Consider a signal processing device connected to a communication channel taking messages from an exogenous source. Messages arrive to the channel with Poisson process with rate 1. In the signal processing device two random subprocesses take place for analyzing the signal. Random subprocesses take exponential amount of time with rates ul and u2. When a message arrives to the signal processing device, it is taken into process immediately if the device is idle. If there is a message being processed, new arrival needs to wait in queue. The device does not take another message into process until both subprocesses are idle, hence existing messages need to wait in queue, if any. In order avoid excessive times for waiting, the communication channel diverts incoming signals to another processor if there are 3 messages (1 in process and two waiting in the queue) in the main device. a. Provide the global balance equations for the limiting probabilities of the system. b. Solve the global balance equations to calculate the fraction of messages diverted to the other processor? Consider a signal processing device connected to a communication channel taking messages from an exogenous source. Messages arrive to the channel with Poisson process with rate 1. In the signal processing device two random subprocesses take place for analyzing the signal. Random subprocesses take exponential amount of time with rates ul and u2. When a message arrives to the signal processing device, it is taken into process immediately if the device is idle. If there is a message being processed, new arrival needs to wait in queue. The device does not take another message into process until both subprocesses are idle, hence existing messages need to wait in queue, if any. In order avoid excessive times for waiting, the communication channel diverts incoming signals to another processor if there are 3 messages (1 in process and two waiting in the queue) in the main device. a. Provide the global balance equations for the limiting probabilities of the system. b. Solve the global balance equations to calculate the fraction of messages diverted to the other processor