In formulas on M/D/c queue it is assumed that service time is the same for all servers. Are there formulas for the case when service times differ between servers (in general case there would be as many service times as there are servers) ? For example there is a group of servers, all providing the same service, but servers capabilities differ, so the service time although constant is not the same among the servers.
I am interested in response time distribution primarily.
Thanks in advance Ilja
Your system description is still slightly vague, is it such that it could be described by the $c+1$ dimensional vector where the first $c$ components describe the remaining service of the job at each of the service nodes and the final element the number of queueing jobs awaiting service?
Suppose there is one job queueing and a server becomes available, but that if the job waited a while a faster server would become available and it would finish earlier. What does the job do in this situation? As you have heterogeneous servers you need to carefully define the system dynamics as there are complications that do not arise in the standard M/D/$c$ model.
You may find simulation is the easiest way to numerical values for a particular situation, if this is what you seek.