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/Ek/1 and El/Ek/1 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.
|Number of pages||9|
|Journal||Journal of the Operational Research Society|
|Publication status||Published - Feb 1995|
ASJC Scopus subject areas
- Management of Technology and Innovation
- Strategy and Management
- Management Science and Operations Research