00:01
Hello students, in the question a we want to find the probability that a boat dock will be idle.
00:06
So, utilization factor is given by the arrival rate divided by service rate multiplied by the number of servers.
00:19
So, this is equal to 6 by 12 into 2 which is equal to 0 .25.
00:28
So, the probability that boat dock will be idle is given by p of 0 which is equal to 1 minus utilization factor divided by 1 minus utilization factor square.
00:41
So, this is equal to 1 minus 0 .25 divided by 1 minus 0 .25 square and this is equal to 0 .8.
01:03
So, then b, the average boats waiting for the service.
01:11
So, the average number of boats waiting for the service is lq and it is given by utilization factor square divided by 1 minus utilization factor into 1 minus s plus 1 into utilization factor to the power s plus s into utilization factor to the power s plus 1.
01:43
Now, just substitute all the values we have here that is lq is equal to 0 .25 square divided by 1 minus 0 .25 into 1 minus 2 plus 1 into 0 .25 square plus 2 into 0 .25 to the power 2 plus 1...