00:01
It is given in the question that average arrival rate, average arrival rate that is lambda is equal to 150 vehicles per hour and the service rate and the service rate that is mu is equal to 1 divided by 20 seconds per vehicle, 1 divided by 20 seconds per vehicle which comes out to be 0 .05 vehicles, 0 .05 vehicles per second.
00:38
Traffic intensity, traffic intensity that is mu, sorry that is rho is equal to lambda divided by mu which is equal to 150 vehicles per hour divided by 0 .05 vehicles per second multiplied with 3600 seconds per hour, 3600 seconds per hour which comes out to be 150 divided by 180 which is equal to 5 divided by 6.
01:17
Now, utilization factor, utilization factor that is u is equal to 1 minus rho which is equal to 1 minus 5 divided by 6 which is equal to 1 divided by 6 and average time, average time in queue, in queue for waiting, for waiting that is wq is equal to u divided by mu minus lambda which is equal to 1 divided by 6 divided by 0 .05 vehicles per second minus 150 vehicles per hour divided by 3600 seconds per hour which comes out to be, which comes out to be 20 seconds.
02:13
So, this is the average time for waiting in the queue.
02:17
Average length of the queue, average length of queue that is lq is equal to lambda multiplied with waiting time in queue which is equal to 150 vehicles per hour multiplied with 20 seconds divided by 3600 seconds, 3600 seconds per hour which comes out to be approximately equal to 0 .833 vehicles...