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A single-server markovian queuing system with discouraged arrivals and retention of reneged customers

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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. | Yugoslav Journal of Operations Research 24 (2014) Number 1, 119-126 DOI: 10.2298/YJOR120911019K A SINGLE-SERVER MARKOVIAN QUEUING SYSTEM WITH DISCOURAGED ARRIVALS AND RETENTION OF RENEGED CUSTOMERS Rakesh KUMAR Assistant Professor, School of Mathematics Shri Mata Vaishno Devi University Sub-Post Office, Katra rakesh_stat_kuk@yahoo.co.in Sumeet KUMAR SHARMA Research Scholar, School of Mathematics Shri Mata Vaishno Devi University Sub-Post Office, Katra Received: September 2012 / Accepted: Аpril 2013 Abstract: 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 p (= 1 − 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. 120 R. Kumar, S. Kumar Sharma / A Single-Server Markovian Queuing System 1. INTRODUCTION Queuing theory plays an important role in modeling real life problems involving congestions in vide areas of applied sciences. Applications of queuing with impatience can be seen in traffic modeling, business and industries, computer-communication, health sectors and medical sciences etc. Queues