Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows

@article{Zwart2000ExactAF,
  title={Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows},
  author={Bert Zwart and Sem C. Borst and Michel Mandjes},
  journal={Industrial \& Engineering Chemistry Research},
  year={2000}
}
We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant” subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a… Expand

Figures from this paper

Exact queueing asymptotics for multiple heavy-tailed on-off flows
  • B. Zwart, S. Borst, M. Mandjes
  • Mathematics, Computer Science
  • Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213)
  • 2001
TLDR
A fluid queue fed by multiple on-off flows with heavy-tailed (regularly varying) on-periods is considered, and it is proved that the workload distribution is asymptotically equivalent to that in a reduced system. Expand
A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows
  • S. Borst, B. Zwart
  • Computer Science, Chemistry
  • Advances in Applied Probability
  • 2003
TLDR
Under mild assumptions, it is proved that the workload distribution is asymptotically equivalent to that in a somewhat ‘dual’ reduced system, multiplied by a certain prefactor. Expand
Fluid queues with heavy-tailed M/G/infinity input
We consider a fluid queue fed by several heterogeneous M / G / 00 input processes with regularly varying session lengths. Under fairly mild assumptions, we derive the exact asymptotic behavior of theExpand
Fluid Queues with Heavy-Tailed M/G/ Input
TLDR
A fluid queue fed by several heterogeneous M/G/∞ input processes with regularly varying session lengths is considered, and the exact asymptotic behavior of the stationary workload distribution is derived. Expand
Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations
TLDR
This work introduces a novel class of Lyapunov functions (piecewise linear and nonincreasing in the length of heavy-tailed queues), whose drift analysis provides exponentially decaying upper bounds to queue-length tail asymptotics despite the presence of heavy tails. Expand
Delay analysis of the Max-Weight policy under heavy-tailed traffic via fluid approximations
TLDR
A single-hop switched queueing network with a mix of heavy-tailed and light-tailed traffic is considered, and how fluid approximations and stochastic Lyapunov theory can be combined with renewal theory in order to prove delay instability results are shown. Expand
Generalized processor sharing queues with heterogeneous traffic classes
TLDR
This work derives the asymptotic workload behaviour of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity, and shows that the workload distribution is asymPTotically equivalent to that in the isolated system, multiplied by a certain prefactor which accounts for the interaction with the heavy-tailed flow. Expand
Two-node fluid network with a heavy-tailed random input: the strong stability case
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of aExpand
Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous Heavy-Tailed On-Off Pr
TLDR
This work derives explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate of a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent On–Off processes. Expand
On Large Delays in Multi-Server Queues with Heavy Tails
We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of theExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 60 REFERENCES
Overflow behavior in queues with many long-tailed inputs
We consider a fluid queue fed by the superposition of n homogeneous on-off sources with generally distributed on and off periods. The buffer space B and link rate C are scaled by n, so that we get nbExpand
Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources
We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. WeExpand
On a reduced load equivalence for fluid queues under subexponentiality
TLDR
A general framework for obtaining asymptotic distributional bounds on the stationary backlog in a buffer fed by a combined fluid process A1 + A2 and drained at a constant rate c is proposed. Expand
Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues
TLDR
A large deviation approach provides a powerful method of studying the tail behavior of the increase in the buffer content during a busy period of the M/G/∞ queue feeding the buffer. Expand
ASYMPTOTIC RESULTS FOR MULTIPLEXING SUBEXPONENTIAL ON-OFF PROCESSES
Consider an aggregate arrival process A N obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τ on .A sN goes to infinity, with λN → � , AExpand
A fluid queue with a finite buffer and subexponential input
  • A. Zwart
  • Physics, Mathematics
  • Advances in Applied Probability
  • 2000
We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue establishedExpand
Queueing at large resources driven by long-tailed M/G/∞-modulated processes
  • N. Duffield
  • Mathematics, Computer Science
  • Queueing Syst. Theory Appl.
  • 1998
We analyze the queue at a buffer with input comprising sessions whose arrival is Poissonian, whose duration is long-tailed, and for which individual session detail is modeled as a stochastic fluidExpand
Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival andExpand
Asymptotics of palm-stationary buffer content distributions in fluid flow queues
We study a fluid flow queueing system with m independent sources alternating between periods of silence and activity; m ≥ 2. The distribution function of the activity periods of one source, isExpand
Fluid queues with long-tailed activity period distributions
TLDR
This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like long-range dependence, and on the effect of this tail behaviour on the steady-state distributions of the buffer content at embedded points in time and at arbitrary time. Expand
...
1
2
3
4
5
...