Limit Theorems for Queueing Systems with Various Service Disciplines in Heavy-Traffic Conditions

In this paper a multi-server queueing system with regenerative input flow and independent service times with finite means is studied. We consider queueing systems with various disciplines of the service performance: systems with a common queue and systems with individual queues in front of the servers. In the second case an arrived customer chooses one of the servers in accordance with a certain rule and stays in the chosen queue up to the moment of its departure from the system. We define some classes of disciplines and analyze the asymptotical behavior of a multi-server queueing system in a heavy-traffic situation (traffic rate rho >= 1). The main result of this work is limit theorems concerning the weak convergence of scaled processes of waiting time and queue length to the process of the Brownian motion for the case rho > 1 and its absolute value for the case rho = 1.