  We present deterministic and randomized algorithms for the problem of online
packet routing in grids in the competitive network throughput model
\cite{AKOR}. In this model the network has nodes with bounded buffers and
bounded link capacities. The goal in this model is to maximize the throughput,
i.e., the number of delivered packets.
  Our deterministic algorithm is the first online algorithm with an
$O\left(\log^{O(1)}(n)\right)$ competitive ratio for uni-directional grids
(where $n$ denotes the size of the network). The deterministic online algorithm
is centralized and handles packets with deadlines. This algorithm is applicable
to various ranges of values of buffer sizes and communication link capacities.
In particular, it holds for buffer size and communication link capacity in the
range $[3 \ldots \log n]$.
  Our randomized algorithm achieves an expected competitive ratio of $O(\log
n)$ for the uni-directional line. This algorithm is applicable to a wide range
of buffer sizes and communication link capacities. In particular, it holds also
for unit size buffers and unit capacity links. This algorithm improves the best
previous $O(\log^2 n)$-competitive ratio of Azar and Zachut \cite{AZ}.
