OPTIMAL CONTROL OF ARRIVAL RATE IN THE MULTI-SERVER QUEUEING SYSTEMS WITH ROUTER AND OCCASIONALLY OBSERVED QUEUE LENGTH ON DEVICES
The article deals with optimal control of arrival rate in the multi-server queueing systems with router and occasionally observed queue length on devices. Two processes of queue length are considered: episodic process of queue length built on observations at stopping time, and the similar model with the added telegraph process. A solution of the problem reduced to finding extreme point of a functional model that depends on average length queue, cost of observations and modeling time. Mathematical model of multi- server queueing systems in term of point processes, construction of algorithm, numerical experiments, resulting graph of system performance are presented in this article. In summary lessons learned about selection of the optimal control of arrival rate for a given occasionally observed queue length on servers.