  In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW)
cosmological models by considering three different forms of variable $\Lambda$:
$\Lambda\sim(\frac{\dot{a}}{a})^2$,$\Lambda\sim(\frac{\ddot{a}} {a})$ and
$\Lambda \sim \rho$. It is found that, the connecting free parameters of the
models with cosmic matter and vacuum energy density parameters are equivalent,
in the context of higher dimensional space time. The expression for the look
back time, luminosity distance and angular diameter distance are also derived.
This work has thus generalized to higher dimensions the well-known results in
four dimensional space time. It is found that there may be significant
difference in principle at least, from the analogous situation in four
dimensional space time.
