A production queueing-inventory system with two-customer and a server subject to breakdown

A queueing-inventory system where the server is subject to breakdown is examined. The products in inventory are provided by production. Two different types of customers are considered. Each customer type arrives in the system according to a Poisson process with different parameters. There is only one server and the service time follows an exponential distribution. Service may be interrupted randomly due to breakdowns. There may be minor or major breakdowns and after the recovery process, the priority customer class gets service first. The described system is formulated as a level-dependent quasi-birth-death process (LDQBD). The stationarity condition is provided and the steady-state probabilities are calculated. A comprehensive numerical study is presented that examines the sensitivity of the performance measures to the change of system parameters and also investigates the optimal inventory policy according to the considered cost function.

Automated summary

This study examines a queueing-inventory system with a server subject to breakdowns. Two types of customers arrive in the system based on Poisson processes. There is a single server with exponential service time. However, service may be randomly interrupted due to breakdowns. After recovery, priority customers are served first. The system is modeled as a level-dependent quasi-birth-death process (LDQBD), and stationary conditions and steady-state probabilities are calculated. A comprehensive numerical study is conducted to analyze the sensitivity of performance measures to system parameter changes and to evaluate the optimal inventory policy based on cost functions.