40 Methods of imitation of the traffic

Possibilities of exact analytical decisions in the teletraffic theory are sometimes limited on ability of carrying out of the analysis of the big dimension in networks of intermedia, control systems of switching with a complex of the strategy of management included in the schedule an overload and managements of routeing etc. Therefore computer modelling can be enclosed to the analytical decision, as alternative approach. Modelling is used not only for those cases when the analytical decision it is not received, but also in those cases where numerical calculations of analytical decisions are complicated. At various stages of planning and management of systems of the teletraffic modelling is used also

1) In the situations explaining problems of the teletraffic to introduce realisation back in system engineering;

2) In the situations estimating realisation to confirm a system applied range;

3) In the situations estimating the answer to an error and overflow to define counter-measures.

For point (1), in system engineering should be more important to receive result quickly and in due time, instead of to spend for nothing time that to the detriment of profit to pursue the aim to receive more split-hair accuracy. Therefore models with the limited scale of imitations are often used. Such models can quickly be under construction and easily change, using imitating language. On the other hand for points (2) and (3), full-scale modelling is required to receive exact characteristics of the traffic for the task of capacity of system.

On fig. 16 process of modelling from planning to a solution of a problem is shown. On the first step the problem is formulated, and in system are specified actions for its implementation (are in detail designated). For example, in a control system of electronic switching of actions of the above-stated specification measurements of time of an establishment of connection and throughput of system are. As soon as the problem is described, the system analysis according to an established order to receive the information for system modelling will follow. The model based on this information, is under construction to solve the put problem. Procedures up to this stage the most important.

After the model is constructed, remains only to transform it to the program for modelling performance. For this process it is necessary to make the reasonable plan for distribution of computing time and memory for the data and programs, according to the computer budget. At modelling performance set time of execution and quantity of operations, especially should be considered if the budget for calculation is limited.

When the imitating result is received, it is used for an estimation of realisation and the system analysis in a question, on what there is a speech. In this process, it is the most important, whether whether to define prospective modelling and correct result is executed is received. The obtained data is used to analyze and estimate system to reach the optimum decision.

The model at imitation should feel abstractly system in the set question, and to be idle time whenever possible to facilitate modelling. Basically two kinds of imitations are considered: continuous and discrete. But traffic modelling is classified as is discrete-casual imitation. On fig. 17 three points of view for modelling at is discrete-casual imitation are shown: event, process and activity.

Depending on the point of view distinguish three cases of modelling: event-oriented modeling, process-oriented simulation, activity-based modeling

At the event-oriented modeling the imitating model is formulated, describing as events, such as generation or end (clearing) of a call, change a system condition. In these cases universal programming languages, such as FORTRAN and PL/1 are used.

When process-oriented simulation the imitating model describes behaviour of the subject (call) existing actually in considered system. Such imitation is called still as subject-oriented modelling, and is applied in cases when imitating languages, such as GPSS and SLAM II, are used for the description of imitating models.

At the activity-based modeling describe time moments инициации and end of activity, such as duration of a call and line employment. It is a corresponding method for modelling of systems at which deduction time depends on a system condition (quantity of existing calls). However as imitation is carried out by detailed consideration of active actions of system time of its execution becomes longer, than at the event-oriented modeling.

Programming is carried out on two classes of languages for modelling: imitating language and universal language. The imitating class includes languages GPSS, SIMSCRIPT and SLAM II, and the universal class includes languages FORTRAN, PL/1 and ALGOL.

Imitating languages contain following functions: generation of random numbers, execution of schedules on time, preservation of the data, the statistical analysis, transformation of a target format. Advantage from use of imitating languages consists in disposal of need to program the functions set forth above, and ease of programming on once formulated protsessno-focused model.

Universal languages more flexible, than imitating languages. Moreover, they can accelerate execution time. The language choice depends on such factors, as convenience of the reference, knowledge of the programmer, model characteristics etc.

The most popular imitating language is GPSS (general purpose simulation system) - universal imitating system. Language GPSS describes the imitating program for the protsessno-focused modelling using about 40 blocks of diagrammes, written by special symbols. Object moving on one step according to the diagramme is called as transaction (transaction) which are linked with each other on one of two chains: a chain of current event and a chain of the future event.

Transactions of a chain of current event, whose planned times of moving are before or about the present exact time, are linked according to an order of a priority or planned time of moving. They cannot be still moved because of some, yet not executed, conditions and remain, expecting moving.

Transactions of a chain of the future event, whose planned times of moving are after the present exact time, are linked as it should be according to moving time.

The universal programming languages used at imitations, realise two methods of execution: a method of the Markovsky chain and a method of tracing (trace) of time.

The method of the Markovsky chain named model of a roulette, directly simulates the Markovsky chain representing conditions of changes of system, advancements not considered in due course forward. The method is based on that fact that the system condition (quantity of calls) raises or decreases for one, thanks to receipt or end (clearing) of a call, accordingly.

The method of a trace of time traces time of epoch in which the call has arrived or has finished employment. Programming of surrounding conditions provides some calendar of events as a breadboard model of the table of events with which will fill in the future. Usually time of receipt of the first call registers in a calendar of events as initial value. During advancement forward imitations time of epoch of receipt of a following call or end of service of calls are defined as a random number, and registers in a calendar. Согласуя the calendar, the program sends exact time to the nearest event and repeats process of execution of imitation.

The method of a trace of time can be considered as any distribution of time intervals and a holding time, and from here this method can be applied to performance of an estimation of the systems including strategy of comprehensive planning.

Though the method of the Markovsky chain is applied only to systems in which condition changes are described by the Markovsky chain, for imitation here it is required to less time and memory of the computer, in comparison with a method of tracing time. Therefore the given method is effective for modelling of systems without a delay, networks representing a speech part.