At the Toyota service center certain type of vehicle service requires three steps to be completed sequentially. The time taken to perform each step follows an exponential distribution with mean= (sum of your roll no. /100, if your roll no. is 15 than 1+5=6, 6/100=0.06) minutes and is independent of each other. The vehicle service follows a Poisson process with rate of 1 per 2 hours. Assuming that there is only one worker who gives the service to each vehicle, find out

i.The expected idle time of a server.

ii.The average waiting time of a vehicle in a queue until it is entertained.

iii.The expected number of vehicle in the queue.

iv.The average number of vehicle which will not serve due to shortage of time