Inventory Control Model on Matrix Geometric Method for Intermittently Obtainable Server with Balking and Feedback in Markovian Queueing Model

The paper deals with the problem of queueing-inventory system that has uncertain service conditions, and it discusses the contribution of server availability and customer behaviours like balking and feedback that are also added in to the system performance. In real life service and production situations, servers are not always available because of maintenance processes, capacity constraints, or other unforeseen disruptions. In order to simulate such characteristics, the system is modelled in a Markovian context where the interdependency between inventory levels, customer inflows, and server capacity is simulated. The time of customer arrivals is random and the time to serve is memoryless, which maintains the Markovian property of the model. Customer impatience is captured through balking and feedback, representing multiple service interactions within the system. The resulting stochastic process has a state space whose structure may be characterized by a quasi-birth-and-death formulation. With this structure the matrix-geometric method may be applied to the obtained long-run behaviour of the system. Some of the measures of performance of practical interest obtained out of the steady-state distribution include average inventory levels, system congestion, service completion rates. An inclusive cost framework is then developed by including ordering costs, holding costs, procurement costs and the service costs. System parameters sensitivity analysis and numerical experiments indicate the way they affect the operational performance and the total inventory cost. The findings demonstrate the significance of the balking and feedback effects to be managed successfully so that to enhance efficiency and customer satisfaction in systems with intermittently available servers.