Retrial Queues with Unreliable Servers and Delayed Feedback

Melikov, Agassi; Aliyeva, Sevinj; Sztrik, János

doi:10.3390/math9192415

Cited by 7 publications

(2 citation statements)

References 19 publications

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“…Rajadura [15] investigated an unreliable M/G/1 retrial queue with feedback and vacations. Melikov [16] developed an approximate method based on the space merging approach to examine unreliable multiserver retrial queues with delayed feedback. Lakaour [17] considered the transmission errors and collisions in an unreliable retrial queuing system.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors

Liu

et al. 2023

Mathematics

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This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators.

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Section: Introductionmentioning

confidence: 99%

Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors

Liu

et al. 2023

Mathematics

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“…The effects of negative customers considered in these papers are close to the effect of breakdowns. Retrial queues with breakdowns have been studied in References [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Resource Retrial Queue with Two Orbits and Negative Customers

et al. 2022

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In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measures.

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