Ocala Software Systems operates a technical support center for its software cust
ID: 469248 • Letter: O
Question
Ocala Software Systems operates a technical support center for its software customers. If customers have problems installing or using Ocala software products, then they may telephone the technical support center and obtain free consultation. Currently, Ocala operates its support center with one consultant. If the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. The customer is then asked to hold and told that a consultant will provide assistance as soon as possible and that customers will be served in the order that calls are received. Incoming calls follow a poison probability distribution with an average rate of 9 calls per hour. The service time follows an exponential probability distribution, and, on average, it takes 5 minutes for a consultant to answer a customer's questions. On average, how many customers will be waiting to speak to the consultant? What is the average time, in minutes, that it takes for a customer to get through the system? What percentage of the time is the consultant idle? What is the probability that there is more than one customer in line, waiting to be helped? Ocala's customer service department has received complaints about long waiting times, so Ocala is thinking about adding another technical support consultant. The second consultant would serve customers at the same rate as the first consultant and would be paid $28 per hour (the same as the first consultant). Incoming calls would be answered by the same automated system and transferred to the first available consultant. Ocala values customer waiting time at $24 per hour (per customer) to reflect possible loss of future sales. What is the difference in total hourly cost between a one-consultant and two-consultant system (using the con- figuration described above)? Should Ocala hire another consultant? Justify your answer by comparing the costs.Explanation / Answer
Arrival Rate, = 9 calls per hour
Service Rate, = 60/5 = 12 calls per hour
a) Number of customers waiting in line to speak to the consultant = 2//(-) = 2.25
b) Average time in system = 1/(-) = 0.33 hours = 20 minutes
c) % of time consultant is idle = 1 - / = 1-9/12 = 25%
d) Probability of more than 1 customers waiting in line = 1 - (Probability of 0 customers waiting in line + Probability of 1 customers waiting in line)
Probability of 0 customers waiting in line =(1-)*n = 25%, where = / = 0.75, n = 0
Probability of 1 customers waiting in line =(1-)*n = 18.75%, where = / = 0.75, n = 1
Probability of more than 1 customers waiting in line = 1 - (25% + 18.75%) = 56.25%
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