on the first machine makes 90 seconds with a mean square deviation of 10 seconds, the average time of processing of a detail on the second machine makes 100 seconds with a mean square deviation also of 10 seconds.

It is necessary to simulate work of the production line for the 8-hour working day and to define the following indicators:

1. Number of the arrived preparations of details.

2. Quantity of the made details.

3. Loading of machines and robot.

4. Average time of production of one detail.

To carry out the analysis of "bottlenecks" in the technological scheme, i.e. to define the equipment, reducing rate of production. To find out how the studied characteristics if two robots together one are engaged in movement of details will change.

2.2 Imitating model

We will accept as unit of model time of 1 seconds. The program of modeling on GPSS World will consist of two segments: main segment and segment of a task of time of modeling.

Basic elements of GPSS model and their compliance to real objects are presented in table 1. The imitating model of a production site on GPSS World is presented in table 2.

The main segment of modeling consists of 34 blocks. The second segment (timer) determines duration of run of the program 8 hour (28800 sec.). For start of model we use the command START 1.

At the beginning of the program table parameters for collecting statistics on time of production of details are described.

We will consider purposes of blocks of the main segment of modeling.

1. GENERATE - is generated an entrance stream of preparations.

2. QUEUE - to occupy turn of preparations on an arrival site.

3. SEIZE - to occupy the robot.

4. DEPART - to leave turn of preparations.

5. ADVANCE - the robot takes a detail.

6. ADVANCE - the robot moves to the machine 1.

7. ADVANCE - the robot establishes a detail.

8. RELEASE - to release the robot.

9. QUEUE - to wait in the following turn.

Table 1 - Basic elements of GPSS model and their compliance to real objects

№ p/p	Elements of GPSS	Corresponding object
1.	Tranzkts: Segment 1 Segment 2	The processed details Timer
2.	Single-channel devices: Mashine1 Mashine2 Robot	Mashine1 Mashine2 Robot
3.	Queue: One Two Three Four Five	Turn of preparations for capture or release by their robot and for their movement from an arrival site to the first machine Turn of details for processing on the first machine Turn of the processed preparations for movement by their robot from the first machine to the second Turn of details for processing on the second machine Turn of ready details for movement by their robot from the second machine to finished goods warehouse
4.	Table: Transit	The table for collecting statistics on time of processing of details

1. SEIZE - to occupy the first machine.

2. DEPART - to leave turn.

3. ADVANCE - processing time on the first machine.

4. RELEASE - to release the machine 1.

5. QUEUE - to get in line.

6. SEIZE - to borrow the robot.

Table 2 - the GPSS program for modeling of the production line

The used GPSS elements
№ p/p	Identifier	Elements of GPSS	Operand
1.	Transit	TABLE	(Exponential(1,0,110))
Segment 1. Main segment of modeling
№ p/p	Tag	Block	Operand
1.		GENERATE	(Exponential(1,0,110))
2.		QUEUE	One
3.		SEIZE	Robot
4.		DEPART	One
5.		ADVANCE	15,1
6.		ADVANCE	13
7.		ADVANCE	15,1
8.		RELEASE	Robot
9.		QUEUE	Two
10.		SEIZE	Machine1
11.		DEPART	Two
12.		ADVANCE	(Normal(1,90,10))
13.		RELEASE	Machine1
14.		QUEUE	Three
15.		SEIZE	Robot
16.		DEPART	Three
17.		ADVANCE	15,1
18.		ADVANCE	14
19.		ADVANCE	15,1
20.		RELEASE	Robot

1. DEPART - to leave turn.

2. ADVANCE - the robot takes a detail.

3. ADVANCE - the robot moves to the machine 2.

4. ADVANCE - the robot establishes a detail.

5. RELEASE - to release the robot.

6. QUEUE - to get in line to the machine 2.

7. SEIZE - to occupy the machine 2.

8. DEPART - to leave turn

9. ADVANCE - processing on the machine 2

10. RELEASE - to release the machine 2

11. QUEUE - to get in line of finished products.

12. SEIZE - to borrow the robot.

13. DEPART - to leave turn.

14. ADVANCE - the robot takes products.

15. ADVANCE - the robot moves to an exit.

16. ADVANCE - the robot establishes a product.

17. RELEASE - to release the robot.

18. TABULATE - collecting statistics.

19. TERMINATE - a detail is processed.

20. GENERATE - to set the timer.

21. TERMINATE - the end of modeling.

22. START - to begin modeling.

2.3 Results of modeling

In 8 hour working day 258 preparations for processing came to the production line, from them were processed - 202. Duration of production of one detail averages 3161 seconds. The greatest waiting time is made in the first (990 seconds), the third (1013 seconds) and a heel (1022 seconds) turns. Thus the robot is strongly loaded (98,6%). Load of machines is made by 73,6% and 76,5%, respectively. Thus, "bottleneck" in the technological scheme is the robot, because of that that it doesn't manage to serve, turns are formed.

