Abstract
The concept of customer reneging has been exploited to a great extent in recent past by the queuing modelers. Economically, if we see, the customer reneging leads to loss of potential customers and thereby results into the loss in the total revenue. Taking into consideration this customers’ loss due to reneging, a new queuing model has been developed that deals with customer retention. According to this model, a reneged customer can be convinced in many cases by employing certain convincing mechanism to stay in the queue for completion of his service. Thus, a reneged customer can be retained in the queuing system with some probability (say, q) and it may leave the queue without receiving service with probability p (=1-q). This process is referred to as customer retention. We consider a single server, finite capacity queuing system with customer retention in which the inter-arrival and service times follow negative-exponential distribution. The reneging times are assumed to be exponentially distributed. The steady state solution of the model has been obtained. Some performance measures have been computed. The sensitivity analysis of the model has been carried out. The effect of probability of retention on the average system size has been studied. The numerical results show that the average system size increases steadily as the probability of retention increases. Some particular cases of the model have been derived and discussed.
Highlights
In the current scenario of population explosion and globalization of international commerce and trade, the queuing problems have gained a lot of significance in the decision making process
The first is balking, deciding not to join the queue at all up on arrival; the second is reneging, the reluctance to remain in the waiting line after joining and waiting, and the third is jockeying between lines when each of a number of parallel service channels has its own queue, Gross and Harris (1985)
He has surveyed various queuing systems according to various dimensions like customer impatience behaviors, solution methods of queuing models with impatient customers and associated optimization aspects
Summary
In the current scenario of population explosion and globalization of international commerce and trade, the queuing problems have gained a lot of significance in the decision making process. The notion of customer impatience appeared in queuing theory in the work of Haight (1957) He considered a model of balking for M/M/1 queue in which there was a greatest queue length at which an arrival would not balk. Bae and Kim (2010) considered a G/M/1 queue in which the patience time of the customers is constant They derived the stationary distribution of the workload of the server, or the virtual waiting time by the level crossing argument. Kapodistria (2011) studied a single server Markovian queue with impatient customers and considered the situations where customers abandoned the system simultaneously. The effect of the probability of retention of reneged customers on the expected system size has been studied
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
