Single-server queuing processes in computing systems

Queues (waiting lines) were first studied systematically by A. K. Erlang1in connection with his investigations of telephone call delays at Danish telephone exchanges. Following this pioneering beginning in the early Twentieth Century, others who have made key contributions to a mathematical theory of queues are Pollaczeck,2,3Kolomogorov,4Khintchine,5Kendall,6,7Lindley,8and Takacs.9–11Queuing theory, which looks to probability theory for much of its structure, has proved useful in developing descriptive and predictive mathematical models that often lead to improvements in the services studied. As a result of this work, the theory of queues has been used in studying and improving such services as communication networks of all kinds, computing systems, production lines, transportation (harbors, tunnels, bus stations, airports, etc.) and in everyday life (e.g., banks, elevators, and supermarket checkouts).