Sojourn-time Distribution for $$M/G^a/1$$ Queue with Batch Service of Fixed Size - Revisited

Goswami, Veena; Chaudhry, M. L.; Banik, Abhijit Datta

doi:10.1007/s11009-022-09963-0

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Kavitha et al [17] have developed a queue model which is used for mobile wallet system by applying blockchain. Goswami and Mohan [18] determine an explicit form of sojourn-time distribution and evaluate the distribution function for any specific time. Haridass and Arumuganathan [19] have considered a mass service queue system with two types of vacations.…”

Section: Literature Surveymentioning

confidence: 99%

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

Lavanya¹,

Vennila²,

Sankoh

2022

Mathematical Problems in Engineering

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The orthodox way of tile printing results in mulish production. To tame this, digital inkjet printing technology was imposed. In this article, a mathematical prototype is designed exclusively for the tile printing wing. The various plants coming under printing are correlated to the proposed prototype. The article throws light on the functioning of the prototype. The prototype turns up subservient to bulk service queue models with two types of vacations. The prototype is resolved under the supplementary variable technique. The prototype with peculiar conditions is proved to be the existing model. Anticipated line distance, awaited active duration, awaited standby time, and expected idle period were computed. Thus, the total average cost is acquired for diverse vacation values. The main intention of the pattern is to downside the total average cost.

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Section: Literature Surveymentioning

confidence: 99%

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

Lavanya¹,

Vennila²,

Sankoh

2022

Mathematical Problems in Engineering

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Sojourn-Time Distribution for $$Geo/G^{a,b}/1$$ Queue with Batch Service

Goswami,

Chaudhry

2023

Int. J. Appl. Comput. Math

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Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers

Koyama,

Nakamura,

Phung-Duc

2024

Mathematics

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There are various types of sharing economy services, such as ride-sharing and shared-taxi rides. Motivated by these services, we consider a single-server queue in which customers probabilistically select the type of service, that is, the single service or batch service, or other services (e.g., train). In the proposed model, which is denoted by the M+M(K)/M/1 queue, we assume that the arrival process of all the customers follows a Poisson distribution, the batch size is constant, and the common service time (for the single- and batch-service customers) follows an exponential distribution. In this model, the derivation of the sojourn time distribution is challenging because the sojourn time of a batch-service customer is not determined upon arrival but depends on single customers who arrive later. This results in a two-dimensional recursion, which is not generally solvable, but we made it possible by utilizing a special structure of our model. We present an analysis using a quasi-birth-and-death process, deriving the exact and approximated sojourn time distributions (for the single-service customers, batch-service customers, and all the customers). Through numerical experiments, we demonstrate that the approximated sojourn time distribution is sufficiently accurate compared to the exact sojourn time distributions. We also present a reasonable approximation for the distribution of the total number of customers in the system, which would be challenging with a direct-conventional method. Furthermore, we presented an accurate approximation method for a more general model where the service time of single-service customers and that of batch-service customers follow two distinct distributions, based on our original model.

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Sojourn-time Distribution for $$M/G^a/1$$ Queue with Batch Service of Fixed Size - Revisited

Cited by 3 publications

References 23 publications

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

Sojourn-Time Distribution for $$Geo/G^{a,b}/1$$ Queue with Batch Service

Sojourn Time Analysis of a Single-Server Queue with Single- and Batch-Service Customers

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