Comparative Analysis of Two Queuing Systems M/He2/1 With Ordinary and With the Shifted Input Distributions

Тарасов, В. Н.; Бахарева, Н. Ф.

doi:10.15588/1607-3274-2019-4-5

Cited by 4 publications

(3 citation statements)

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“…The study of polynomial (7) with coefficients (6) using the Vietta formulas confirms the presence of two negative real roots as well as three positive real roots or one positive and two complex conjugate roots with positive real parts. The study of the sign of the least coefficient 0 0 c > of the polynomial (9) shows that it is always in the case of a stable system when 0 ρ / 1 μ λ < = τ τ < . In the general case, the presence of such roots follows from the existence and uniqueness of the spectral decomposition [1] or factorization [4].…”

Section: Methodsmentioning

confidence: 99%

“…Finally, the average wait time for the HE 2 /H 2 /1 system Thus, for the average waiting time in the QS HE 2 /H 2 /1, the solution in closed form (10) is obtained. From the expression (9), if necessary, you can also determine the moments of higher orders of the waiting time, for example, the second derivative of the transformation (9) , which allows you to determine the dispersion of the waiting time. Given the definition of jitter in telecommunications as the spread of the waiting time around its average value [12], we will thereby be able to determine jitter through dispersion.…”

Section: Methodsmentioning

confidence: 99%

“…, and in [8] -on systems with a delay based on the QS HE 2 /M/1. Article [9] presents the results for a system with a delay M/HE 2 /1, and article [10] summarizes the results for eight systems with a delay in time.…”

Section: Review Of the Literaturementioning

confidence: 99%

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Controlled Queueing Systems G/G/1 with Time Shift

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Delay Models Based on Systems With Usual and Shifted Hyperexponential and Hypererlangian Input Distributions

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Context. In the queueing theory, the study of systems with arbitrary laws of the input flow distribution and service time is relevant because it is impossible to obtain solutions for the waiting time in the final form for the general case. Therefore, the study of such systems for particular cases of input distributions is important. Objective. Getting a solution for the average delay in the queue in a closed form for queuing systems with ordinary and with shifted to the right from the zero point hyperexponential and hypererlangian distributions in stationary mode. Method. To solve this problem, we used the classical method of spectral decomposition of the solution of the Lindley integral equation. This method allows to obtaining a solution for the average delay for two systems under consideration in a closed form. The method of spectral decomposition of the solution of the Lindley integral equation plays an important role in the theory of systems G/G/1. For the practical application of the results obtained, the well-known method of moments of probability theory is used. Results. For the first time, a spectral decomposition of the solution of the Lindley integral equation for systems with ordinary and with shifted hyperexponential and hyperelangian distributions is obtained, which is used to derive a formula for the average delay in a queue in closed form. Conclusions. It is proved that the spectral expansions of the solution of the Lindley integral equation for the systems under consideration coincide; therefore, the formulas for the mean delay will also coincide. It is shown that in systems with a delay, the average delay is less than in conventional systems. The obtained expression for the waiting time expands and complements the wellknown incomplete formula of queuing theory for the average delay for systems with arbitrary laws of the input flow distribution and service time. This approach allows us to calculate the average delay for these systems in mathematical packages for a wide range of traffic parameters. In addition to the average waiting time, such an approach makes it possible to determine also moments of higher orders of waiting time. Given the fact that the packet delay variation (jitter) in telecommunications is defined as the spread of the waiting time from its average value, the jitter can be determined through the variance of the waiting time.

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Comparative Analysis of Two Queuing Systems M/He2/1 With Ordinary and With the Shifted Input Distributions

Cited by 4 publications

References 0 publications

Teletraffic Model Based on He2/H2/1 Systems With Ordinary and With Shifted Input Distributions

Teletraffic Model Based on He2/H2/1 Systems With Ordinary and With Shifted Input Distributions

Controlled Queueing Systems G/G/1 with Time Shift

Delay Models Based on Systems With Usual and Shifted Hyperexponential and Hypererlangian Input Distributions

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