Name
Abstract | ||
|---|---|---|
The one-and two-dimensional distributions of the occupation time and of the local time of Brownian excursion are derived. These results follow from a suitable conditioned weak limit theorem. More specifically we shall prove that the normalized virtual waiting time process of the M/M/1 queue, conditioned by the length of its first busy period, weakly converges to the Brownian excursion process. At the end of this paper we shall discuss the connection between the local time of the Brownian excursion process and the number of downcrossings during the first busy period of an M/G/1 queue. This connection seems to be very interesting for the theory of branching processes. |
Year | DOI | Venue |
|---|---|---|
1981 | 10.1287/moor.6.4.608 | Math. Oper. Res. |
Keywords | DocType | Volume |
conditioned limit theorems,downcrossings,branching processes,distribution of occupation time---local time,m/g/1 queue,brownian excursion | Journal | 6 |
Issue | ISSN | Citations |
4 | 0364-765X | 6 |
PageRank | References | Authors |
0.91 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. W. Cohen | 1 | 40 | 6.76 |
| G. Hooghiemstra | 2 | 6 | 1.25 |