Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls to the restaurant 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 $20 per hour, but because of lost goodwill and sales, CWD loses about $50 per hour of customer time spent waiting for the clerk to take an order. What is the average time a customer waits for service(Wq)? e. What is the average time in the system (W) ?- f. What is the probability that a customer will have to wait for service (Pw)? g What is the probability that there is exactly 2 customers in the system

Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls to the restaurant 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 $20 per hour, but because of lost goodwill and sales, CWD loses about $50 per hour of customer time spent waiting for the clerk to take an order. What is the average time a customer waits for service(Wq)? e. What is the average time in the system (W) ?- f. What is the probability that a customer will have to wait for service (Pw)? g What is the probability that there is exactly 2 customers in the system

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

See similar textbooks

Similar questions

International Cranberry Uncooperative (ICU) is a competitor to the National Cranberry Cooperative (NCC). At ICU, barrels of cranberries arrive on trucks at a rate of 150 barrels per hour and are processed continuously at a rate of 100 barrels per hour. Trucks arrive at a uniform rate over eight hours, from 6:00 a.m. until 2:00 p.m. Assume the trucks are sufficiently small so that the delivery of cranberries can be treated as a continuous inflow. The first truck arrives at 6:00 a.m. and unloads immediately, so processing begins at 6:00 a.m. The bins at ICU-can hold up to 200 barrels of cranberries before overflowing. If a truck arrives and the bins are full, the truck must wait until there is room in the bins. If each truck can hold 25 barrels, how many trucks are waiting at 2 pm? 8 trucks 10 trucks 6 trucks 9 trucks
YourNurse (YN) Inc. uses certified nurses to answer medical queries from customersover the phone. When patients call into YN, they are first asked to provide their zipcode, which then allows YN to route their call to the call center nearest to the patient(it operates 10 across the country). Which single suggestion in the following list (andexplanation) is most likely to reduce the average time callers wait before speaking witha nurse?a. Run an advertising campaign to increase demand and to better utilize its nurses.b. Train its nurses so that they spend more time answering the patients’ questions.c. Instead of using callers’ zip codes, route calls to the call center with the fewest callersto help prevent situations in which there are idle nurses at the same time that there arecallers on hold.d. Play a recording of useful medical information while callers are on hold so as todecrease their perception of how long they are waiting.e. None of the above
The arrival rate at the second server in a two stage serial queuing
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 29 calls per hour. The service rate per line is 19 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = P(1) = P(2) = P(3) = (b) What is the probability that an agent will be denied access to the…
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 37 calls per hour. The service rate per line is 24 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0)=P(1)=P(2)=P(3)= (b) What is the probability that an agent will be denied access to the…
Please answer the attached Queuing Model problem solving. Thanks
Many of a bank’s customers use its automated banking machine (ABM). During the early eveninghours in the summer months, customers arrive at an ABM at the rate of one every other minute(assume Poisson). Each customer spends an average of 99 seconds completing the transaction.Transaction times are exponentially distributed. Assume that the length of the queue is not aconstraint. Determine the average time customers spend at the machine, including waiting in line and completing transactions. Determine the probability that a customer will not have to wait upon arrival at the ABM. Determine the utilization of the ABM.
1.)The arrival rate is the rate of arrivals to the service facility all of these rate items arrive at the server after being in the queue time between arrivals to the service facility 2.) what is "queue discipline"?
A server operates with 80 % utilization. Coefficient of variation of service process is 0.5. Coefficient of variation of arrival process is 0.9. Average processing fime is 3 minutes. What is the average time a customer spends in the system using the single server queueing model 7 Show all formulas used, calculations and results.
Mr. Bader is a regular visitor at Muscat Private Hospital for his aged mother’s treatment. Which type of queuing system is Mr. Bader likely to encounter in a hospital? a. Multi-channel, single phase. b. Single channel, multi-phase. c. Multi-channel, multi-phase. d. Single channel, single phase.
Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle? What is the average number of trucks in the queue? truck(s) What is the average number of trucks in the system? truck(s) What is the average time a truck spends in the queue waiting for service? hour(s) What is the average time a truck spends in the system? hour(s) What is the probability that an arriving truck will have to wait? What is the probability that more than two trucks are waiting for service?
Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls to the restaurant 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 $20 per hour, but because of lost goodwill and sales, CWD loses about $50 per hour of customer time spent waiting for the clerk to take an order. Skyline is considering adding a second clerk to take calls. The store would pay that person the same $20 per hour. Should it hire another clerk? Explain by showing the cost savings.