Consider the job sharing computer system illustrated below. Incoming jobs arrive from the left in a Poisson stream. Each job, independently of other jobs, requires pre-processing in system 1 with probability Q. Jobs in system 1 are served FCFS and the service times for successive jobs entering system 1 are IID with an exponential distribution of mean 1/µ
1. The jobs entering system 2 are also served FCFS and successive service times are IID with an exponential distribution of mean 1/µ
2. The service times in the two systems are independent of each other and of the arrival times. Assume that µ1 > Q and that µ
2> λ. Assume that the combined system is in steady state.
a Is the input to system 1 Poisson? Explain.
b) Are each of the two input processes coming into system 2 Poisson? Explain.
d) Give the joint steady-state PMF of the number of jobs in the two systems. Explain briefly.
e) What is the probability that the first job to leave system 1 after time t is the same as the first job that entered the entire system after time t?
f) What is the probability that the first job to leave system 2 after time t both passed through system 1 and arrived at system 1 after time t?