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 probability that there are more than 3 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 probability that there are more than 3 customers in the system

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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. a. What is the probability that no customers are in the system (Po)? b. What is the average number of customers…
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. Part A Answer the following questions: a. What is the probability that no customers are in the system (Po)? 2 b. What is the average number of customers waiting for service ( Lq)? c. What is the average number of customers in the…
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. Using the multiple channel model, answer the following questions a. What is the probability that no customers are…
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…
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.
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. e. What is the average time in the system (W)? f. What is the probability that a customer will have to wait for…
(a) Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service imes tend to be negative exponential. The cost of the clerk is RM10 per hour, but because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 perhour of customer time spent waiting for the clerk to take an order.i) What is the suitable method to solve this problem?ii) Compute the average time that customers must wait before their calls aretransferred to the clerk.
Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential. The cost of the clerk is RM10 per hour, but because of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 per hour of customer time spent waiting for the clerk to take an order. 1. What is the suitable method to solve this problem? 2. Compute the average time that customers must wait before their calls are transferred to the clerk. 3. Prepare the total cost for this waiting line…
Jeruk Pak Abu's Store in Butterworth, Pulau Pinang, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an average of 4 minutes. Calls tend to follow a Paisson distribution, and service times tend to be negative exponential. The cost of the clerk is RM10 per bour, but because of lost good -will and sales, Jeruk Pak Abu's Store loses about RM25 per hour of customer time spent waiting for the clerk to take an order. iii) Prepare the total cost for this waiting line system.
Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successfulcatalog sales department in which a clerk takes orders by telephone. If the clerk isoccupied on one line, incoming phone calls to the catalog department areanswered automatically by a recording machine and asked to wait. As soon as theclerk is free, the party who has waited the longest is transferred and serviced first.Calls come in at a rate of about 12 per hour. The clerk can take an order in anaverage of 4 minutes. Calls tend to follow a Poisson distribution, and servicetimes tend to be negative exponential. The cost of the clerk is RM10 per hour, butbecause of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 perhour of customer time spent waiting for the clerk to take an order. a) Prepare the total cost for this waiting line system.
Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successfulcatalog sales department in which a clerk takes orders by telephone. If the clerk isoccupied on one line, incoming phone calls to the catalog department areanswered automatically by a recording machine and asked to wait. As soon as theclerk is free, the party who has waited the longest is transferred and serviced first.Calls come in at a rate of about 12 per hour. The clerk can take an order in anaverage of 4 minutes. Calls tend to follow a Poisson distribution, and servicetimes tend to be negative exponential. The cost of the clerk is RM10 per hour, butbecause of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 perhour of customer time spent waiting for the clerk to take an order a.Prepare the total cost for this waiting line system.
Jeruk Pak Abu’s Store in Butterworth, Pulau Pinang, maintains a successfulcatalog sales department in which a clerk takes orders by telephone. If the clerk isoccupied on one line, incoming phone calls to the catalog department areanswered automatically by a recording machine and asked to wait. As soon as theclerk is free, the party who has waited the longest is transferred and serviced first.Calls come in at a rate of about 12 per hour. The clerk can take an order in anaverage of 4 minutes. Calls tend to follow a Poisson distribution, and servicetimes tend to be negative exponential. The cost of the clerk is RM10 per hour, butbecause of lost good –will and sales, Jeruk Pak Abu’s Store loses about RM25 perhour of customer time spent waiting for the clerk to take an order. a) Compute the average time that customers must wait before their calls are transferred to the clerk.