Bacala Software Systems operates a technical support center for its software customers. If customers have installation or user problems with Bacala software products, they may telephone the technical support center and obtain free consultation. Currently, Bacala 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 the consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution with an arrival rate of five calls per hour. On average, it takes 7.5 minutes for a consultant to answer a customer’s questions. The service time follows an exponential probability distribution. (Please Answer a-c) thank you!  a. What is the service rate in terms of customers per hour? b. What is the probability that no customers are in the system and the consultant is idle? c. What is the average number of customers waiting for a consultant? d. What is the average time a customer waits for a consultant?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
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Bacala Software Systems operates a technical support center for its software customers. If customers have installation or user problems with Bacala software products, they may telephone the technical support center and obtain free consultation. Currently, Bacala 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 the consultant will provide assistance as soon as possible. The customer calls follow a Poisson probability distribution with an arrival rate of five calls per hour.
On average, it takes 7.5 minutes for a consultant to answer a customer’s questions. The service time follows an exponential probability distribution. (Please Answer a-c) thank you! 


a. What is the service rate in terms of customers per hour?
b. What is the probability that no customers are in the system and the consultant is idle?
c. What is the average number of customers waiting for a consultant?
d. What is the average time a customer waits for a consultant? 

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