A Single-server Markovian Queuing System with Discouraged Arrivals and Retention of Reneged Customers

Customer impatience has a very negative impact on the queuing system under investigation. If we talk from business point of view, the firms lose their potential customers due to customer impatience, which affects their business as a whole. If the firms employ certain customer retention strategies, then there are chances that a certain fraction of impatient customers can be retained in the queuing system. A reneged customer may be convinced to stay in the queuing system for his further service with some probability, say q and he may abandon the queue without receiving the service with a probability ( 1 ) p q = − . A finite waiting space Markovian single-server queuing model with discouraged arrivals, reneging and retention of reneged customers is studied. The steady state solution of the model is derived iteratively. The measures of effectiveness of the queuing model are also obtained. Some important queuing models are derived as special cases of this model. Keyword: Probability of Customer Retention, Reneging, Discouraged arrivals, Cost-Profit Analysis. MSC: 60K25-68M20-90B22. R. Kumar, S. Kumar Sharma / A Single-Server Markovian Queuing System 120