Abstract
We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.
Highlights
The competition resulting from a decade of deregulation in the Ghanaian banking industry is becoming more intense, due to the regulatory imperatives of worldwide banking and to the customers becoming increasingly aware of their rights [1,2]
We model a server–customer interaction occurring in the banking sector, using a Double-X cascade network
Each server has a renewal customer with general i.i.d. inter-arrival times and general i.i.d. service times
Summary
The competition resulting from a decade of deregulation in the Ghanaian banking industry is becoming more intense, due to the regulatory imperatives of worldwide banking and to the customers becoming increasingly aware of their rights [1,2]. Bank customers have become increasingly demanding, requiring high quality, low priced and immediate service delivery [3], a key development being the entry of private banks into the market and the expansion of branches of existing banks. Queuing theory aims at developing mathematical and numerical models to investigate the formation and congestion of waiting lines when a service is requested, its basic ideas being proposed by A. Common experience suggests that the act of queuing is associated with waiting, which is an inevitable part of modern life. This leads to the idea that queuing theory has very wide applications [7]. Customers waiting to be served at grocery stores, banks and post offices, people having to wait for an operator during a telephone call, people waiting for a taxi or a bus on the way to the workplace can be thought as subjects of queuing theory [8,9]
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