Simulation of Queueing Theory: Calculating Queue Length, Waiting Time, Service Rate, Arrival and Departure Times, and Other Metrics

In queueing theory simulations, we need to consider key performance indicators such as queue length, waiting time, service rate, and arrival/departure timestamps. These metrics provide comprehensive insights into various aspects of queue behavior. Queue length refers to the average number of customers waiting in the queue, which can be computed using cumulative sum algorithms tracking customer arrivals and departures. Waiting time represents the duration a customer spends waiting in the queue before service begins, typically calculated through timestamp comparisons between arrival and service start times. Service rate indicates the average time required to process a single customer, often implemented using probability distributions (exponential, Poisson) to model service completion events. Arrival and departure timestamps capture the exact times when customers enter and leave the queue system, usually managed through event-driven simulation architectures. By conducting comprehensive analysis of these metrics through discrete-event simulation frameworks, we can better understand and manage queue systems, improve service efficiency, reduce waiting times, and enhance customer satisfaction. Common implementation approaches involve maintaining event calendars, statistical counters, and state variables to track system dynamics over simulation time.