Abstract
The usual procedure for obtaining the equilibrium probability distribution of the queue length in a queueing system is by constructing and solving the difference-differential equations. In this paper, a new approach for deriving the equilibrium probability distributions of the queue length in the M/M/1, M/Ejl and EjEjl queueing systems is presented, based on the generating function of the number of the minimal lattice paths. The proposed procedure obtains the equilibrium probability distribution more easily than the usual procedure, which solves difference-differential equations.
| Original language | English |
|---|---|
| Pages (from-to) | 245-253 |
| Number of pages | 9 |
| Journal | Journal of the Operational Research Society |
| Volume | 46 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Feb 1995 |
| Externally published | Yes |
Keywords
- Combinatorial theory
- Equilibrium probability distribution
- Minimal lattice paths
- Queue¬ing systems
ASJC Scopus subject areas
- Management Information Systems
- Strategy and Management
- Management Science and Operations Research
- Marketing