Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System

Jeganathan, Kathirvel; Harikrishnan, Thanushkodi; Lakshmanan, Kumarasankaralingam; Melikov, Agassi; Sztrik, Janos

doi:10.3390/math11224581

Cited by 3 publications

(2 citation statements)

References 43 publications

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“…Also, the team of scientists led by Jeganathan developed a model of mass service based on a two-level service system: junior and senior servers. Such a model takes place when the junior servers do not have the data to solve the problem and they turn to the senior server [15].…”

Section: Optimization Of Technical Resourcesmentioning

confidence: 99%

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

Galimulina,

Barsegyan

2024

Mathematics

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An interdisciplinary approach to management allows for the integration of knowledge and tools of different fields of science into a unified methodology in order to improve the efficiency of resource management of different kinds of systems. In the conditions of global transformations, it is economic systems that have been significantly affected by external destabilizing factors. This determines the focus of attention on the need to develop tools for the modeling and optimization of economic systems, both in terms of organizational structure and in the context of resource management. The purpose of this review study is to identify the current gaps (shortcomings) in the scientific literature devoted to the issues of the modeling and optimization of economic systems using the tools of mass service theory. This article presents a critical analysis of approaches for the formulation of provisions on mass service systems in the context of resource management. On the one hand, modern works are characterized by the inclusion of an extensive number of random factors that determine the performance and efficiency of economic systems: the probability of delays and interruptions in mobile networks; the integration of order, inventory, and production management processes; the cost estimation of multi-server system operation; and randomness factors, customer activity, and resource constraints, among others. On the other hand, controversial points are identified. The analytical study carried out allows us to state that the prevailing majority of mass service models applied in relation to economic systems and resource supply optimization are devoted to Markov chain modeling. In terms of the chronology of the problems studied, there is a marked transition from modeling simple systems to complex mass service networks. In addition, we conclude that the complex architecture of modern economic systems opens up a wide research field for finding a methodology for assessing the dependence of the enterprise performance on the effect of optimization provided by using the provisions of mass service theory. This statement can be the basis for future research.

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Section: Optimization Of Technical Resourcesmentioning

confidence: 99%

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

Galimulina,

Barsegyan

2024

Mathematics

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“…Many researchers have concentrated on homogeneous servers in prior studies of multi-server queueing systems. Readers can refer to the following research works for studying the analysis of multi-server systems with homogeneous servers: [4,8,15,16,28,43,44]. Nevertheless, it is crucial to recognize that manual servers or service providers frequently exhibit varying skill levels, experience, or work speeds in practical situations, resulting in differences in service rates.…”

Section: Introductionmentioning

confidence: 99%

A Finite Source Stock-dependent Stochastic Inventory System with Heterogeneous Servers and Retrial Facility

Thanushkodi,

Kathirvel,

Krishnasamy

et al. 2023

Preprint

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This article deals with a finite-source stock-dependent stochastic inventory system with heterogeneous servers and retrial facility. The system can store up to S number of items, and the lifetime of each item follows an exponential distribution. The primary customers arrive in a finite waiting hall from a finite source and get service from the multi-channel (c-heterogeneous servers). The customer’s arrival rate depends on the present stock level. Those customers who arrive while the waiting hall is full enter into the finite orbit. Also, customers in the waiting hall can become impatient and enter the orbit. The (s,Q) ordering policy is adopted for the replenishment of stocks. In the steady state, the joint probability distribution of a number of items in the inventory, busy servers, customers in the waiting hall, and orbit is computed. The comparative numerical analysis of heterogeneous and homogeneous servers on the expected total cost, the average number of customers in the waiting hall and orbit, the fraction of successful retrial rate, and the average impatient customer rate are also carried out.

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An M/G/1 Queue with Repeated Orbit While in Service

Hanukov,

Barron,

Yechiali

2024

Mathematics

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Orbit and retrial queues have been studied extensively in the literature. A key assumption in most of these works is that customers “go to orbit” when they are blocked upon arrival. However, real-life situations exist in which customers opt to go to orbit to efficiently use their orbit time rather than residing dormant at the service station while waiting for their service to be completed. This paper studies such a system, extending the scope of traditional orbit and retrial queues. We consider an M/G/1 queue where customers repeatedly go to orbit while their service remains in progress. That is, if a customer’s service is not completed by within a specified “patience time”, the customer goes to orbit for a random “orbit time”. When the customer orbits, the server continues rendering her/his service. If, on return, the service is already completed, the customer leaves the system. Otherwise, s/he waits for another patience time. This policy is repeated until service completion. We analyze such an intricate system by applying the supplementary variable technique and using Laplace–Stieltjes transforms. Performance measures are derived, and a comparison analysis is provided between various service time distributions.

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Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System

Cited by 3 publications

References 43 publications

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

Application of Mass Service Theory to Economic Systems Optimization Problems—A Review

A Finite Source Stock-dependent Stochastic Inventory System with Heterogeneous Servers and Retrial Facility

An M/G/1 Queue with Repeated Orbit While in Service

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