Effect of upper and lower withdrawal limits on queue length

A customer has to make transaction through a bank ATM (automated teller machine) if his withdrawal amount is less than the lower limit of withdrawal through a bank teller, or through a bank teller if his withdrawal amount is greater than the upper limit of withdrawal through an ATM. In order to decrease the long customer queue at counters, a bank increases the lower withdrawal limit and/or the upper one. Through a finite-source queue model, this paper analyzes the effects of the lower and/or upper limits on the length of customer queue at counters. Main conclusions are: (1) A bank may simultaneously shorten the queue at counters and improve satisfaction level of customers by increasing the withdrawal limit through an ATM and/or the one through a bank teller and ameliorating waiting environment; (2) The length of the queue at counters decreases with the number of the customers who are free in selecting service provider, bank teller or ATM.