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Avtomat. i Telemekh., 2018, Issue 12, Pages 57–70 (Mi at15223)  

Stochastic Systems

Extension of the class of queueing systems with delay

V. N. Tarasov

Povolzhskiy State University of Telecommunications and Informatics, Samara, Russia

Abstract: We consider the problem of determining the characteristics of queuing systems with delay by the classical spectral decomposition method for the solution of the Lindley integral equation. As input distributions for the systems we choose mixtures of exponential distributions shifted to the right of the zero point, for which the spectral decomposition approach allows one to obtain a solution in closed form. We show that in such systems with delay, the average waiting time is shorter than in conventional systems.

Keywords: system with delay, QS $H_2/H_2/1$, $H_2/M/1$, $M/H_2/1$, Laplace transform, average waiting time in the queue.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-29-09639__
This work was supported in part by the Russian Foundation for Basic Research, project no. 16-29-09639.


DOI: https://doi.org/10.31857/S000523100002857-6

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English version:
Automation and Remote Control, 2018, 79:12, 2147–2158

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Presented by the member of Editorial Board: . . 

Received: 18.11.2015

Citation: V. N. Tarasov, “Extension of the class of queueing systems with delay”, Avtomat. i Telemekh., 2018, no. 12, 57–70; Autom. Remote Control, 79:12 (2018), 2147–2158

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