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1. CWD Business systems maintains a successful Telecom sales department for Top up cl credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. Th clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order.

1. CWD Business systems maintains a successful Telecom sales department for Top up cl credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. Th clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order.

Practical Management Science
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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4. CWD Business systems maintains a successful Telecom sales department for Top up call credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order. Part B CWD is considering adding a second clerk to take calls. The store would pay that person the same $15 per hour. Using appropriate formula for the multiple channel model, answer the following questions: a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service (La)? c. What is the average number of customers in the system (L)?
Transcribed Image Text:4. CWD Business systems maintains a successful Telecom sales department for Top up call credit in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the department are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per hour. The clerk is capable of taking an order in an average of 3 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $15 per hour, but because of lost goodwill and sales, CWD loses about $30 per hour of customer time spent waiting for the clerk to take an order. Part B CWD is considering adding a second clerk to take calls. The store would pay that person the same $15 per hour. Using appropriate formula for the multiple channel model, answer the following questions: a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service (La)? c. What is the average number of customers in the system (L)?
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