The generalized M/G/C//N-queue as a model for time-sharing systems

Generalized M/G/C//N queues are extended to include load-dependent servers of which time-sharing systems are a special case. These systems can be viewed as systems with population-size constraints. The recursive form of the equations yields an algorithm that requires the computational effort of at least an order of magnitude less than those commonly used to solve quasi-birth-death processes. The class of generalized queues, which is described in detail, includes the class of Jackson networks as a proper subset. Since these queues treat the line waiting to enter a restricted subsystem correctly, they can be used to study time-sharing systems where the degree of multiprogramming is restricted. Calculations of some simple models are reported and compared with calculations using the natural decomposition and aggregation approximation. The discrepancy between the two sets of calculations, as expected, was small for very light and very heavy loads. However the discrepancy in the intermediate region was as much as 50%, thereby indicating that the approximation must be used with caution