i need solution e and f

25 2 Lubrication activity is a part of maintenance activities served by ABC Automotive Services. Lubrication activities start at 8:30 in the morning and finish at 12:30 in the afternoon. According to the past data, interarrival times for lubrication is 15 minutes on average and lubrication of each car takes 20 minutes on average. Interarrival times and service times are assumed to be exponentially distributed. It is known that the cars arrive from an infinite resource. There are three lubrication channels in the system. If a lubrication channel is idle, the lubrication activity starts. Otherwise, the cars wait in the queue on an appropriate place. According to these data, answer the following questions: a. Write the Kendall Lee notation of the queueing system. b. Write the u, 2, and p values. c. Assume that the nodes in the following figure shows the number of cars (in queue and being served) in the system. Write the transition frequencies between states on arcs. 20 = ... 21 = ... 22 = ... 23 = ... 0 1 2. 3 4 Hi = .... U2 = .... H3 = .... H4 = .... d. What is the probability that there are no cars in the system? e. What is the probability that two lubrication channels are busy at any time? f. What is the average number of cars waiting in the queue? 25 2 Lubrication activity is a part of maintenance activities served by ABC Automotive Services. Lubrication activities start at 8:30 in the morning and finish at 12:30 in the afternoon. According to the past data, interarrival times for lubrication is 15 minutes on average and lubrication of each car takes 20 minutes on average. Interarrival times and service times are assumed to be exponentially distributed. It is known that the cars arrive from an infinite resource. There are three lubrication channels in the system. If a lubrication channel is idle, the lubrication activity starts. Otherwise, the cars wait in the queue on an appropriate place. According to these data, answer the following questions: a. Write the Kendall Lee notation of the queueing system. b. Write the u, 2, and p values. c. Assume that the nodes in the following figure shows the number of cars (in queue and being served) in the system. Write the transition frequencies between states on arcs. 20 = ... 21 = ... 22 = ... 23 = ... 0 1 2. 3 4 Hi = .... U2 = .... H3 = .... H4 = .... d. What is the probability that there are no cars in the system? e. What is the probability that two lubrication channels are busy at any time? f. What is the average number of cars waiting in the queue