Bank Queueing Theory Simulation Model

Queueing theory is a mathematical methodology used to study waiting phenomena in service systems. In banking scenarios, it helps analyze key metrics such as customer arrival times, service window efficiency, and average waiting durations.

MATLAB serves as a powerful computational tool ideal for simulating such stochastic processes. The computer simulation of bank queueing systems can be implemented through the following logical framework:

First, establishing a customer arrival model is essential. Typically, a Poisson process is employed to simulate random customer arrivals, where MATLAB's random number generation functions like exprnd() can generate inter-arrival times following an exponential distribution.

Service time modeling is equally critical. Based on actual banking transaction data, service durations may follow normal or exponential distributions, which can similarly be generated using random number functions such as normrnd() or exprnd().

The core component involves designing queueing rules. For a basic single-queue multi-window system, the algorithm must handle: when a customer arrives, direct service if idle windows exist, otherwise join the queue; when a window completes service, fetch the next customer from the queue head using a First-In-First-Out (FIFO) approach.

During simulation, recording each customer's arrival time, service start time, completion time, and waiting duration is necessary. These datasets form the basis for subsequent performance indicator calculations through matrix operations or table structures in MATLAB.

Finally, key metrics like average waiting time, mean queue length, and window utilization rates can be computed. Comparative analysis of system performance under different window configurations can be achieved using MATLAB's statistical functions such as mean(), max(), and custom utilization formulas.

This simulation approach bypasses complex mathematical derivations, generating statistically realistic results through numerous randomized trials. It provides practical guidance for bank branch window allocation and queue management strategies, with potential for extension to multi-queue systems or priority-based servicing through modified algorithm logic.