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In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula [1] [2]) is a theorem by John Little which states that the long-term average number L of customers in a stationary system is equal to the long-term average effective arrival rate λ multiplied by the average time W that a customer spends in the system.
The efficiency of queueing systems is gauged through key performance metrics. These include the average queue length, average wait time, and system throughput. These metrics provide insights into the system's functionality, guiding decisions aimed at enhancing performance and reducing wait times. [43] [44] [45]
The average response time or sojourn time (total time a customer spends in the system) does not depend on scheduling discipline and can be computed using Little's law as 1/(μ − λ). The average time spent waiting is 1/(μ − λ) − 1/μ = ρ/(μ − λ). The distribution of response times experienced does depend on scheduling discipline.
The Erlang B formula (or Erlang-B with a hyphen), also known as the Erlang loss formula, is a formula for the blocking probability that describes the probability of call losses for a group of identical parallel resources (telephone lines, circuits, traffic channels, or equivalent), sometimes referred to as an M/M/c/c queue. [5]
where τ is the mean service time; σ 2 is the variance of service time; and ρ=λτ < 1, λ being the arrival rate of the customers. For M/M/1 queue, the service times are exponentially distributed, then σ 2 = τ 2 and the mean waiting time in the queue denoted by W M is given by the following equation: [5]
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Wait times have been averaging roughly 35 minutes. In September, the latest data available, the average time on hold was 34.7 minutes. The shortest average wait so far this year came in May, 28.8 ...
3 Average delay/waiting time. 4 Inter-departure times. 5 ... [11] [12] [13] The first such was given in 1959 using a factor to adjust the mean waiting time in an M/M ...