M-Vollständigkeit von Warteschlangensystemen (Q761943)

A queuing system for which Poisson arrivals imply Poisson departures is called M-complete. In the queuing systems investigated it is assumed that the number of servers is always equal to the number of customers present but servers may be idle. A service discipline is given by the assignment of the total service capacity and of the arriving customers to the individual servers. If this assignment is such that the incoming workload is distributed proportionally to the capacity of the individual servers for all possible numbers of customers in the system then the queuing system is M-complete if the service-time distributions have finite first moments and continuous derivatives. Several examples of M-complete systems are given.