Problem $1$

You are given an M$/$M$/1$ queueing system in which the expected waiting time and expected number in the system are $120$ minutes and $8$ customers, respectively. Using one hour as the unit of time determine the

average expected customer's arrival rate, l$,$

average service rate m

the utilization factor r of the system.

Problem $2$

Find the critical path, Finish Time, Early Start & Early Finish, Late Start & Late Finish, and slack time for all tasks of the following project given this information.

A$-3,$ B$-4,$ C$-2,$ D$-2,$ E$-4,$ F$-4,$ G$-6,$ H$-5,$ I$-2,$ J$-3,$ K$-4,$ L$-6,$ M$-4,$ N$-5$

Problem $3$

Find the shortest path using the Dijkstra's algorithm model for the following given information of this network.