A summer camp that offers one-week programs faces the challenges of long queues asparents try to check in their children each Saturday morning. If they were to add morestaff to assist with the check-in process, then which of the following will occur?i. The average time parents wait decreases.ii. The maximum time the parents wait decreases.iii. The average number of parents waiting to check in their child decreases. a. Just Ib. Just IIc. Just IIId. I and IIe. I and IIIf. II and IIIg. I, II, and III

A summer camp that offers one-week programs faces the challenges of long queues asparents try to check in their children each Saturday morning. If they were to add morestaff to assist with the check-in process, then which of the following will occur?i. The average time parents wait decreases.ii. The maximum time the parents wait decreases.iii. The average number of parents waiting to check in their child decreases. a. Just Ib. Just IIc. Just IIId. I and IIe. I and IIIf. II and IIIg. I, II, and III

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

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True or False? The average number of customers in queue plus the number of servers equals the average number of customers in the system. The main cause of delay at Logan Airport was overbooking, and building a new runway solved the delay problem. If a company hopes to increase the capacity of a process, the company needs to try to shorten the process’s cycle time. Little’s Law only applies to an M/M/1 queue, which is a special case of a G/G/C queue. If a queuing system has deterministic arrival rate λ and service rate μ, and λ < μ, then Lq = 0 in this queue.
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 five trucks per hour. Use the Single Server Queue Excel 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?
In most cases, if a firm increases its service capacity by 10 percent, it would expect waiting times to be reduced by what percentage? Assume customerarrivals and service times are random. An ice cream stand has a single window and one employee to serve customers. During their busy season, 30 customers arrive each hour, on average. It takes 1.5 minutes, on average, to serve a customer.What is the utilization of the employee? How long would customers have to wait in line, on average, at the ice cream shop discussed in question 7? Random service times can be modeled by this. A bank teller takes 2.4 minutes, on average, to serve a customer. What would be the hourly service rate used in the queuing formulas? There are three teller windows in the bank described in the prior question. On average, 60 customers per hour arrive at the bank. What will be the average number of customers in line at the bank?
Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a “slow” time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?
The Solomon, Smith, and Samson law firm produces manylegal documents that must be word processed for clients andthe firm. Requests average eight pages of documents perhour, and they arrive according to a Poisson distribution. Thesecretary can word process 10 pages per hour on average ac-cording to an exponential distribution.a. What is the average utilization rate of the secretary?b. What is the probability that more than four pages are wait-ing or being word processed?c. What is the average number of pages waiting to be wordprocessed?
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?
Please do not give solution in image format thanku A bank has an average of 10 customers per hour arriving into the system, and it takes an average of 30 minutes for the clerk to complete a transaction with a customer. What is the average length of the queue in the bank? And A store open 24 hours per day is interested in determining store traffic. It found that customers arrive uniformly at the rate of 10 customers per hour. The store has a single worker to process customers. The worker takes an average of 5 minutes to process a customer. If we assume that every customer must be processed, what is the average number of customers in the store?
There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or μ=90 per hour (according to a negative exponential distribution). a) The percentage of time the machine is used = 4444 percent (round your response to the nearest whole number). The average length of the queue = 35.35 students (round your response to two decimal places).The average number of students in the system = 0.80 students (round your response to two decimal places).The average time spent waiting in the queue = 0.53minutes (round your response to two decimal places). The average time in the system = minutes (round your response to two decimal places).
A chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every 2 minutes (Poisson distributed). The average request requires 1.7 minutes to fill (exponential service times). Maintenance employees are paid $20 per hour, and warehouse employees are paid $12 per hour. The warehouse is open 8 hours each day. What is the optimal number of warehouse employees to hire? (Hint: Time spent by maintenance workers waiting in line for supplies should be considered an expense.) What is the total cost per hour (waiting plus warehouse employee labor cost) of your solution?
Priority-Discipline Queueing Models Southeast Airlines is a small commuter airline serving primarily the state of Florida. Their ticket counter at a certain airport is staffed by a single ticket agent. There are two separate lines—one for first-class passengers and one for coach-class passengers. When the ticket agent is ready for another customer, the next first-class passenger is served if there are any in line. If not, the next coach-class passenger is served. Service times have an exponential distribution with a mean of 3 minutes for both types of customers. During the 12 hours per day that the ticket counter is open, passengers arrive randomly at a mean rate of 2 per hour for first-class passengers and 10 per hour for coach-class passengers. A. What kind of queueing model fits this queueing system? B. Find the main measures of performance—L, Lq, W, and Wq—for both first-class passengers and coach-class -passengers. C. What is the expected waiting…