messages arrive at a node in a communication network according to a poisson process with rate lambda. each arriving message is temporarily stored in an infinite- capacity buffer until it can be transmitted. the messages have to be routed over one of two communication lines each with different transmission time. the transmission time over the communication line is i exponentially distributed with mean 1/miu i (i = 1,2), where 1/miu1 < 1/miu2 and miu1+miu2 > lambda. the faster communication line is always available for service, but the slower line will be used only when the number of messages in the buffer exceeds some critical level. each line is only able to handle one message at a time and provides non-pre-emptive services. with the goal of minimizing the average sojourn time (including transmission time) of a message in the system, the following control rule with switching level L is used. the slower line is turned on for transmitting a message when the number of messages in the system exceeds the level L and is turned off again when it completes a transmission and the number of messages left behind is at or below L . show how to calculate the average sojourn time of messages in the system.
