Queuing Theory - Azure Valley Electric & TRP

1. Azure Valley Electric Co-operative has for many years contracted with a neighboring utility to handle emergency service requests which occur, primarily due to storm damage, at the average rate of 2 per hour. It now feels that it should probably assume this responsibility itself and has been presented with two proposals for vehicle service purchase. It can either buy 2 standard dispatch trucks where each can handle 3 service restoration calls per hour and whose cost to own and operate is estimated at $10.00 per hour. Alternatively, it can buy a single GPS-monitored, radio-dispatched truck which can handle 4 service restoration calls per hour, but whose cost to own and operate is estimated at $14.00 per hour. It has also been estimated that in terms of customer ill-will and issued billing credits, the average outage cost to Azure of a customer awaiting service is $8.oo per hour.

a. Which purchase option should Azure choose
b. Assuming Azure maintains around-the-clock, 8760 annual hours of electric service operation, how much would the preferred option save Azure yearly.

2. TRP is offering ski chalet condos for sale at its new Colorado resort and has invited future prospective buyers to call a toll-free number to speak with sales representatives who can discuss various ownership options and costs. TRP would like to keep its sales line open from 8am to 8pm. It has contracted with a call center which has handled previous TRP promotions. The call center estimates that the incoming call intensity is likely to vary by time of day, averaging 4 calls per hour during 8 am- noon period; 6 calls per hour during the noon- 4 pm period; and 12 calls per hour during the peak 4pm- 8pm after-work-hours period. Based on prior experience, it is estimated during any of these times, each caller will speak to the sales representative (i.e. call center operator) for about 12 minutes. The center is prepared to meet TRP's requirement regarding the average length of time a caller should be placed on hold listening to a recorded intro message about TRP before speaking to a representative. TRP has specified an average caller hold of 5 minutes. TRP has negotiated with the center an hourly fee of $50 per representative hour. The center has contractually committed to its ability to meet the desired hold-time requirement, promising to use no more then 4 representatives in any one of the 3 time periods and to bill TRP only to the actual number of representatives that are needed during each period to satisfy TRP's hold-time requirement.

a. How many representatives must the call center dedicate to TRP in each of the 3 daily time periods in order to fulfill its commitment?
b. If I should call the center at 2:37 pm one afternoon during the week, what is the probability my call will be picked up immediately with no waiting time at all?
c. What is the expected daily contract to TRP?