14.3M/M/2/3 Figure 14.8 shows a 2 -server system with a waiting room that can hold only 1 job. Any arrival that sees 3 jobs already in the system is dropped. Jobs arrive from outside according to a Poisson process with rate =1. Whenever a server finishes serving a job, it grabs the job from the waiting area, if there is one. Job sizes are Exponentially distributed with rate =1. SERVER VARMS: st/Mt/k AND m/M/k/k Figure 14.8. The M/M/2/3 system. (a) Draw a CTMC where the state represents the total number of jobs in the system. (b) Suppose that there are exactly 2 jobs in the system. What is the probability that a job arrives before a job completes? (c) Use your CTMC to determine the probability that the system is idle (both servers are idle). (d) What is the throughput of the system? (e) What is E[N], the expected number of jobs in the system? (f) What is E[T], the expected response time (for those jobs not dropped)? (g) Consider the process of arrivals to the system that are not dropped. Is this a Poisson process? Why or why not