A Note on Queuing Models

Queues (or waiting lines) are common in modern life. We wait in lines at the campus cafeteria, to board an airplane, in the emergency room, and when we call a company for customer service. We even wait for applications to be initiated and processed by our smartphone processors, and our online orders wait to be fulfilled at companies’ warehouses before being shipped to us. How long we wait in line depends on several factors and parameters. It may depend on the number of servers working and the amount of time it takes to serve each individual customer (the system’s capacity) or on how many customers arrive at any given time (the system’s demand or flow rate). Most importantly, queues form due to random variations in arrival patterns and service times.