Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time
Queueing Systems: Theory and Applications
On the self-similar nature of Ethernet traffic
SIGCOMM '93 Conference proceedings on Communications architectures, protocols and applications
Source models for VBR broadcast-video traffic
IEEE/ACM Transactions on Networking (TON)
Long-tail buffer-content distributions in broadband networks
Performance Evaluation
Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models
Mathematics of Operations Research
A practical guide to heavy tails
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
Fluid queues with long-tailed activity period distributions
Fluid queues with long-tailed activity period distributions
Tail probabilities for a multiplexer with self-similar traffic
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 3
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 3
The effect of multiple time scales and subexponentiality in MPEG video streams on queueing behavior
IEEE Journal on Selected Areas in Communications
A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation
Performance Evaluation
Finite buffer queue with generalized processor sharing and heavy-tailed input processes
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Heavy-Traffic Limits for Loss Proportions in Single-Server Queues
Queueing Systems: Theory and Applications
Tail asymptotics for the queue length in an M/G/1 retrial queue
Queueing Systems: Theory and Applications
Queue analysis and multiplexing of heavy-tailed traffic in wireless packet data networks
Mobile Networks and Applications
Fluid Queues with Heavy-Tailed M/G/∞ Input
Mathematics of Operations Research
Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue
Performance Evaluation
On the flexibility of M/G/∞ processes for modeling traffic correlations
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
Queueing Systems: Theory and Applications
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Consider a single server queue with i.i.d. arrival and service processes, \{A,\ A_n,n\geq 0\} and \{C,\ C_n,n\geq 0\}, respectively, and a finite buffer B. The queue content process \{Q^B_n,\ n\geq 0\} is recursively defined as Q^B_{n+1}=\min((Q^B_n+A_{n+1}-C_{n+1})^+,B), q^+=\max(0,q). When \mathbb{E}(A-C), and A has a subexponential distribution, we show that the stationary expected loss rate for this queue \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+ has the following explicit asymptotic characterization: \mathbb{E}(Q^B_n+A_{n+1}-C_{n+1}-B)^+\sim \mathbb{E}(A-B)^+ \quad \hbox{as} \ B\rightarrow \infty, independently of the server process C_n. For a fluid queue with capacity c, M/G/\infty arrival process A_t, characterized by intermediately regularly varying on periods \tau^{\mathrm{on}}, which arrive with Poisson rate \Lambda, the average loss rate \lambda_{\mathrm{loss}}^B satisfies {\lambda_{\mathrm{loss}}^B}\sim \Lambda \mathbb{E}(\tau^{\mathrm{on}}\eta-B)^+ \quad \hbox{as}\ B\rightarrow \infty, where \eta=r+\rho-c, \rho=\mathbb{E}A_t; r (c\leq r) is the rate at which the fluid is arriving during an on period. Accuracy of the above asymptotic relations is verified with extensive numerical and simulation experiments. These explicit formulas have potential application in designing communication networks that will carry traffic with long-tailed characteristics, e.g., Internet data services.