What study area focuses on predicting queue lengths and waiting times in service systems?

The study area that focuses on predicting queue lengths and waiting times in service systems is queuing theory. This branch of mathematics deals specifically with the analysis of queue formation and behavior, which means it provides the tools and models necessary to understand how services are provided over time. By studying various factors such as arrival rates, service rates, and the number of servers, queuing theory helps in making informed decisions on how to improve service efficiency, reduce waiting times, and manage resources optimally.

In contrast, statistical inference is primarily concerned with making predictions or generalizations about a population based on sample data. Process optimization aims to improve the efficiency of a process but does not specifically focus on queues and waiting times. Time series analysis involves analyzing time-ordered data points to detect trends, seasonal variations, or cycles but does not address queuing dynamics directly. The specialized focus of queuing theory on the intricacies of waiting lines and service times makes it the correct answer to the question.