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

Wei Xu, Liwei Liu (), Linhong Li, Zhen Wang and Sabine Wittevrongel
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Wei Xu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
Liwei Liu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
Linhong Li: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
Zhen Wang: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
Sabine Wittevrongel: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University, B-9000 Gent, Belgium

Mathematics, 2023, vol. 11, issue 16, 1-23

Abstract: 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.

Keywords: retrial G-queue; finite source; collisions; transmission errors; reliability indices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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