  Achieving optimal transmission throughput in data networks in a multi-hop
wireless networks is fundamental but hard problem. The situation is aggravated
when nodes are mobile. Further, multi-rate system make the analysis of
throughput more complicated. In mobile scenario, link may break or be created
as nodes are moving within communication range. `Route Discovery' which is to
find the optimal route and transmission schedule is an important issue. Route
discovery entails some cost; so one would not like to initiate discovery too
often. On the other hand, not discovering reasonably often entails the risk of
being stuck with a suboptimal route and/or schedule, which hurts end-to-end
throughput. The implementation of the routing decision problem in one
dimensional mobile ad hoc network as Markov decision process problem is already
is discussed in the paper [1]. A heuristic based on threshold policy is
discussed in the same paper without giving a way to find the threshold. In this
paper, we suggested a rule for setting the threshold, given the parameters of
the system. We also point out that our results remain valid in a slightly
different mobility model; this model is a first step towards an `open' network
in which existing relay nodes can leave and/or new relay nodes can join the
network.
