Analysis of Interconnected Arrivals on Queueing-Inventory System with Two Multi-Server Service Channels and One Retrial Facility

Jeganathan, K.; Harikrishnan, T.; Selvakumar, S.; Anbazhagan, N.; Amutha, S.; Acharya, Srijana; Dhakal, Rajendra; Joshi, Gyanendra Prasad

doi:10.3390/electronics10050576

Cited by 19 publications

(6 citation statements)

References 32 publications

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“…Recently, Jeganathan et al, (2021) developed a Neuts matrix geometric technique to estimate the optimal holding cost of the product that are waiting in a queue in the inventory system. By minimizing the queue length, the inventory cost can be reduced.…”

Section: Literature Reviewmentioning

confidence: 99%

Formulation and Performance Assessment for Multiple Server Queueing Models

Alam¹,

Azrin²,

U³

et al. 2023

Preprint

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Queueing theory has grown in prominence as it provides the numerical foundation for decision-making assessment. Queueing models with multiple servers provide extensive decision-making data, which is critical for evaluating a server's performance. The purpose of this study is to formulate multiple server queueing models and provides a performance assessment to evaluate the appropriate models. A three-phased structured approach has been used to model and analyze performance for multiple server queueing models. The "Multiple Server Finite Queue Length Infinite Queue Population Model" is most desirable for a customer who has to wait for less time (approximately 43.14%) in the system as well as in the queue (approximately 62.16%) and reduces the system length by approximately 47.02% and the queue length by approximately 64.76%. However, the "Multiple Server Infinite Queue Length Infinite Queue Population Model" is preferable from a managerial perspective, as the "Multiple Server Finite Queue Length Infinite Queue Population Model" has fewer customers in the system, indicating a loss from a managerial standpoint. When the arrival rate of customers, service rate, and the number of servers are increased, length of the system and queue remain nearly constant, whereas the waiting time in the system nearly doubles for both queueing models. The paper develops a performance evaluation of the “Multiple Server Infinite Queue Length Infinite Queue Population Model” and “Multiple Server Finite Queue Length Infinite Queue Population Model”, which are capable of adapting to an unpredictable decision in any service system. Furthermore, this study provides decision-makers with a perspective-based evaluation of the mentioned servers, with a focus on a manager and a customer.

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Section: Literature Reviewmentioning

confidence: 99%

Formulation and Performance Assessment for Multiple Server Queueing Models

Alam¹,

Azrin²,

U³

et al. 2023

Preprint

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“…Hanukov et al [16] studied the preparatory service in order to decrease the waiting time of customers during the idle time in a multi-server QIS with stock-dependent arrival. Jeganathan et al [17] considered two groups of multi-servers in such a way that each group of servers is designed to operate for two types of customers. The first type of customers can purchase the commodity whereas the second type can receive the service only.…”

Section: Literature Reviewmentioning

confidence: 99%

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

Jeganathan,

Harikrishnan,

Lakshmanan

et al. 2023

Mathematics

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This article deals with the queuing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged with another junior server. The approaching junior servers await their turn in a finite waiting area with a capacity of c for consultation. Concerning this, we study the performance of junior servers approaching the senior server in the retrial queuing-inventory model with the two finite waiting halls dedicated to the primary customers and the junior servers for consultation. We formulate a level-dependent QBD process and solve its steady-state probability vector using Neuts and Rao’s truncation method. The stability condition of the system is derived and the R matrix is computed. The optimum total cost has been obtained, and the sensitivity analyses, which include the expected total cost, the waiting time of customers in the waiting hall and orbit, the number of busy servers, and a fraction of the successful retrial rate of the model, are computed numerically.

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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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Analysis of Interconnected Arrivals on Queueing-Inventory System with Two Multi-Server Service Channels and One Retrial Facility

Cited by 19 publications

References 32 publications

Formulation and Performance Assessment for Multiple Server Queueing Models

Formulation and Performance Assessment for Multiple Server Queueing Models

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

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

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