M/M/c is not the right model for a typical loadbalancer, since a loadbalancer typically does not manage a shared queue but simply passes the jobs to one of the servers. The models are:
- M/M/1 (vertical scaling, one queue and one fast server): fastest response time
- M/M/c (thread-pool, one shared queue, c slow servers): c-times slower for low loads, asymptotically similar to M/M/1 for high loads
- c-times M/M/1 (loadbalancer, c slow servers each which its own queue): always c-times slower than M/M/1.
Only the response times are different. Throughtput is the same in the ideal case.
- M/M/1 (vertical scaling, one queue and one fast server): fastest response time
- M/M/c (thread-pool, one shared queue, c slow servers): c-times slower for low loads, asymptotically similar to M/M/1 for high loads
- c-times M/M/1 (loadbalancer, c slow servers each which its own queue): always c-times slower than M/M/1.
Only the response times are different. Throughtput is the same in the ideal case.