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

Ch. 8. P. 1529–1538.

Grishunina S.

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 to a certain rule and stays in the chosen queue up to the moment of its departure from the system. We define some classes of disciplines and analyze the asymptotical behaviour of a multi-server queueing system in a heavy-trac situation (trac rate is more or equals 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 when the traffic rate is more then one and its absolute value for the case when the traffic rate equals one.

Keywords: heavy-traffic, queueing system, service disciplines, limit theorems

In book

Methodology and Computing in Applied Probability

Vol. 22: Methodology and Computing in Applied Probability. Issue 4: Methodology and Computing in Applied Probability. , Netherlands: Springer, 2020.