28 Models with a priority

In practice the certain class of calls is sometimes set to improve degree of service GOS(Grade of Service- класс обслуживания) on comparisons with other classes. For example, in the operating system of the computer operating group of calls and time division of service (TSS) of own operations, it is required to have for TSS operations higher priority over maintenance of interactive process. Similar models appear even in electronic switching and computer systems. Distinguish two kinds of a priority: external (associates with a call before input in system) and internal (associates with a call after input in system) priorities with reference to a system situation.

It is necessary to study typical examples of an external priority (model with the right of priority to a priority and model without the right of priority), indicators of quality of their work.

The law of preservation of work of model M/G/1 means that the specific general waiting time is a constant proportional to the general offered loading r0 and average residual holding time W0, and does not depend on appointment of a priority among classes.

29 Models with multidimensional transport loading

The multidimensional traffic is defined as calls with the various characteristics dividing the general resources of system. Examples include the mixed traffic of speech signals and data flows with various speeds of transfer (or width of a frequency range), dividing the general group of channels of transfer. It is necessary to familiarise with multidimensional system with losses in which calls are served низкоскоростные (given) and high-speed (voice). To explain the reason of occurrence of effect of crushing of the channel.

The system of linear reservation is used to guarantee grade of service GOS(Grade of Service- класс обслуживания) of the preferential traffic at the expense of reservation of certain number of lines under the given traffic. Study system of linear reservation and familiarise with a numerical method of the analysis of systems with the delay, using the scheme of linear reservation for two classes of the traffic: priority (high-speed calls) and ordinary (низкоскоростные calls) the traffic.

Familiarise with algorithm of iterative calculation of probabilities of a steady condition at performance of individual measurements of indicators of quality of system: average of expecting calls, probability of blocking (probability of overflow of the buffer) and an average waiting time for priority and ordinary calls.

30 Mixed systems with losses and with expectation

Systems with the integrated calls, such as a voice demanding of service in real time, and also the delayed calls like the data, are called as the mixed systems with losses and with expectation. Such systems are integrated in networks ISDN(Integrated Services Digital Network- цифровая сеть с интеграцией служб), where various media divide network resources.

Indicators of quality of mixed system M1+M2/s (0, ¥) are the interconnected losses and average time expectation. It is necessary to familiarise with the given interrelation, to learn to count structural parametres of such systems on the set loadings and to solve a return problem, i.e. to count demanded loading on the set losses and an average waiting time.

Systems GI+M/s (¥, 0) and GI+M/s (0, ¥) pay off about use of so-called pulsing approximation GI. It is known that association of two pulsing streams, generally speaking, does not form pulsing process. At the same time a target stream dare to approximate pulsing approximation. Thus receive analytical decisions (probability of blocking and an average waiting time).