The effect of related message transfer and process times on waiting times and buffer sizes in switch architectures

A node in a switch architecture is examined. The node receives messages, stores and processes them locally, and transmits them to other nodes. Both message transmission and processing times depend on the message length, which is a random variable. The node is modeled as a queue with a single server where the interarrival and service times are related, and different cases are studied where this relation ranges from direct dependence to moderate correlation. Exponential and uniform probability density functions (pdf's) are examined, and the results are compared to the independent model. A relationship is developed for the system time pdf of a message, which is used to find the system time pdf and the system state probabilities. These quantities are directly related to buffer sizes and transmission delays within the architecture.<
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