## Research and Reports on Mathematics

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Editorial, Res Rep Math Vol: 5 Issue: 5

# Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access

In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving consistent with a marked Markovian arrival process. Each class of consumers differs naturally of the service they seek and different priorities are assigned for every class leading to different levels of inventory admitted to exhaust for patrons of every class. one service node is provided for every class with exponential services having classdependent service rates. All classes of consumers are served from one source of inventory replenished consistent with (s,S) policy with exponentially distributed time interval . Stability condition and steady state probabilities are obtained by matrix-analytic method. Some important performance measures also are derived. Inventory recycle time was analyzed intimately . Useful cost function and numerical illustrations also are given. The optimization problem is interesting and may be solved in similar real scenario. Keywords: Heterogeneous Inventory Access • Multi-Server System • Queuing-Inventory • Matrix Analytic Model

## Abstract

In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving consistent with a marked Markovian arrival process. Each class of consumers differs naturally of the service they seek and different priorities are assigned for every class leading to different levels of inventory admitted to exhaust for patrons of every class. one service node is provided for every class with exponential services having class-dependent service rates. All classes of consumers are served from one source of inventory replenished consistent with (s,S) policy with exponentially distributed time interval . Stability condition and steady state probabilities are obtained by matrix-analytic method. Some important performance measures also are derived. Inventory recycle time was analyzed intimately . Useful cost function and numerical illustrations also are given. The optimization problem is interesting and may be solved in similar real scenario.

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###### Citations : 34

Research and Reports on Mathematics received 34 citations as per Google Scholar report

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