Waitingtime

Waitingtime refers to the elapsed time that a person, item, or data unit spends in a queue or in a service system before receiving the requested service or completing processing. It is a central concept in queueing theory, operations research, and service design, where reducing unnecessary waits can improve efficiency and user experience.

In queueing theory, waiting time depends on the pattern of arrivals, the service process, the number of servers, and the queue discipline. Common models include M/M/1 (Poisson arrivals, exponential service, single server), M/M/c, and M/G/1. For an M/M/1 system with arrival rate lambda and service rate mu, the utilization is rho = lambda / mu. The average waiting time in the queue is Wq = lambda / (mu (mu - lambda)), and the average time in the system (waiting plus service) is W = 1 / (mu - lambda).

Practically, waiting time is used to assess performance, plan capacity, and set service standards. Little's law relates average number in the system, arrival rate, and average time in the system. Data on arrivals, service times, and queue lengths feed estimates of Wq and W, enabling comparisons across designs and time periods.

Applications span healthcare, call centers, airports, and online services. Longer waiting times are associated with lower satisfaction and higher abandonment. Managers address waits by increasing capacity, changing scheduling rules, prioritizing certain customers, or redesigning processes to reduce bottlenecks.

Related concepts include lead time, latency in computing, and service level agreements. While waiting time is often a statistical expectation, actual waits can vary widely based on real-time conditions and randomness in arrivals and service times.