👉 Queue math is a branch of mathematics that studies the behavior and properties of queues, which are abstract data structures used to model waiting lines or buffers. It combines concepts from probability theory, stochastic processes, and combinatorics to analyze the dynamics of queue formation, service, and departure. Key topics include arrival processes (often modeled by Poisson processes), service times (which can be exponential or arbitrary), queue lengths, waiting times, and performance metrics like the average number of customers in the system or the probability that a customer waits. Queue math provides tools to predict and optimize performance in real-world scenarios, such as call centers, computer networks, and manufacturing systems, by balancing service rates, customer arrival rates, and resource availability. It also explores phenomena like queueing discipline (e.g., FIFO, LIFO), queue capacity, and the impact of varying parameters on system efficiency, offering insights to minimize delays and maximize throughput.
