Traffic grooming in optical networks employing wavelength division multiplexing has gained prominence due to the prevailing sub-wavelength capacity requirements of users. One approach to achieving wavelength sharing is through time division multiplexing. Connection requests can have a varying number of time slot requirements. Analytical modeling for computing the blocking performance of establishing multi-rate connections in WDM grooming networks involves extensive combinatorial complexity and thus requires prohibitively large state-space for solution. In this paper, we develop an analytical model that employs an approximation to the exact distribution of number of calls of a certain bandwidth requirement on a wavelength. We validate the approximation through simulation results for two different networks that have high and low link-load correlation. It is observed that up to an order of magnitude performance improvement is obtained by improving the grooming capability in the network for calls that require two time slots.