Analyzing Queuing-Inventory Systems with Customer Attraction-Retention andAsynchronous Vacations: The Ethio Telecom Case

Abstract Quality of Service (QoS) is a critical factor for businesses, directly impacting customer satisfaction and competitiveness. At Ethio Telecom in Ethiopia, effective mechanisms for attracting and retaining impatient customers are essential. Additionally , incorporating synchronous or asynchronous server vacations enhances the realism of queuing-inventory systems. Multi-server vacation models offer greater flexibility and applicability than single-server systems. This paper examines a finite-capacity, multi-server, Markovian queuing-inventory system (MQIS) with attraction-retention mechanisms for impatient customers and C-removable servers under an asynchronous vacation policy. In this model, D (0 < D < C) servers take a vacation together when no customers are waiting at a service completion epoch, while the remaining (C − D) servers either continue serving (if inventory permits) or remain idle (if inventory is depleted). Service and vacation times follow independent exponential distributions, and inventory is managed with a (0, q, Q) ordering policy, which triggers an order to replenish inventory to Q when levels drop to q (q < Q). Using Markov process theory, we develop the queuing-inventory model, derive its steady-state solutions, and compute various performance metrics. Additionally, we propose a cost-loss model to determine the optimal service rate and the optimal number of vacationing servers, applying a genetic algorithm for cost analysis. Finally, we explore how system parameters influence the optimal number of vacationing servers, inventory policy, and cost-loss value. The model is illustrated using data from Ethio Telecom?s service center in Arba Minch City, Ethiopia, with potential applications in supermarkets , telecommunication centers, and restaurants. Future research may examine queuing-inventory systems with batch services, retrial customers, and warehouse disruptions.