Optimizing bank teller service efficiency using the M/M/s queueing model and server scenario simulation
DOI:
https://doi.org/10.55749/rmm.v1i1.177Keywords:
Bank queueing system, FCFS, M/M/s model, Server optimization, Steady state, Teller serviceAbstract
This study analyzes the optimal teller service system at Bank X using a multi-server queueing model. Customer waiting time and teller utilization are important indicators of service quality in banking operations, particularly when customer arrivals exceed service capacity. The objective of this study is to determine the appropriate queueing model and evaluate the optimal number of service servers based on arrival and service-time distributions. Secondary data consisting of customer arrivals and service times over 30 observation days were analyzed using the Kolmogorov–Smirnov test. The results show that customer arrivals follow a Poisson distribution, while service times follow an exponential distribution. Therefore, the queueing system was modeled as an (M/M/5):(FCFS/∞/∞) system, representing five servers, first-come-first-served discipline, unlimited queue capacity, and infinite customer population. The average arrival rate was 0.3246 customers per minute, while the average service rate was 0.2839 customers per minute. The average steady-state value was ρ=0.2348<1, indicating that the existing system is stable and does not require additional servers. The average probability of idle tellers was 34.08%, the average number of customers in the queue was 0.0163, the average waiting time in the queue was 0.0310 minutes, and the average time spent in the system was 3.6520 minutes. Server scenario simulation showed that the system remains optimal with a minimum of three servers, resulting in an (M/M/3):(FCFS/∞/∞) model. These findings indicate that queueing theory can support service efficiency improvement and resource allocation in banking operations.
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