1. Akala Software systems operates a technical support center for its software customers. If customers have installation or use problems with Akala software products, they may telephone the technical support center and obtain free consultation. Currently, Akala 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 a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution with an arrival rate of four calls per hour. On average, it takes 12 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. a) What is the service rate in terms of customers per hour? b) What is the average number of customers waiting for a consultant? c) What is the average time a customer waits for a consultant? d) What is the probability that a customer will have to wait for a consultant? e) Akala's customer service department recently received several letters from customers complaining about the difficulty in obtaining technical support. If Akala's customer service guidelines state that no more than 45% of all customers should have to wait for technical support and that the average waiting time in the system should be six minutes or less, does your waiting line analysis indicate that Akala is or is not meeting its customer service guidelines? What action, if any, would you recommend?
1. Akala Software systems operates a technical support center for its software customers. If customers have installation or use problems with Akala software products, they may telephone the technical support center and obtain free consultation. Currently, Akala 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 a consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution with an arrival rate of four calls per hour. On average, it takes 12 minutes for a consultant to answer a customer's questions. The service time follows an exponential probability distribution. a) What is the service rate in terms of customers per hour? b) What is the average number of customers waiting for a consultant? c) What is the average time a customer waits for a consultant? d) What is the probability that a customer will have to wait for a consultant? e) Akala's customer service department recently received several letters from customers complaining about the difficulty in obtaining technical support. If Akala's customer service guidelines state that no more than 45% of all customers should have to wait for technical support and that the average waiting time in the system should be six minutes or less, does your waiting line analysis indicate that Akala is or is not meeting its customer service guidelines? What action, if any, would you recommend?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Transcribed Image Text:1. Akala Software systems operates a technical support center for its software customers.
If customers have installation or use problems with Akala software products, they may
telephone the technical support center and obtain free consultation. Currently, Akala
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 a
consultant will provide assistance as soon as possible. The customer calls follow a Poisson
probability distribution with an arrival rate of four calls per hour. On average, it takes
12 minutes for a consultant to answer a customer's questions. The service time follows an
exponential probability distribution.
a) What is the service rate in terms of customers per hour?
b) What is the average number of customers waiting for a consultant?
c) What is the average time a customer waits for a consultant?
d) What is the probability that a customer will have to wait for a consultant?
e) Akala's customer service department recently received several letters from customers
complaining about the difficulty in obtaining technical support. If Akala's customer
service guidelines state that no more than 45% of all customers should have to wait
for technical support and that the average waiting time in the system should be six
minutes or less, does your waiting line analysis indicate that Akala is or is not meeting
its customer service guidelines? What action, if any, would you recommend?
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