[8 marks] Consider a queueing system which is basically M/M/2/2, with hourly arrival and service rates X = n = 2. However, the second server is half-ill today, so that her service time has changed from Exponential with parameter j = 2 to Exponential with parameter u* = 1. The first (healthy) server is always employed when a customer arrives to an empty system, and the second server is employed only for customers arriving when the first server is busy. Whenever a customer is finished being served when both servers have been busy, then it is always the quickest first server that continues the service of the remaining customer in the system. a) [6 marks] Find the stationary distribution of this modified (with a server being half-ill) queueing system. b) [2 marks] On average, how many potential customers per hour are lost due to the finite capacity of the system? [8 marks] Consider a queueing system which is basically M/M/2/2, with hourly arrival and service rates X = n = 2. However, the second server is half-ill today, so that her service time has changed from Exponential with parameter j = 2 to Exponential with parameter u* = 1. The first (healthy) server is always employed when a customer arrives to an empty system, and the second server is employed only for customers arriving when the first server is busy. Whenever a customer is finished being served when both servers have been busy, then it is always the quickest first server that continues the service of the remaining customer in the system. a) [6 marks] Find the stationary distribution of this modified (with a server being half-ill) queueing system. b) [2 marks] On average, how many potential customers per hour are lost due to the finite capacity of the system