Name
Title | ||
|---|---|---|
Queueing systems fed by many exponential on-off sources: an infinite-intersection approach |
Abstract | ||
|---|---|---|
In queueing theory, an important class of events can be written as `infinite intersections'. For instance, in a queue with constant service rate c, busy periods starting at 0 and exceeding L 0 are determined by the intersection of the events $$\bigcap_{t\in[0,L]}\{Q_0=0,\;A_t ct\}$$ , i.e., queue Q t is empty at 0 and for all t驴 [0, L] the amount of traffic A t arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue, can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called `many-sources regime'). If the sources are of the exponential on-off type, and the queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The techniques used stem from large deviations theory (particularly sample-path large deviations). |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s11134-006-7781-7 | Queueing Syst. |
Keywords | Field | DocType |
Sample-path large deviations,On-off processes,Busy period,Tandem queue,Priority queue | M/M/1 queue,Kendall's notation,Combinatorics,M/D/1 queue,Bulk queue,M/M/c queue,M/G/k queue,M/D/c queue,Real-time computing,M/M/∞ queue,Mathematics | Journal |
Volume | Issue | ISSN |
54 | 1 | 0257-0130 |
Citations | PageRank | References |
4 | 0.51 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michel Mandjes | 1 | 534 | 73.65 |
| Petteri Mannersalo | 2 | 234 | 18.96 |