On a multilevel controlled bulk queueing system \(M^ X /G^{r,R} /1\)
The authors study a general bulk queueing system with a multilevel control and a queue length dependent service delay discipline. Earlier works on queueing system with service delay discipline deals with the case that bulk input on the service times depends on the group sizes. In this work, interval times of the input stream, the sizes of arriving batches of customers, and service time distributions of groups of customers taken for service, all depend upon the queue length. Necessary and sufficient conditions for the ergodicity of the queueing process with discrete and continuous time parameters are established. Techniques of the analysis of a class of general Markov chains is used. The stationary distribution of the continuous time queueing process is obtained by using semi-regenerative techniques.
scientific article; zbMATH DE number 98945