Queue modelling for successful implementation of the cash-less policy in Nigeria

In line with the realization of the vision of the cash-less policy as being fronted by the Central Bank of Nigeria, this paper seeks to solve problems of long waiting time and queue lengths of customers known to be associated with the queuing system of the Automated Teller Machine (ATM), an indispensable piece of machinery for successful implementation of the policy. To this end, the M/G/1 model, a single-channel queuing model with Poisson arrivals, General distribution service time has been applied in modelling the ATM queuing system across three commercial banks: Guarantee Trust Bank (GTB), Diamond bank and Ecobank all located in Lafia, Nasarawa State Nigeria, in order to reveal the associated queuing problems and proffer solutions via an empirical approach of distribution fitting to real time data of inter arrival and service times. The result revealed problems of long queue length, long waiting time and ATM (Server) over utilization to be common in all the three banks. The result of sensitivity analysis established that, an upgrade of ATM processor speed such that customers spend one (1) minute on the average in service, will ensure that no customer wait in queue and an average utilization of the ATM to check breakdown.