Hi Chandan. I've been out of the travel demand management world for a while, so please take this with a grain of salt. Maybe this tip will help you reach out to some urban transportation planners (or Google/Waze) within your organization or region that may already have the TAZs and O&D matrices setup to help do this? Here is an article that kind of describes what is bouncing around my skull.
Estimating O-D Trips Between Sub-divided Smaller Zones Within a Traffic Analysis Zone | Request PDF
Basically you would want to use existing transportation zones (TAZs) that may generate or attract trips (based upon land use types and population characteristics) that will ultimately be assigned to the road/corridor you want to evaluate. This would provide you with the number of vehicles (and vehicle miles) that could potentially travel that corridor. I would think there are some geoprocessing tools that could help review desire lines to summarize this?
I've also read a little about a new Google/Waze pilot where they are releasing cellphone-level tracking data that might be usable to "count" trips from home to where ever.
Hope I'm not sending you on too much of a wild goose chase. Good luck.