QUEUES AND MARKED POINT PROCESSES

We suggest a queuetng system with phase type input and phase type output,descri- bed by a marked point process with values in a double-Lusin space.The case with inde- pendent input and output is discussed in detail.An existence theorem of optimal stocha- stic control dealing with the queueing system is obtained.In addition,we get a necessary and sufficient condition for mutual independence of two jump processes which admit no common jump time.