On queueing systems with a fractional number of devices

Queueing systems with several servers and a special discipline whereby demands are successively received by servers until the servicing is completed are considered. Among these systems, there are such systems whose characteristics constantly depend on a certain positive parameter. Given integer values of the latter, the waiting probability and average sojourn time coincide with those calculated using the Erlang C formula. Therefore, these systems can be considered as generalizations of the classical M/M/s system to a fractional number of servers.