That wording is a little confusing in that a claim is either to a method or to a thing. Of course methods can involve things and sometimes things can be characterized by steps they perform. Without the framework of the wording of your claim 1 it is not 100% clear that the dependent claim you suggest would be proper.
If claim 1 is a well formed method claim, the dependent claim could be "The method of claim 1 where the network-connected device is an application server." This assumes the words "network-connected device" appear in claim 1 and claim is indeed a method claim. And that it is clear what application server means in the context of your application.
Many would use "wherein", I prefer the simpler "where".