A closed, cyclic, two-stage multiprogrammed system model and its diffusion approximation solution

• Authors: Baruch Halachmi;W. R. Franta
• Venue: SIGMETRICS '74 Proceedings of the 1974 ACM SIGMETRICS conference on Measurement and evaluation
• Year: 1974

In this paper attention is focused on closed multiprogrammed computer type systems. In particular, two-stage closed queueing systems are considered. The first stage can be associated with the CPU (Central Processing Unit) and the other with the I/O (Input-Output) operations. For all the models discussed. For the first model we consider the {GI1/MS/N} system, which allows the service times of a single CPU to obey any general probability distribution, with finite variance, while the I/O servers are taken to be exponential. The second model is an extension of the first where the concept of feedback is implemented in the CPU stage. This concept plays an important role in computer environments where the operating system includes the multiplexing or page on demand property. The third model, the {MS1/MS2/N}, deals with multiprocessing computer systems where possibly more than one CPU is available, but all servers are assumed to be exponential. In the spirit of the approximation to the GI/G/S open system, as a final model, we construct the approximate solution to the {GIS1/GIS2/N} closed system and discuss the circumstances under which its use is advisable. Several numerical examples for each of the models are given, each accompanied by appropriate simulation results for comparison. It is on the basis of these comparisons that the quality of the suggested diffusion approximations can be judged. The diffusion approximating formulas should be regarded not only as a numerical technique, but also as a simplifying approach, by which deeper insight can be gained into complicated queueing systems. Considerable work remains to be done, using as a methodology the approach, given here, and several possible extensions are presented.