We will consider a service case two robots. For this purpose in model we will present the robot in the form of the two-channel device and together SEIZE and RELEASE blocks we will use ENTER and LEAVE blocks, respectively. We will set number of robots the STORAGE team. In this case the full standard report on results of modeling has the Appendix B appearance.

The analysis of results of modeling in the second case shows that duration of production of one detail decreases till 512 seconds, i.e. almost by 6 times. From 256 preparations which came to the production line were processed - 249. Thus loading of robots makes 56,5%, and loading of machines made 79,2% and 85,9%, respectively.

3. Imitating modeling of the automated site with parallel processing of details

3.1 Problem definition

Preparations of details of two types on the conveyor 1 come to a production site. The robot 1 removes preparations from the entrance conveyor and depending on their types gives or to the conveyor 2 (preparation of details of the 1st type), or to the conveyor 3 (preparation of details of the 2nd type). Preparations of details of the 1st type are processed on the machine 1, and details 2 - on the machine 2.

The following basic data are set:

1. The interval of receipt of preparations on the entrance conveyor (conveyor 1) submits to the uniform law in the range from 8 till 12 minutes. The arriving preparation can be preparation of a detail 1 or details 2 are equal.

2. Loading capacity of the entrance conveyor is 5 preparations. The conveyor counter counts number of the transported preparations. If the number of the preparations transported by the conveyor equally 10, the next arriving preparation expects the turn.

3. Time of transportation of preparation by the conveyor 1 makes 2 minutes.

4. The robot 1 takes preparation of a detail from the entrance conveyor, distinguishes its type, and depending on its type, gives it either to the conveyor 2, or to the conveyor 3. Delivery time the robot of 1 preparation to conveyors 2 and 3 makes 15 seconds.

5. Time of transportation of preparation by the conveyor 2 to the machine 1 makes 8 minutes, and the conveyor 3 to the machine of 2 - 4 minutes. Loading capacity of conveyors 2 and 3 is made by 5 preparations. In case of excess of loading capacity of the conveyor 2 or 3 the robot 1 leaves preparation in the conveyor 1 until there is a number of preparations in the conveyor less than five.

3.2 Imitating model

We will accept as unit of model time of 1 seconds. The program of modeling on GPSS World will consist of two segments: main segment and segment of a task of time of modeling.

Basic elements of GPSS model and their compliance to real objects are presented in table 3. The imitating model of a production site on GPSS World is presented in table 4.

Table 3 - Basic elements of GPSS model and their compliance to real objects

№ p/p	Elements of GPSS	Corresponding object
1.	Tranzakts: Segment 1 Segment 2	Requests of users Timer
2.	Parameters: P1	Type of the processed detail
3.	Single-channel devices: Mashine1 Mashine2 Robot 1 Robot 2 Robot 3	Mashine 1 Mashine 2 Robot 1 Robot 2 Robot 3
4.	Multichannel devices: Conv1 Conv2 Conv3	Conveyer 1 Conveyer 2 Conveyer 3
5.	Queue: Conveyor1	Entrance turn of preparations
6.	Table: ProsTime	The table for collecting statistics on time of processing of details

Table 4 - The GPSS program for modeling of a production site

The used GPSS elements
№ p/p	Identifier	Elements of GPSS	Operand
1.	Conv1	STORAGE	5
2.	Conv2	STORAGE	5
3.	Conv3	STORAGE	5

The main segment of modeling consists of 38 blocks. The second segment (timer) determines duration of run of the program 8 hour (28800 sec.). For start of model we use the command START 1.

At the beginning of the program capacities of three conveyors are described. We will consider purposes of blocks of the main segment of modeling.

