Explicit Solutions of M/G/C /N-type Queueing Loops with Generalizations.

Using recently developed Matrix-Algebraic techniques, we find explicit steady-state solutions of M/G/C//N-type loops that depend on a set of recursively defined matrices. We show that such systems are special cases of arbitrary service centers that contain (load dependent) exponential servers in which no more than C customers can be active simultaneously. We also outline a recursive algorithm that can be used to evaluate the properties of small- to moderate-sized systems. The solution to the M/G/C open system is then found by letting the overall customer population N go to infinity. The solutions for closed systems in general are not of the matrix geometric typo, and only in the limit does the solution become geometric in form. [ABSTRACT FROM AUTHOR]

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