A Stochastic Feedback Queuing Model with Encouraged Arrivals and Retention of Impatient Customers

Globalization has introduced never ending competition in business. This competition empowers customers and somewhat ensures quality at reduced cost. High competition along with uncertain customer behavior complicates the situation further for organizations. In order to stay ahead in the competition, organizations introduce various discounts and offers to attract customers. These discounts and offers encourage customers to visit the particular firm (online or offline). Encouraged arrivals result in heavy rush at times. Due to this, customers have to wait longer in queues before they can be serviced. Long waiting times results in customer impatience and a customer may decide to abandon the facility without completion of service, known as reneging. Reneging results in loss of goodwill and revenue both. Further, heavy rush and critical occupation of service counters may lead to unsatisfactory service and some customers may remain unsatisfied with the service. These customers (known as feedback customers) may rejoin the facility rather than leaving satisfactorily. Unsatisfactory service in these situations may cause harm to the brand image and business of the firm. If the performance of the system undergoing such pattern can be measured in advance with some probability, an effective management policy can be designed and implemented. A concrete platform for measuring performance of the system can be produced by developing a stochastic mathematical model. Hence, in this paper, a stochastic model addressing all practically valid and contemporary challenges mentioned above is developed by classical queuing theory model development approach. The model is solved for steady-state solution iteratively. Economic analysis of the model is also performed by introduction of cost model. The necessary measures of performance are derived, and numerical illustrations are presented. MATLAB is used for analysis as and when needed.