The number of sensors increases in instrumentation systems. And the advancements of computers make possible the collection of large quantities of sensor data. This paper considers the computational complexity of analyzing the sensor data in a distributed instrumentation network. The network is composed of many sensors, preprocessors and processors. The processors are connected by a local area network containing token rings and buses. The lower and upper bounds for some distributed algolithms of data analysis are derived for the network where each of loops makes one ring. And the time complexity and communication complexity required for processing all the data of the processors are given.