An Imbedded Markov Chain Analysis for Finite Queues: An Analytical Approach to Numerical Results.

摘要

Imbedded Markov chains of finite queueing systems with unit jumps at regeneration points have an almost left triangular (in systems of the type G/M/s/N - in Kendall notation modified to include system capacity) or an almost right triangular (in systems of the type M/G/1/N) structure. Using this structure a fundamental recursion on the elements of the transition probability matrix is developed, which in turn helps derive first passage as well as equilibrium results in computationally feasible forms.