Queues with regular variation (Q2760875)

This is a PhD thesis defended in September, 2001, at Eindhoven University of Technology. It is devoted to the study of queueing models with heavy-tailed service time distribution. Four queueing models are on the discussion: (i) the \(M/G/1\) queue with priority classes (studied on the base of the heavy-traffic limit theorem); (ii) the tandem queueing system with Poisson input processes and identical service time at both servers (asymptotic analysis of such polling system is done); (iii) polling systems with gated or exhaustive service (the tail behaviour of the waiting time distributions is investigated in the case when at least one of service and/or switchover time distributions has a regularly varying tail); (iv) the \(M/G/2\) queue with heterogeneous servers (exact analysis of the queue length and waiting time distribution in the case when the general service time distribution has a rational Laplace-Stiltjes Transform as well as an asymptotic analysis of the waiting time tail with regularly varying general service time distribution is made). It is obtained also heavy traffic limit theorem for sojorn time distribution on the second server for the tandem system with regularly varying service time distribution with infinite and finite variance.