Allocating servers in infostations for bounded simultaneous requests

The Server Allocation with Bounded Simultaneous Requests problem arises in isolated infostations, where mobile users going through the coverage area require immediate high-bit rate communications such as web surfing, file transferring, voice messaging, email and fax. Given a set of service requests, each characterized by a temporal interval and a category, an integer $k$, and an integer $h_c$ for each category $c$, the problem consists in assigning a server to each request in such a way that at most $k$ mutually simultaneous requests are assigned to the same server at the same time, out of which at most $h_c$ are of category $c$, and the minimum number of servers is used. Since this problem is computationally intractable, a $2$-approximation on-line algorithm is exhibited which asymptotically gives a $left(2-frac{h}{k}right)$-approximation, where $h = min {h_c}$. Generalizations of the problem are considered, where each request $r$ is also characterized by a bandwidth rate $w_r$, and the sum of the bandwidth rates of the simultaneous requests assigned to the same server at the same time is bounded, and whereeach request is characterized also by a gender bandwidth. Such generalizations contain Bin-Packing, Multiprocessor Task Scheduling, and Interval Graph Coloring as special cases, and they admit on-line algorithms providing constant approximations.