Analysis of $M/M/1$ queueing system with state dependent Arrival and detainment of retracted customers

E. Ramesh kumara,* and Sree Dharsanab

Analysis of $M/M/1$ queueing system with state dependent Arrival and detainment of retracted customers

Authors :

E. Ramesh kumar^a,* and Sree Dharsana^b

Author Address :

^a,bDepartment of Mathematics, CMS college of Science and Commerce, Coimbatore-641049, Tamil Nadu, India.

*Corresponding author.

Abstract :

The queueing system will have a negative impact if the customers are not satisfied with the service. The reneged customer can be made to stay for further service in the queueing system with some probability, say q or the customer can leave the queue neglecting the service with probability $p=(1-q)$ . A finite waiting space Markovian single-server queueing model with state dependent arrivals and retention of reneged customers is studied. The steady state solution of the model is derived iteratively. The performances of effectiveness of the queueing model are also obtained. Some particular cases are derived as special cases for this model.

Keywords :

Customer impatience, state-dependent arrival, Reneging, slow service,fast service.

DOI :

Article Info :

Received : April 13, 2015; Accepted : June 12, 2015.