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Processing correlated traffic in a network node type G/G/1

Keywords:

I.V. Kartashevsky – Ph. D. (Eng.), Associate Professor of Department of Software and Management in Technical Systems, Volga State University of Telecommunications and Informatics (Samara)
E-mail: ivk@psuti.ru
A.V. Saprykin – Engineer, JSC «Concern «Avtomatika» (Moscow)
E-mail: mail@ao-avtomatika.ru


For analysis of the operation of a network node, modeled by the G/G/1 queuing system, the classical queuing theory assumes that the time intervals between incoming requests for service form a sequence of independent random variables. In real conditions confirmed by the collected data of IPTV traffic at the access level and the aggregation level, the distributions of these time intervals may belong to the class of heavy-tailed distributions and have pronounced correlation properties, which seriously complicates the use of the apparatus of the classical queueing theory. To solve this problem we propose, firstly, to approximate the original traffic by some second-order renewal process with a given interval dispersion index, which takes into account the correlation properties of the sequence of inter-arrival time. Secondly, we approximate the initial distribution of intervals by a hyper-exponential distribution with the method of equating the moments while maintaining the specified system utilization coefficient. Similar conversions are performed for the sequence of service time intervals of incoming traffic. As a result, the task of analyzing the G/G/1 queueing system while processing correlated traffic is reduced to the task of analyzing the equivalent system H2/ H2/1 with non-correlated traffic. Finding the average waiting time of the request in the queue in H2/ H2/1 system reduces to solving the Lindley equation by the spectral method. The presented method of G/G/1 queueing system analysis allows to estimate the effect of correlation properties of traffic on average waiting time of an request in a queue.

References:
  1. Sheluxin O.I., Tenyakshev A.M., Osin A.V. Fraktal'ny'e proczessy' v telekommunikacziyax / Pod red. O.I. Sheluxina. M.: Radiotexnika. 2003. 480 s.
  2. Nazarov A.N., Sy'chev K.I. Modeli i metody' rascheta pokazatelej kachestva funkczionirovaniya uzlovogo oborudovaniya i strukturno-setevy'x parametrov setej svyazi sleduyushhego pokoleniya. Krasnoyarsk: Polikom. 2011. 491 s.
  3. Buranova M.A., Samojlov M.S. Issledovanie statisticheskix svojstv mul'timedijnogo trafika // Trudy' 16 j Mezhdunar. konf. «Czifrovaya obrabotka signalov i ee primenenie». M.: 2014. S. 234−236.
  4. Dubniczkij V.Yu., Petrenko O.E. Oczenivanie parametrov raspredelenij Bredforda, Barra i Daguma metodom maksimal'nogo pravdopodobiya // Sistemi obrobki informaczii-2011. № 4(94). S. 126−129.
  5. Klejnrok L. Teoriya massovogo obsluzhivaniya: Per. s angl. pod red. V.I. Nejmana. M.: Mashinostroenie. 1979. 432 s.
  6. Balcioglu B., Jagerman D.L., Altiok T. Merging and splitting autocorrelated arrival processes and impact on queueing performance / Technical report TR-2005-020, Department of Industrial & Systems Engineering, Rutgers University, Piscataway, NJ 08854.
  7. Jagerman D.L., Balcioglu B., Altiok T., Melamed B. Mean Waiting Time Approximations in the G/G/1 Queue // Queueing Systems. 2004. 46. P. 481−506.
  8. Balcioglu B., Jagerman D.L., Altiok T. Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures // IIE Trasactions. 2007. 39. № 10. P. 985−996.
  9. Kartashevskij I.V., Tarasov V.N. Sposoby' approksimaczii vxodny'x raspredelenij dlya sistemy' G/G/1 i analiz poluchenny'x rezul'tatov // Sistemy' upravleniya i informaczionny'e texnologii. 2015. № 3.1(61). S. 182−185.
  10. Koks D., L'yuis P. Statisticheskij analiz posledovatel'nostej soby'tij: Per. s angl. I.A. Maxovoj i V.V. Ry'kova / Pod red. N.P. Buslenko. M.: Mir. 1969. 312 s.
  11. Yanke E., E'mde F., Lyosh F. Speczial'ny'e funkczii (formuly', grafiki, tabliczy'): Per. s nemeczkogo / Pod red. L.I. Sedova. M.: Nauka. 1968. 344 s.
  12. Kartashevskij I.V. Model' trafika dlya programmno-konfiguriruemy'x setej // Radiotexnika. № 6. 2016. S. 124−129.
June 24, 2020
May 29, 2020

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