Queuing-Inventory System with Attraction-Retention Mechanisms Under a Partial Synchronous Vacation Policy: The Case of Ethio Telecom Service Center in Arba Minch, Ethiopia

Abstract

Quality of service (QoS) is a critical factor for customer satisfaction and operational
efficiency, particularly in service-driven organizations such as Ethio Telecom in
Ethiopia. To address congestion and customer impatience, this study investigates a finitecapacity
multi-server Markovian queuing-inventory system (MQIS) that explicitly incorporates
attraction-retention mechanisms alongside C removable servers operating under a
partial synchronous vacation policy. The attraction-retention strategies are modeled to influence
customer arrival rates and patience levels by encouraging customers to remain in
the system through incentives or improved service quality, thereby mitigating balking and
reneging behaviors. In this setting, any D servers (0 < D < C) may take simultaneous
vacations as a group when no customers are waiting at a service completion epoch, while
the remaining C − D servers continue to operate, either actively serving or idling depending
on the inventory status. Both service and vacation times are exponentially distributed,
and inventory is managed using a continuous-review (q,Q) policy that replenishes stock to
level Q once it drops to q. A continuous-time Markov process is formulated to analyze the
system and steady-state probabilities are derived to evaluate performance measures. To minimize
the total cost, a cost-loss model is proposed and solved using a genetic algorithm to
determine the optimal service rate and the number of servers allocated for vacation. Numerical
experiments based on primary data collected from Ethio Telecom’s Arba Minch branch
demonstrate how attraction-retention mechanisms, along with other system parameters, impact
optimal policies and cost metrics. The proposed model is applicable to a wide range of
service environments, including supermarkets, telecom centers, hospitals, production systems
and restaurants, and can be extended to incorporate batch service, customer retrials, or
catastrophic events.