Consider anM/M/1 queueing system with arrivaland service rate(

1. (a)(5 points) LetNbe the number of customers in the systemin the steady-stateas covered in class. Calculate itsztransform, i.e.,E{zN}.
2. (b)(15 points) Calculate theztransform ofNd, i.e.,E{zNd}in terms of,,z. You must clearly show your steps.

4. (20 points): (from past exam) Consider an M/M/1 queueing system with arrival ) and service rate M ()