Ski rental with two general options

We define and solve a simple extension of the ski-rental problem [A.R. Karlin, M.S. Manasse, L. Rudolph, D.D. Sleator, Competitive snoopy caching, Algorithmica 3 (1) (1988) 77-119]. In the classical version, the algorithm needs to decide when to switch from renting to buying. In our version, no pure buy option is available: even after switching to the buy option, the algorithm needs to pay some reduced rent.

[1]  Anna R. Karlin,et al.  Competitive snoopy caching , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[2]  Boaz Patt-Shamir,et al.  Rent, Lease, or Buy: Randomized Algorithms for Multislope Ski Rental , 2008, SIAM J. Discret. Math..

[3]  Claire Mathieu,et al.  Dynamic TCP Acknowledgment and Other Stories about e/(e - 1) , 2003, Algorithmica.

[4]  Sandy Irani,et al.  Competitive analysis of dynamic power management strategies for systems with multiple power saving states , 2002, Proceedings 2002 Design, Automation and Test in Europe Conference and Exhibition.

[5]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .