Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

Lee, Se Won; Kim, Bara; Kim, Jeongsim

doi:10.1007/s10479-020-03717-2

Cited by 8 publications

(4 citation statements)

References 15 publications

(18 reference statements)

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“…Substituting decomposition (17) in (18), taking ε → 0 and after performing some actions on the equations, we get the following system:…”

Section: Asymptotic Analysis Of the Number Of Returns Of The Tagged Rmentioning

confidence: 99%

“…The waiting time distribution, the time a request spends in the orbit, is very complicated problem in the retrial queue system theory. Different approaches to the investigation of the waiting time can be found in Artalejo, Chakravarthy, Lopez-Herrero [1], Artalejo, Gomez-Corral [4], Choi, Chang [6], Falin, Artalejo [8], Gharbi, Dutheillet [14], Sudyko, Nazarov, Sztrik [27], Tóth, Bérczes, Sztrik [28], Zhang, Feng, Wang [29] for finite retrial group of sources and Chakravarthy, Dudin [7], Falin, Fricker [9], Falin [1,10,12], Gomez-Corral, Ramalhoto [15], Neuts [20], Nobel, Tijms [25], Lee, Kim, Kim [18] for infinite number of sources.…”

Section: Introductionmentioning

confidence: 99%

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Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

Nazarov

Samorodova

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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In our paper, the waiting time analysis of a M/M/1 retrial queueing system is presented and the asymptotic distribution of the number of returns of the tagged request to the orbit is driven since they are connected to each other. The research was conducted by the use of asymptotic analysis method. Two different cases are considered. First we conduct analysis under a heavy load condition and then under a low rate of retrials condition. Two different characteristic functions of the waiting time were obtained. The analysis was carried out using asymptotic distributions of the number of requests in the orbit under a heavy load condition and a low rate of retrials condition, which were also obtained. To show the effectiveness of asymptotic results for the considered retrial queuing system, the approximation of the distribution of the number of returns of the tagged request to the orbit in prelimit situation, numerical illustrations and results are given. Keywords: Retrial queue • Asymptotic analysis • Waiting time • Number of returns • Number of retrials

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“…Substituting decomposition (17) in (18), taking ε → 0 and after performing some actions on the equations, we get the following system:…”

Section: Asymptotic Analysis Of the Number Of Returns Of The Tagged Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

Nazarov

Samorodova

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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“…Ayyappan and Gowthami [10] performed a stationary analysis of a feedback retrial queue with impatient customers, vacations, and two types of arrivals. Lee et al [11] analyzed the waiting time distribution of a two-way communication retrial queue. Sztrik et al [12] examined the unreliable operation of a finite-source two-way communication retrial queue and compared the different distribution of failure time on performance measures.…”

Section: Introductionmentioning

confidence: 99%

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Liu,

Chiou,

Chen

et al. 2024

Mathematics

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This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

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“…Here source host and the destination host are arrivals and servers, respectively. More applications of retrial queueing models with breakdown can be seen in Upadhyaya ( 2014 ), Kim and Kim ( 2016 ), Taleb and Aissani ( 2016 ), Lan and Tang ( 2020 ), Lee et al ( 2020 ), Dragieva and Phung-Duc ( 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Optimization of a stochastic model having erratic server with immediate or delayed repair

Agarwal

Upadhyaya

et al. 2022

Ann Oper Res

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The thought to put forward a queuing model proposed in this work was its pertinence in everyday life wherever we can see the uses of computing and networking systems. Industrial software developers and system managers can consider the results of the model to evolve their system for better results. Here we present a novel queueing model having erratic server with delayed repair and balking. Two distinct breakdowns i.e. active and passive breakdown for the system are also considered with their respective amendments. This model is closely related with the smooth functioning of the system during some internal faults (virus attack, electricity failures etc.). The performance indicators which are utilized in enhancing the service standards are obtained using supplementary variable technique. Using ANFIS soft computing technique we have compared the analytical results with those of neuro fuzzy results. Furthermore single and bi-objective minimization problems are considered and minima is obtained using particle swarm optimization and multi objective genetic algorithm respectively. Also, the minimization problems are shown as a convex programming problem to ensure the global optimality of the result. The proposed approach makes it conceivable to accomplish a relevant harmony between operational expenses and administration quality.

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Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

Cited by 8 publications

References 15 publications

Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

Optimization of a stochastic model having erratic server with immediate or delayed repair

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