Name
Abstract | ||
|---|---|---|
We identify conditions under which relatively large buffers will be required in broadband communication networks. For this purpose, we analyze an infinite-capacity stochastic fluid model with a general stationary environment process (without the usual independence or Markov assumptions). With that level of generality, we are unable to establish asymptotic results, but by a very simple argument we are able to obtain a revealing lower bound on the steady-state buffer-content tail probability. The bounding argument shows that the steady-state buffer content will have a long-tail distribution when the sojourn time in a set of states with positive net input rate itself has a long-tail distribution. If a set of independent sources, each with a general stationary environment process, produces a positive net flow when all are in high-activity states, and if each of these sources has a high-activity sojourn-time distribution with a long tail, then the steady-state buffer-content distribution will have a long tail, but possibly one that decays faster than the tail for any single component source. The full buffer-content distribution can be derived in the special case of a two-state fluid model with general high- and low-activity-time distributions, assuming that successive high- and low-activity times come from independent sequences of i.i.d. random variables. In that case the buffer-content distribution will have a long tail when the high-activity-time distribution has a long tail. We illustrate by giving numerical examples of the two-state model based on numerical transform inversion. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1016/S0166-5316(96)00059-4 | Perform. Eval. |
Keywords | Field | DocType |
stochastic fluid models,b-isdn,subexponential distributions,long-tail distributions,tail probabilities,regularly variation,long-tail buffer-content distribution,power tails,broadband network,broadband networks,buffer content,atm,asynchronous transfer mode,stochastic fluid model,long tail | Statistical physics,Random variable,Upper and lower bounds,Markov chain,Fluid queue,Heavy-tailed distribution,Broadband networks,Statistics,Mathematics,Distributed computing,Special case,Bounding overwatch | Journal |
Volume | Issue | ISSN |
30 | 3 | Performance Evaluation |
Citations | PageRank | References |
27 | 8.44 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gagan L. Choudhury | 1 | 445 | 75.32 |
| Ward Whitt | 2 | 3562 | 697.71 |