ASYMPTOTIC STATIONARITY OF QUEUES IN SERIES AND THE HEAVY TRAFFIC APPROXIMATION

One deals with a system of queues in series: that is to say, a number of queues through which a unit passes in turn, spending a waiting time including service in any particular one, and proceeding to the next succeeding queue immediately the service time is completed. The first main result deals with the asymptotic behaviour of the vector of waiting times of a unit in each queue and of the time which a unit spends in the tandem queue. The second main result deals with the heavy traffic approximation of the mentioned characteristics