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Service Queue III

# Service Queue III - Model 3 Multiple Servers Poisson...

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1 Model 3: Multiple Servers, Poisson Arrivals, Infinite Buffer Exponential Service Time Distribution Use the Qmmc.xls program. Be sure to use consistent units for R i and T p . M/M/c queuing computations Arrival rate 4 per hour Service time 0.16667 Number of servers 1 (max of 40) Time Unit hour Utilization 66.67% P(0), probability that the system is empty 0.3333 Ii, expected queue length 1.3333 I, expected number in system 2.0000 Ti, expected time in queue 0.3333 hours T, expected total time in system 0.5000 hours Probability that a customer waits 0.6667

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2 Call Center A call center is staffed by 18 people. The average service time per call is 5 minutes and on average 190 calls are received per hour. Management wants the average customer waiting time to be no more than 30 seconds. Do you think they will meet the 30 seconds target? One day a staff person calls in sick and only 17 people are on duty. The supervisor expects that average waiting time will increase by about 5 percent, since staffing was reduced by about five percent. Do you agree? On another day, two people call in sick and only 16 are on duty. Now the supervisor expects the average waiting time to increase by about 10 percent since the staff on duty was reduced by about 10 percent. Do you agree?
3 City Hospital Emergency Room Assume an average arrival rate to surgery of 5.9 patients per hour and the average time spent by a doctor with a patient is 29 minutes. That is, each doctor can serve an average of (60/29) = 2.07 patients per hour. There are 3 doctors on duty in surgery. How long on average do patients have to wait? (What if there were 4 doctors?) Now we consider the medicine area as well. It is found that the average time spent by a doctor with a patient is also 29 minutes. There are 4 doctors on duty in medicine, and the average arrival rate to that area is 7.9 patients per hour. How long on average do patients have to wait in the medicine area? The hospital feels the waiting times in these two areas are too long. What can be done about it?

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4 Independent vs. “Pooled” System Independent System wait here wait here “Pooled” System
5 “Pooling” and Waiting

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