1. GENERATE - is generated an entrance stream of preparations (all numerical data are translated in seconds).

2. ASSIGN - the first parameter of a tranzakt is used for definition like detail, the first type of details is set.

3. TRANSFER - type of details can be equal.

4. ASSIGN - is set the second type of details.

5. QUEUE - preparations occupy entrance turn.

6. ENTER - preparations occupy the entrance conveyor.

7. DEPART - preparations leave the entrance conveyor.

8. ADVANCE - imitation of time of advance on the entrance conveyor.

9. TEST E - check like details.

10. ENTER - if the first type, preparation will be directed on the conveyor 2.

11. ADVANCE - imitation of advance on the conveyor 2.

12. TRANSFER - unconditional transition.

13. ENTER - an entrance to the conveyor 3.

14. ADVANCE - imitation of advance on the conveyor 3.

15. LEAVE - releases of the conveyor 1.

16. SEIZE - to occupy the robot 1.

17. ADVANCE - imitation of operating time of the robot 1.

18. RELEASE - to release the robot 1.

19. TEST E - definition like detail.

20. GATE NU - check of an unemployment of the machine 1.

21. LEAVE - to leave the conveyor 2.

22. SEIZE - to borrow works 2.

23. ADVANCE - imitation of operating time of the robot 2.

24. RELEASE - to release the robot 2.

25. SEIZE - to occupy the machine 1.

26. ADVANCE - imitation of processing on the machine 1.

27. RELEASE - to release the machine 1.

28. TRANSFER - unconditional transition.

29. GATE NU - check of an unemployment of the machine 2.

30. LEAVE - to leave the conveyor 3.

31. SEIZE - to borrow works 3.

32. ADVANCE - imitation of operating time of the robot 3.

33. RELEASE - to release the robot 3.

34. SEIZE - to occupy the machine 2.

35. ADVANCE - imitation of processing on the machine 2.

36. RELEASE - to release the machine 2.

37. TABULATE - collecting statistics on results of modeling.

38. TERMINATE - the processed detail leaves a production site.

39. GENERATE - start of the timer.

40. TERMINATE - the counter of completion of modeling.

41. START - to begin modeling.

3.3 Results of modeling

In 8 hour working day I came to a site 48 details, from them only 25 were processed. At the time of the end of modeling were in all conveyors on 5 preparations. And in entrance turn also there were 5 preparations.

The equipment are loaded as follows:

- conveyer 1 - 51,0%;

- conveyer 2 - 31,4%;

- conveyer 3 - 75,2%;

- robot 1 - 2%;

- robot 2 - 0,3%;

- robot 3 - 0,2%;

- machine 1 - 93,3%

- machine 2 93,9%.

The detail is on average made 7707/60=128 minutes, i.e. during over two hours. The full standard report on results of modeling is submitted in Appendix A.

The analysis shows, "bottleneck" in the technological scheme is productivities of machines.

We will consider a case of double increase in productivity of machines. In this case the full standard report on results of modeling has the Appendix B appearance.

Results of modeling show that all conveyors are empty (there are no intermediate accumulation), also the entrance turn is also empty. From 46 arrived details 42 are processed. Other 4 details at the time of the end of modeling were in processing by machines and robots. The average time of production of a detail decreased till 2939/60=48 minutes.

Conclusion

imitating modeling program mathematical

In the diploma project questions of development of imitating means of an assessment of efficiency of functioning of technological lines of productions are considered. The developed imitating models allow to carry out an assessment of quality of functioning of the studied productions, to carry out the reasonable technical and economic analysis of options of realization of difficult production systems.

All basic data when modeling are taken on the example of concrete production companies. The developed imitating models allow to estimate important parameters of production and technological processes and can be used for improvement of the studied processes. In particular are estimated: useful loading of equipment, average time of duration of this or that process and number of necessary resources (for example, installations, equipment). Making numerous imitating experiments at various parameters and methods of the organization of processes, the developed models allow to carry out the analysis as the existing methods of the organization of work of shops, and to make recommendations about its improvement.

The list of the used literature

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2. V.D Sypchenko R.P Fights. Computer modeling. Elements of the theory and practice. Studies. grant. - SPb.: Military academy of communication, 2009. - 432 pages.

3. Brazhnik A.N,. Imitating modeling: possibilities of GPSS World. - SPb.: Reputation, 2006. - 439 pages.

4. Varzhapetyan A.G. Imitating modeling on GPSS/H. Manual. - SPb.: St. Petersburg State University of space instrument making, 2007. - 384 pages.

5. Kudryavtsev E.M. GPSS World. Bases of modeling of various systems. Manual. - M.: DMK Press, 2004. - 320 pages.

6. Kurmanov B.K. Sistem of program imitating modeling of GPSS. Methodical instructions to performance of independent work of students. - Almaty: КазПТИ, 1987. - 32 pages.

7. Kurmanov B.K., Kurmanov G.B. Development of imitating models on GPSS World. Manual. - Almaty: Publishing center JSC LBTU, 2011. - 221 pages.

8. Litvinov V.V., Maryanovich T.P. Methods of creation of imitating systems. Kiev: Naukova Dumka, 1991. 120 pages.

9. Maksimey I.V. Imitation of modeling on the COMPUTER. M.: Radio and communication, 1988. 232 pages.

10. Manual on modeling on GPSS/PC. Under Yakimov I.M. edition. - Kazan, 1989. - 230 with.

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