At a railway station one train is handled at a time. The railway yard is sufficient...

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At a railway station one train is handled at a time. The railway yard is sufficient only for two trains to wait while the other given signal to leave the station. Trains arrive at the station at an average rate of 6 per hour and the rail way station can handle them on average of 12 per hour. Assuming Poisson arrivals and exponential service distribution, find The steady state probabilities for the various number of trains in the system. The average number of trains at the railway station. The average waiting time of a new train coming into the yard. Question 4 [10] [4] [8] Show that when 1 for the (M/M/C/N/) model, the expected number in the queue L, equals P^(N-CN-C+I), Pa- 2c! [10] At a railway station one train is handled at a time. The railway yard is sufficient only for two trains to wait while the other given signal to leave the station. Trains arrive at the station at an average rate of 6 per hour and the rail way station can handle them on average of 12 per hour. Assuming Poisson arrivals and exponential service distribution, find The steady state probabilities for the various number of trains in the system. The average number of trains at the railway station. The average waiting time of a new train coming into the yard. Question 4 [10] [4] [8] Show that when 1 for the (M/M/C/N/) model, the expected number in the queue L, equals P^(N-CN-C+I), Pa- 2c! [10]