Allocation of Clients to Multiple Servers on Large Scale Heterogeneous Platforms

We consider the problem of allocating a large number of independent, equal-sized tasks to a heterogeneous large scale computing platform. We model the platform using a set of servers (masters) that initially hold (or generate) the tasks to be processed by a set of clients (slaves). All resources have different speeds of communication and computation and we model contentions using the bounded multi-port model. This model corresponds well to modern networking technologies, but for the sake of realism, another parameter needs to be introduced in order to bound the number of simultaneous connections that can be opened at a server node. We prove that unfortunately, this additional parameter makes the problem of maximizing the overall throughput NP-complete. On the other hand, we also propose a polynomial time algorithm, based on a slight resource augmentation, to solve this problem. More specifically, we prove that, if
d

_j
denotes the maximal number of connections that can be opened at server node
S

_j
, then the throughput achieved using this algorithm and
d

_j
+ 1 simultaneous connections is at least the same as the optimal one with
d

_j
simultaneous connections. This algorithm also provides a good approximation for the dual problem of minimizing the maximal number of connections that need to be opened in order to achieve a given throughput, and it can be turned into a standard approximation algorithm (
i
.
e
., without resource augmentation). Finally, we also propose extensive simulations to assess the performance of the proposed algorithm.