S.A. Bukashkin - Dr. Sc. (Eng.), Professor, Member of Russian Cryptography Academy, General Designer, JSC «Concern «Avtomatika» E-mail: mail@ao-avtomatika.ru V.G. Kartashevskiy - Dr. Sc. (Eng.), Professor, Head of Department «Multiservices Networks and Information Security», Volga State University of Telecommunications and Informatics (Samara) E-mail: kartash@psati.ru A.V. Saprikin - Deputy Commander of Military Unit (Moscow)

The paper provides an analysis of the average waiting time in the queue for the application of special purpose node network, the si-mulated system G/D/1. It is assumed that one of the parameters input to the processing traffic is known accurately. In the analyzed traffic random intervals of time between the receipt of applications at the service of independent and have a Pareto distribution. The value of the Pareto distribution forms known inaccurately and belongs to some interval. Solution of the problem is reduced to finding a certain averaged probability density obtained under the assumption that all values are equally likely form parameter in this range. Pareto distribution averaging is made in two versions - with discrete and continuous change in the shape parameter. Calculation of the average waiting time in the queue and the application is carried out in two variants. In a first embodiment, the cal-culation is based on the introduction of the concept of «remaining time» of a random variable, which is the duration of the free state of the system. In the second embodiment, the average waiting time is found by solving the equation Lindley spectral method. To simplify the solution of the equation Lindley used approximation averaged Pareto probability density of the sum of decaying expo-nential. It is also used by the replacement of some non-linear polynomial in the spectral plane of the line, but a higher order. Comparison of the two options the average waiting time in the queue calculation application showed a satisfactory agreement between the results.

 

1. SHelukhin O.I., Tenjakshev A.M., Osin A.V. Fraktalnye processy v telekommunikacijakh / Pod red. O.I. SHelukhina. M.: Radiotekhnika. 2003. 480 s.
2. Klejjnrok L. Teorija massovogo obsluzhivanija: Per. s angl. pod red. V.I. Nejjmana. M.: Mashinostroenie. 1979. 432 s.
3. Goncharenko V.A. Analiz reaktivnosti uzla vychislitelnojj seti v uslovijakh intervalnojj neopredelennosti // Izvestija VUZov. Ser. Priborostroenie. 2008. T. 51. № 7. S. 34−39.
4. Kuznecov V.P. Intervalnye statisticheskie modeli. M.: Radio i svjaz. 1991. 352 s.
5. Klejjnrok L. Vychislitelnye sistemy s ocheredjami: Per. s angl. pod red. B.S. Cybakova. M.: Mir. 1979. 600 s.
6. Gradshtejjn I.S., Ryzhik I.M. Tablicy integralov, summ, rjadov i proizvedenijj. M.: Nauka. 1971. 1108 s.
7. Spravochnik po specialnym funkcijam / Pod red. M. Abramovica i I. Stigan / Per. s angl. pod red. V.A. Ditkina i L.N. Karmazinojj. M.: Nauka. 1979. 832 s.
8. Greshilov A.A. Nekorrektnye zadachi cifrovojj obrabotki informacii i signalov. M.: Radio i svjaz. 1984. 160 s.
9. Blatov I.A., Kartashevskijj V.G., Kireeva N.V., CHupakhina L.R. Metod approksimacii proizvolnojj plotnosti raspredelenija summami ehksponent // Vestnik VGU. 2013. № 2. S. 53−57.
10. Blatov I.A., Kartashevskijj V.G., Kireeva N.V., CHupakhina L.R. Reshenie uravnenija Lindli spektralnym metodom dlja sistem massovogo obsluzhivanija obshhego vida // EHlektrosvjaz. 2014. № 11. S. 48−50.