Analysis of $$MAP, PH_{2}^{OA}/PH_{1}^{I}, PH_{2}^{O}/1$$ retrial queue with vacation, feedback, two-way communication and impatient customers

Ayyappan, G.; Gowthami, R.

doi:10.1007/s00500-020-05318-4

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…We can rewrite Equations ( 1)- (10) in the matrix form as ΠQ = 0 and ∑ ∞ n=0 Π(n)e = 1, where 0 and e represent a row and a column vector with an appropriate size with all zero and all one entries, respectively.…”

Section: Stationary Distributionmentioning

confidence: 99%

“…In such systems, the server's utilization is always a critical issue; for an example, see [6][7][8][9]. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Stationary Distributionmentioning

confidence: 99%

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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“…Ayyappan and Gowthami [16] considered a queueing model along with the arrival types, such as incoming and outgoing calls. Customers who appear on the system under the MAP make incoming calls, and the server makes outgoing calls during idle time.…”

Section: Literature Reviewmentioning

confidence: 99%

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

et al. 2021

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This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

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Asymptotic Analysis of RQ-System with Feedback and Batch Poisson Arrival Under the Condition of Increasing Average Waiting Time in Orbit

Nazarov

Rozhkova

Titarenko

2020

Communications in Computer and Information Science

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Analysis of $$MAP, PH_{2}^{OA}/PH_{1}^{I}, PH_{2}^{O}/1$$ retrial queue with vacation, feedback, two-way communication and impatient customers

Cited by 5 publications

References 28 publications

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

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

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

Asymptotic Analysis of RQ-System with Feedback and Batch Poisson Arrival Under the Condition of Increasing Average Waiting Time in Orbit

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