Analysis of a Switching System Subject to Malfunction and Repair of Control Units

A switching circuit with two control units (CU I and CU II), each acting as standby for the other, is analyzed; the standby mode is active. The switching circuit services calls arriving from N transmitters according to a definite distribution function. The task of CU I and CU II is to set up the connections by which the subsequent “conversation” is to take place (i.e., servicing of calls). If one CU malfunctions in the course of operation, the remainder of the task is executed by the other CU. The failure-free operating times and repair times of the CU have exponential distribution functions. The probabilistic characteristics (distribution of the number of calls in the system and number of operative CU) of the given system are analyzed by the embedded Markov chain model. The transition and end-state probabilities of the chain are determined. The principal term is found in the expansion of the expectation value of the increase in the switching time relative to the case in which both control units are 100