Assessment of stationary middle earth in system with related priorities

DOI №______

Abstract

A system M|GJ|1|∞ with relative priorities is considered. In the case of continuous priorities, the minimum value of the stationary average queue is obtained if the priorities are arranged in the order of increasing average requirement lengths. In the M|GJ|1|∞ system, without interruption of service, the discipline of preferential service of the shortest requirement without service interruption is optimal in the sense of minimizing the stationary average queue. The problem of finding the lower estimate of the stationary average waiting time for the commencement of the maintenance of the requirement in the discipline of the priority service of the shortest requirement without interrupting the service for the given first and second moments of the length of the requirement is considered. To solve this problem, the methods of the calculus of variations are used. Based on the results obtained, a comparison is made between the stationary average waiting time for the commencement of maintenance of the priority service discipline of the shortest requirement without interrupting the maintenance with the FIFO discipline. The maximum benefit from using the discipline of preferential maintenance of the shortest requirement without interrupting maintenance is obtained at large second moments of the requirements lengths. With small loads, the discipline of preferential servicing of the shortest requirement without interrupting the maintenance of the win in comparison with the FIFO discipline practically does not.

Keywords: system; requirement; queue; time; priority; expectation; length; service; interrupt; evaluation.

References
1. Толубко В. Б., Беркман Л. Н. Методи оптимізації. Київ: ДУТ, 2016. 442 с.
2. Стеклов В. К., Беркман Л. Н. Телекоммуникационные сети. Київ: Техніка, 2000. 392 с.
3. Интеллектуальные сети связи / Б. Я. Лихтциндер, М. А. Кузякин, А. В. Росляков, С. М. Фомичев. Москва: Эко-Трендз, 2000. 205 с.