Samsung - Delay in service

I had placed a request for Samsung Ac service on **/**/**** (Tracking No ********** / Samsung Ref. No **********). I have been following up with Samsung customer care on every alternate day to send some executive for AC servicing but every day they keep on telling that they have sent intimation to the service centre to send someone for the service and they will be reaching me out on my contact no. ie; +** ********** but I haven't received any call nor any of the service engineers have visited my place for service.
Today I had been calling Samsung support from morning ** am to expedite my request as its almost ** days and they keep telling that they have put the request on priority and nothing happened so far. I have got the contact details of Mr Shabbir (+** **********) the Star digital service manager from one of this worker. Even he is not receiving calls and nor replying with the text. In this case, whom shall I approach for escalation I am not sure on that as the Samsung customer service guys keep telling me that we are forwarding your case to concern department they will get back to you.
Every time I have got installation/de-installation and service done via Samsung for my AC. I don't want to go for any *rd party service and if Samsung service is not able to provide an engineer in ** days not sure where I need to go for my AC service. I want to file a case against Samsung for this irrational behaviour and not taking responsibility for providing a service engineer for general AC servicing.