This article studies a single-server queueing system with autonomous service and ℓ priority classes. Arrival and departure processes are governed by marked point processes. There are ℓ buffers corresponding to priority classes, and upon arrival a unit of the kth priority class occupies a place in the kth buffer. Let N (k), k = 1,2,…, ℓ denote the quota for the total kth buffer content. The values N (k) are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values N (k) characterize buffer capacities. This article discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents, particularly buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.
Stochastic Models, Vol. 24, no. 4 (2008), pp. 527-557