Pollaczek–Khinchine_formula
In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue length and service time distribution Laplace transforms for an M/G/1 queue (where jobs arrive according to a Poisson process and have general service time distribution). The term is also used to refer to the relationships between the mean queue length and mean waiting/service time in such a model.[1]
The formula was first published by Felix Pollaczek in 1930[2] and recast in probabilistic terms by Aleksandr Khinchin[3] two years later.[4][5] In ruin theory the formula can be used to compute the probability of ultimate ruin (probability of an insurance company going bankrupt).[6]