Abstract
We study a service system with a fixed upper bound for its workload and two independent inflows of customers: frequent 'small' ones and occasional 'large' ones. The workload process generated by the small customers is modelled by a Brownian motion with drift, while the arrival times of the large customers form a Poisson process and their service times are exponentially distributed. The workload process is reflected at zero and at its upper capacity bound. We derive the stationary distribution of the workload and several related quantities and compute various important characteristics of the system.
Original language | English |
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Pages (from-to) | 1155-1166 |
Number of pages | 12 |
Journal | Journal of Applied Probability |
Volume | 36 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1999 |
Externally published | Yes |
Keywords
- Brownian motion
- Heavy traffic
- Poisson process
- Queueing
- Workload process
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty