Question 4: Consider the following queueing network in hospital that patients arrive to the emergency department based on Poisson distribution and receive care in different units based on exponential distribution. The arrival rate to the system is 4 patient per hour and after triage, they are sent to either outpatient lab or treatment room with equal probabilities. Only 60 percent of patients are treated and send out from the hospital. The service time at each node is presented in the table below: Part a) Compute the arrival rate for each node. Part b) Find the steady state distribution of the number of patients at each node. Part c) What is the probability of having empty queue before the outpatient lab node. Part d) Find the expected total number of patients in the system