  In the Multislope Ski Rental problem, the user needs a certain resource for
some unknown period of time. To use the resource, the user must subscribe to
one of several options, each of which consists of a one-time setup cost
(``buying price''), and cost proportional to the duration of the usage
(``rental rate''). The larger the price, the smaller the rent. The actual usage
time is determined by an adversary, and the goal of an algorithm is to minimize
the cost by choosing the best option at any point in time. Multislope Ski
Rental is a natural generalization of the classical Ski Rental problem (where
the only options are pure rent and pure buy), which is one of the fundamental
problems of online computation. The Multislope Ski Rental problem is an
abstraction of many problems where online decisions cannot be modeled by just
two options, e.g., power management in systems which can be shut down in parts.
In this paper we study randomized algorithms for Multislope Ski Rental. Our
results include the best possible online randomized strategy for any additive
instance, where the cost of switching from one option to another is the
difference in their buying prices; and an algorithm that produces an
$e$-competitive randomized strategy for any (non-additive) instance.
