Queueing systems

General terms

1. Model is a material or abstract object which substitutes an original object in the research (studying) process, preserving some important and typical characteristics and features for investigation

2. Modelling/modeling is a process where one object (the original) is substituted another one (the model) and fixes the original object’s characteristics by means of studying model characteristics without depicting time parameters (не перепутаны ли original и model? Здесь выходит, что оригинал заменяет модель, как и в следующем определении)

3. Simulation is a process where one object (the original) is substituted another one (the model) and fixes the original object characteristics by means of studying model characteristics with depicting time parameters

4. Modeling boundary is the width of coverage of subject area and depth of detailed elaboration

5. Verification (validity, checking) is the act of reviewing, inspecting or testing in order to establish and document that a product, service or system meets regulatory or technical standards

6. Adequacy is the degree/measure of conformity/correspondence of a model to the original object, which we obtained in the process of model investigation, testing tasks and experiments

7.1 Modeling target (purpose, aim, objective, goal) 1 is the rule and/or the idea of model development

7.2 Modeling target 2 The modeling target is defined from answers to the following questions:

1. Why this process should be simulated?

2. What should the model show?

3. What can the client receive?

Conditions

9. Hierarchy means classifications which are made with regard to rank, importance, seniority, power status or authority. Hierarchy is simply an ordered set or graph

10. Open model is a model that takes into account the interaction of the simulated object with its environment (external relations), in contrast to the closed model, where such ties are not taken into account (cf. open system).

11. Closed model is a model that has no inputs and outputs (or they recognized the same and therefore not taken into account in the analysis). Thus, a system that is modeled, is adopted as if isolated from the external environment (such a system is called closed or closed).

12. Dynamic model describes the behaviour of a distributed parameter system in terms of how one qualitative state can turn into another. A qualitative state is described by a static model, i.e. the distributions and intersections of the qualitative fields at a particular time instant or interval

13. Static model describes the structure of a distributed parameter system, i.e. its state at a specific time instant

14. Deterministic model is a model in which outcomes are precisely determined through known relationships among states and events, without any room for random variation

15. Stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s)

16. Stable model means that after introducing disturbances into such system it returns to the equilibrium/initial state

17. Unstable system means that after introducing disturbances into such system it moves away from the equilibrium

18. Analytical models are mathematical models that have a closed form solution, i.e. the solution to the equations used to describe changes in a system can be expressed as a mathematical analytic function under any initial conditions

19. Numerical models are mathematical models that use some sort of numerical time-stepping procedure to obtain the model’s behaviour over time. The mathematical solution is represented by a generated table and/or a graph under fixed initial conditions

20. Simulation model is a mathematical model that calculates the impact of uncertain inputs and decisions we make on outcomes that we care about, such as profit and loss, investment returns, environmental consequences, and the like. Such a model can be created by writing code in a programming language, statements in a simulation modeling language, or formulas in a Microsoft Excel spreadsheet. Regardless of how it is expressed, a simulation model will include:

1. Model inputs that are uncertain numbers – we'll call these uncertain variables

2. Intermediate calculations as required

3. Model outputs that depend on the inputs – we'll call these uncertain functions

Ideal model

22. Material model or physical model is a smaller or larger physical copy of an object. The object being modeled may be small (for example, an atom) or large (for example, the Solar System)

Petri nets

23. Place is a base structural element of Petri net which is depicted on a graph as a circle

24. Edge is a base structural element of Petri net which is depicted on a graph as an arrow

25. Token is an element which will be processed/serviced in the Petri net

26. Transition is a base structural element of Petri net which is depicted on a graph as a vertical bar/line

27. Marking is represented on a graph with tokens

28. Firing a transition means an action which shows a process

29. Net is an interconnection of objects in space

30. Graph is a view/type/kind of model representation

Queueing systems

31. Queue isa rule according to which each service chooses an entity for processing (FIFO, LIFO, priority queue)

32. Service is a processing unit associated with the queue. It has a definite time of entity processing

33. Generator creates arriving entities in the model and the time of arrival

Arena

Arena

Chance

36. Schedule is a timetable diary

37. Flowchart modules are sets of objects that are placed in the model window to describe the simulation process

38. Data modules are sets of objects in the spreadsheet view of the model that define the characteristics of various process elements, such as resources and queues

39. Entity is an element which will be processed/serviced in the Arena’s model

Delay

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