Palm calculus

In the study of , Palm calculus, named after Swedish teletrafficist Conny Palm, is the study of the relationship between probabilities conditioned on a specified event and time average probabilities. A Palm probability or Palm expectation, often denoted ${\displaystyle P^{0}(\cdot )}$ or ${\displaystyle E^{0}[\cdot ]}$, is a probability or expectation conditioned on a specified event occurring at time 0.

A simple example of a formula from Palm calculus is Little's law ${\displaystyle L=\lambda W}$, which states that the time-average number of users (L) in a system is equal to the product of the rate (${\displaystyle \lambda }$) at which users arrive and the Palm-average waiting time (W) that a user spends in the system. That is, the average W gives equal weight to the waiting time of all customers, rather than being the time average of "the waiting times of the customers currently in the system".

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