Generally service rate distribution is a term used in queuing theory, where different queues have different service times (and hence different service rates) distributed according to various mathematical models, and therefore different applications.
1. In an M/M/1 queue, the arrival rate (time) is Poisson distributed, and M/G/1 is exponentially distributed.
Application: Any basic queuing system, like people arriving at a railway station counter to buy tickets to travel.
2. In an M/G/1 queue the arrival rate is Markovian (regulated by a Poisson process) and the service rate distribution is general.
Application: Measuring the performance of a fixed head hard disk.