Abstract
We study a single server queueing system with general service time distribution and memoryless inter-arrival times. The arrival rate is not constant but varies with the number of customers in the system. A recursive formula for the conditional distribution of the remaining service time given the queue length is derived for an arbitrary epoch. It is also shown that this conditional distribution holds for arrival epochs. The recursion for the corresponding Laplace-Stieltjes transforms and expected values is given in a simple formula.
| Original language | English |
|---|---|
| Pages (from-to) | 364-375 |
| Number of pages | 12 |
| Journal | Stochastic Models |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Jul 2008 |
| Externally published | Yes |
Keywords
- Residual service time
- Single server queue
- State department arrival process
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics