queuewaiting

Queuewaiting refers to the experience of waiting for service in a queue or for entry into a process. It is a central concern of queuing theory, a field of operations research that analyzes how items or people arrive, wait, and are served. In practice, queuewaiting describes both the time a person spends waiting and the length of the queue itself.

Key quantities in queuewaiting include the arrival rate (lambda), service rate (mu), and utilization (rho = lambda/mu). Common performance metrics are the average waiting time in the queue (Wq), the total time in the system (Ws), and the average number in the queue (Lq) or in the system (L). Basic models, such as the M/M/1 queue with Poisson arrivals and exponential service, provide baseline expectations, while M/M/c or M/G/1 extend to more servers or general service-time distributions.

Factors influencing queuewaiting include variability in arrivals and service times, the number of servers, and the queueing discipline (for example first-come, first-served or priority rules). Behavioral aspects such as balking, reneging, and abandonment can also alter wait. Information about expected wait can affect perceived duration.

Management approaches aim to reduce undesirable wait through staffing optimization, appointment systems, self-service options, and process improvements. Queue design, single versus multiple queues, and signaling of expected waits can influence both actual and perceived wait times.

Applications span banks, retail, call centers, healthcare, and computer networks. Models are useful tools but rely on assumptions about arrivals and service times; real systems may require empirical analysis or simulation to capture complexity.