Analysis of Finite Buffered Multistage Combining Networks

Analyzing the performance of finite buffered multistage networks has been considered a difficult task because of dynamic blocking effects due to finite sized buffers. With the multistage networks enhanced with combining capability, in which multiple requests directed to a shared location combine together to form a single request to be forwarded, the analysis becomes even more difficult due to the interactions between combining probability and queuing delay. Performance bounds for combining networks are known under two extreme assumptions: infinite combining queues and saturated finite combining queues. We analyze multistage combining networks with the consideration of blocking due to finite combining queues. Our analysis provides iterative solutions for combining probability, blocking probability, and queuing delay.