Queueing systems with heavy tails (Q2760877)

The first chapter of the monograph serves as a general introduction to motivate the analysis of queueing systems with heavy-tailed input. Chapter 2 gives an introduction to heavy-tailed distributions, treats some basic results for queueing systems with heavy tails, and gives some heuristics for constructing a proof. Chapter 3 contains results for the steady-state sojourn-time distribution of the M/G/1 processing sharing queue. The main result obtained here is the following: the tails of the service- and sojourn-time distribution are equally heavy. A fluid queue with a finite buffer is considered in Chapter 4. Chapter 5 investigates busy-period asymptotics in single-server queues. The central subject of investigation of Chapters 6 and 7 is the fluid queue fed by a finite number of on-off sources with heavy-tailed on- and/or off-periods, and possibly some additional light-tailed input. Both chapters focus on the asymptotic behaviour of the workload distribution, Chapter 8 considers fluid queues with heavy-tailed M/G/\(\infty\) input.