Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
Characteristics of wide-area TCP/IP conversations
SIGCOMM '91 Proceedings of the conference on Communications architecture & protocols
The physics of the Mt/G/ ∞ symbol Queue
Operations Research
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Empirically derived analytic models of wide-area TCP connections
IEEE/ACM Transactions on Networking (TON)
SIGCOMM '95 Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates
IEEE/ACM Transactions on Networking (TON)
Self-similarity in World Wide Web traffic: evidence and possible causes
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Conditioned asymptotics for tail probabilities in large multiplexers
Performance Evaluation
The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
Queueing Systems: Theory and Applications
Asymptotic Expansions for the Congestion Period for the M/M/∞ Queue
Queueing Systems: Theory and Applications
A Markov Renewal Based Model for Wireless Networks
Queueing Systems: Theory and Applications
Two-parameter heavy-traffic limits for infinite-server queues
Queueing Systems: Theory and Applications
Using different response-time requirements to smooth time-varying demand for service
Operations Research Letters
Dynamic staffing in a telephone call center aiming to immediately answer all calls
Operations Research Letters
| Hi-index | 0.00 |
We develop deterministic fluid approximations to describe the recovery from rare congestion events in a large multi-server system in which customer holding times have a general distribution. There are two cases, depending on whether or not we exploit the age distribution (the distribution of elapsed holding times of customers in service). If we do not exploit the age distribution, then the rare congestion event is a large number of customers present. If we do exploit the age distribution, then the rare event is an unusual age distribution, possibly accompanied by a large number of customers present. As an approximation, we represent the large multi-server system as an M/G/\infty model. We prove that, under regularity conditions, the fluid approximations are asymptotically correct as the arrival rate increases. The fluid approximations show the impact upon the recovery time of the holding-time distribution beyond its mean. The recovery time may or not be affected by the holding-time distribution having a long tail, depending on the precise definition of recovery. The fluid approximations can be used to analyze various overload control schemes, such as reducing the arrival rate or interrupting services in progress. We also establish large deviations principles to show that the two kinds of rare events have the same exponentially small order. We give numerical examples showing the effect of the holding-time distribution and the age distribution, focusing especially on the consequences of long-tail distributions.