Concept explainers
a)
To determine: The average number of customers waiting on line.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
b)
To determine: The average time that the customer spend at the restaurant.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
c)
To determine: The fraction of time that is more than three cars in line.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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Chapter 12 Solutions
Practical Management Science
- A fast-food restaurant has one drive-through window.On average, 40 customers arrive per hour at thewindow. It takes an average of one minute to serve acustomer. Assume that interarrival and service timesare exponentially distributed.a. On average, how many customers are waiting in line?b. On average, how long does a customer spend at therestaurant (from time of arrival to time service iscompleted)?c. What fraction of the time are more than three carsin line? (Here, the line includes the car, if any,being serviced.)arrow_forwardThe office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?arrow_forwardCustomers of Golden Crust Bakery arrive at the single cashier at the rate of 10 per hour. The average service time for the cashier is five minutes. Arrivals follow a Poisson distribution, and service times follow an exponential distribution. a. What is the average utilization of the cashier? b. What is the average number of customers in the system? c. What is the average number of customers in line? What is the average time spent in the system? e. What is the average time spent in line? d.arrow_forward
- Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22arrow_forwardA single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 11 customers per hour and an average service rate of 14 customers per hour. The average length of time customers will spend in the system is: a. 15.71 minutes b. 20 minutes c. 0.2619 minutes d. 0.3333 minutesarrow_forward13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.arrow_forward
- One field representative services five customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every four working days. The field representative can handle an average (Poisson-distributed) of one call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s) Please answer part Carrow_forwardAt a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)arrow_forwardDrivers who come to get their licenses at the Department of Motor Vehicles have their photograph taken by an automated machine that develops the photograph onto the license card and laminates the complete license. The machine requires a constant time of 4 minutes to prepare a complete license. The interarrival time between two drivers is 6 minutes distributed exponential. a) What type of queuing model this system follow ? b) Determine the average length of the waiting line. c) Determine the average waiting time.arrow_forward
- The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of the canteen arrive at an average of 50 an hour. Suppose that management wants to evaluate the desirability of opening a second order-processing station so that two customers can be served simultaneously. Assume a single waiting line with the first customer in line moving to the first available server. a. How long in minutes would it take the customer from lining up until he leaves the waiting line? b.How long in minutes would a customer wait to be served on average? c.Find the probability that there are 7 customers in the system.arrow_forwardPatients arrive at a dentist’s office with an arrival rate of 2.8 patients per hour. The dentist can treat patients at a service rate of 3 patients per hour. A study of patient waiting times shows that a patient waits an average of 30 minutes before seeing the dentist. Note the M/M/1 model does not necessarily apply here. What are the arrival and service rates in terms of patients per minute? What is the average number of patients in the waiting room? If a patient arrives at 10:10am, at what time is the patient expected to leave the office?arrow_forwardNeed helparrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,