Queueing Model Simulation for Banking Systems

Application Background

In contemporary society, banks as financial institutions provide numerous conveniences to the public. To enhance customer service efficiency, the implementation of bank branch queuing systems has become increasingly critical. This program establishes a unified queuing mechanism where multiple teller windows serve customers from a centralized queue. The bank can initiate n service windows and dynamically scale the number of operational counters based on demand. Multiple queuing terminals are deployed throughout the lobby, allowing customers to obtain queue numbers upon entry. The system automatically directs tellers to serve the next customer in sequence upon completion of each service, ensuring optimal queue management.

Technical Implementation

This queuing theory simulation program primarily models M/M/1 (Markovian arrival/Markovian service) and M/D/1 (Markovian arrival/Deterministic service) systems. The program accepts queuing model parameters (arrival rate λ, service rate μ, etc.) and returns computational results including average queue length and waiting time. The simulation core implements event-driven scheduling using priority queues to manage customer arrivals and service completions. Key algorithms include exponential distribution generators for arrival intervals and service durations, with statistical collectors tracking performance metrics. This simulation framework provides theoretical support for optimizing real-world bank queuing systems through parametric analysis and scenario testing.