On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON)
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
Queueing at large resources driven by long-tailed M/G/\infty-modulated processes
Queueing Systems: Theory and Applications
On a reduced load equivalence for fluid queues under subexponentiality
Queueing Systems: Theory and Applications
M|G|Infinity Input Processes: A Versatile Class of Models for Network Traffic
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
Performance evaluation of a queue fed by a Poisson Pareto burst process
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Fluid Queues with Heavy-Tailed M/G/∞ Input
Mathematics of Operations Research
Performance analysis of a Poisson-Pareto queue over the full range of system parameters
Computer Networks: The International Journal of Computer and Telecommunications Networking
Snapshot simulation of internet traffic: queueing of fixed-rate flows
Proceedings of the 2nd International Conference on Simulation Tools and Techniques
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We consider a fluid queue fed by sessions, arriving according to a Poisson process; a session has a heavy-tailed duration, during which traffic is sent at a constant rate. We scale Poisson input rate @L, buffer space B, and link rate C by n, such that we get n@l,nb, and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n; we examine the specific situation in which b is also large. In Duffield (Queueing Syst. 28 (1998) 245-266) this setting is considered. A crucial role was played by the function v(t)@?-logP(D^*t) for large t,D^* being the residual session duration. Duffield covers the case that v(.) is regularly varying of index strictly between 0 and 1 (e.g., Weibull); this note treats slowly varying v(.) (e.g., Pareto, Lognormal). The proof adds insight into the way overflow occurs. If v(.) is slowly varying then, during the trajectory to overflow, the input rate will exceed the link rate only slightly. Consequently, the buffer will fill 'slowly', and the typical time to overflow will grow 'faster than linearly' in the buffer size. This is essentially different from the 'Weibull case', where the input rate will significantly exceed the link rate, and the time to overflow is essentially proportional to the buffer size. In both cases there is a substantial number of sessions that remain in the system during the entire path to overflow.