Repair calls are handled by one repairman at a photocopy shop. Repair time, incl
ID: 371527 • Letter: R
Question
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.1 hours per call. Requests for copier repairs come in at a mean rate of 2.4 per eight hour day (Assume Poissson)
Determine:
a. The average number of customers awaiting repairs (Round your answer to 2 decimal places)
.b.System utilization.(Round your answer to 2 decimal places)
c.The amount of time during an eight-hour day that the repairman is not out on a call. (Round your answer to 2 decimal places)
d.The probability of two or more customers in the system (Round your answer to 4 decimal places)
Explanation / Answer
Arrival rate (A) = 2.4 per day
Service rate (S) = 2.1 hours or 8/2.1 = 3.81 per day
a) Average number of customers waiting = Lq = A^2/(S*(S-A)) = 2.4^2/(3.81*(3.81-2.4)) = 1.07
b) System utilization = A/S = 2.4/3.81 = 0.63 or
c) Time not on call = (1-System utilization)*Time per day = (1-0.63)*8 = 2.96 hours
d) Probability of two or more customers = (A/S)^2 = (0.63)^2 = 0.3969