Time dependent solution of a Non-Markovian Queue with Triple stages of service having Compulsory vacation and service interruptions

Sundari, S. Maragatha; Srinivasan, S.

doi:10.5120/5556-7631

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…U(χ) = P (1) (χ) + P (2) (χ) + G (1) (χ) + G (2) (χ) + G (3) (χ) + R (1) (χ) + R (2) (χ) + S (1) (χ) + S…”

Section: Queue Size Distributionunclassified

“…Researchers Baskar et al [1], Sundari and Srinivasan [2], Balamani [3], Khalaf [4], Ayyappan and Sathiya [5] have examined queues experiencing disruptions in service. Jain et al [6] provide a comprehensive review and literature analysis on the performance modeling and evaluation of a single-server, general service queueing system incorporating service interruptions through the application of supplementary variable techniques.…”

Section: Introductionmentioning

confidence: 99%

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Metaheuristic Cost Optimization of MX/G1,G2/ 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

2024

Contemp. Math.

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We presented a MX /G1, G2 /1 queueing system with a Bernoulli schedule that includes service disruption, working breakdown, balking, catastrophe and extended server vacations. All customers that arrive are served by a single server, with service time determined by general distribution. As soon as the system fails, the server keeps serving the current client at a reduced rate while repairs are made. It is believed that the vacation schedule is broad. Random disruptions to the server occur, with an exponential distribution in the length of the disruption. We assume that besides a Poisson stream of positive arrivals, there is a Poisson stream of negative arrivals, which we refer to as catastrophes. Using the supplementary variable technique, the Laplace transforms of the time-dependent probability of the system state are derived. We can infer steady-state outcomes from this. The average waiting time and queue size were also obtained. An additional topic of discussion is Adaptive Neuro-Fuzzy Inference system (ANFIS). Furthermore, this work uses Particle Swarm Optimisation (PSO), Artificial Bee Colonies (ABC), and Genetic Algorithms (GA) to swiftly find the system’s optimal cost. Additionally, we examined the convergence of several graph-optimisation strategies.

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“…U(χ) = P (1) (χ) + P (2) (χ) + G (1) (χ) + G (2) (χ) + G (3) (χ) + R (1) (χ) + R (2) (χ) + S (1) (χ) + S…”

Section: Queue Size Distributionunclassified

Section: Introductionmentioning

confidence: 99%

Metaheuristic Cost Optimization of MX/G1,G2/ 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

2024

Contemp. Math.

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“…Theorem 4.1. The system of differential-difference equations to describe an M [X] /G/1 queue with essential service with service interruption and two phases of vacation are given by equations ( 1) to ( 14) with initial conditions (15) and the generating functions of transient solution are given by equation (58a) to (61).…”

Section: Definitions and Equations Governing The Systemmentioning

confidence: 99%

“…Igaki [12], Levi and Yechilai [13], and Madan and Abu-Davyeh [14] studied vacation queues with different vacation policies. S. Maragathasundari and S. Srinivasan [15] analyzed the M/G/1 feedback queue with three stages multiple server vacations. S. Maragathasundari and S. Srinivasan [16] analyzed the triple stages of service having compulsory vacation and service interruptions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions

Sundari¹,

Srinivasan²,

Ranjitham³

2014

Missouri J. Math. Sci.

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We study a batch arrival queueing system of phase vacation with two stages of service based on a Bernoulli schedule. A single server provides essential service to all arriving customers with service time following a general distribution. After two stages of service completion, the server leaves for phase one vacation of random length with probability p or to continue staying in the system with probability 1−p. As soon as the completion of phase one vacation, the server undergoes phase two vacation. On completion of two heterogeneous phases of vacation the server returns back to the system. The vacation times are assumed to be general. The server is interrupted and the service interruption follows an exponential distribution. The arrivals follow a Poisson distribution. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived. From this we deduce the steady state results. We also obtain the average queue size and average waiting time.

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“…S.Maragathasundari and S.Srinivasan [14], they studied about analysis of M/G/1 feedback queue with three stage multiple server vacation. S.Maragathasundari and S.Srinivasan [15], they studied about analysis of triple stage of service having compulsory vacation and service interruptions. S.Maragathasundari and S.Srinivasan [16], they studied about three phase M/G/1 queue with Bernoulli feedback and multiple server vacation.…”

Section: Introductionmentioning

confidence: 99%

Batch arrival queueing system with two stages of service

Maragathasundari¹,

Srinivasan²,

Ranjitham³

2014

ijma

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This Paper studies batch arrival queue with two stages of service. Random breakdowns and Bernoulli schedule server vacations have been considered here .After a service completion, the server has the option to leave the system or to continue serving customers by staying in the system. It is assumed that customers arrive to the system in batches of variable size, but served one by one. After completion of first stage of service, the server must provide the second stage of service to the customers. Vacation time follows general distribution, while we consider exponential distribution for repair time.We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers ,and the average waiting time in the queue.

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Time dependent solution of a Non-Markovian Queue with Triple stages of service having Compulsory vacation and service interruptions

Cited by 3 publications

References 12 publications

Metaheuristic Cost Optimization of <i>M<sup>X</sup>/G<sub>1</sub>,G<sub>2</sub>/</i> 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

Metaheuristic Cost Optimization of <i>M<sup>X</sup>/G<sub>1</sub>,G<sub>2</sub>/</i> 1 Queue with Service disruption, Working breakdown, Balking, Catastrophe and Extended Server Vacation with Bernoulli Schedule

Analysis of Batch Arrival Queue with Two Stages of Service and Phase Vactions

Batch arrival queueing system with two stages of service

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