Queueing systems with fractional number of servers

In this paper we introduce multi-server queueing systems that can be considered as extensions of conventional M/M/s queue to fractional number of servers. We show that the extended Erlang's delay function can be used to calculate delay probabilities for such systems. This approach enables the delay analysis in networks with fractional number of servers in the nodes using classical methods. -- Erlang's delay function ; multi-server system ; state dependent service times