Multi-Class, Multi-Server Queueing Inventory System with Batch Service

Khamis A. K. ALMaqbali (), Varghese C. Joshua and Achyutha Krishnamoorthy
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Khamis A. K. ALMaqbali: Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
Varghese C. Joshua: Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
Achyutha Krishnamoorthy: Department of Mathematics, CMS College Kottayam, Kottayam 686001, India

Mathematics, 2023, vol. 11, issue 4, 1-29

Abstract: In this paper, we consider a queueing inventory system with batch arrival and batch service processes. Customers arrive in batches of sizes 1 , 2 , … , k , according to a marked compound Poisson process. We call a batch of customers as belonging to j when there are j individual customers in that batch. The service facility has waiting rooms for each category of customers and also a room to serve them. Except for category 1, all other customers have finite waiting rooms. The service room has only a limited number of seats. These seats are arranged in such a fashion that customers belonging to category j have groups of seats, each with j seats for j = 1 , 2 , … , k . Customers are taken for service according to the availability of seats designated to each category. A category j customer can be taken for service only if j items are available in the inventory. The service time of customers of category j is exponentially distributed with parameter depending on j for j = 1 , 2 , … , k . The number of seats available in the service room for each category of customers is restricted to a finite number. The replenishment for items follows the ( s , S ) policy: fill up to S at the time of replenishment. Lead time follows an exponential distribution. We analyze the system in the equilibrium state. Performance characteristics are evaluated and a number of numerical illustrations are provided.

Keywords: queueing inventory; lead time; marked compound poisson process; batch arrival; batch service; matrix analytic method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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