You have determined that walting times at a toll booth are uniformly distributed over the interval 30 to 80 seconds. Your simulation generates the following random numbers. Complete the table with the waiting time associated with each random number. (Round your answers to the nearest whole number.) Random Number Waiting Time 0.49 0 23 0.74
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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.. For the MyMy1 queueing model, why do the following results hold? (Hint: Remember that 1ym is the meanservice time. Then think how long a typical arrival must wait in the system or in the queue.) a. W 5 (L 1 1)ym b. WQ 5 LymThe manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?
- One way to manage the psychology of waiting is to inform the customers when long waitsare anticipated.o Trueo False10. Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentiallydistributed and has a mean of 14 minutes per machine. The machines operate for an average of86 minutes between adjustments. While running, each machine can turn out 50 pieces per hour.Find the following:a. The probability that a machine will have to wait for an adjustmentb. The average number of machines waiting for adjustmentc. The average number of machines being servicedd. The expected hourly output of each machine, taking adjustments into accounte. Machine downtime represents a cost of $70 per hour; operator cost (including salary andfringe benefits) is $15 per hour. What is the optimum number of operators?Suppose a bank has three tellers that are each busy 80 percent of the time. Estimatethe probability of delay for a randomly arriving customer.
- Each airline passenger and his or her luggage must bechecked to determine whether he or she is carrying weaponsonto the airplane. Suppose that at Gotham City Airport, anaverage of 10 passengers per minute arrive (interarrivaltimes are exponential). To check passengers for weapons,the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a check-point is in operation, two employees are required. A checkpoint can check an average of 12 passengers perminute (the time to check a passenger is exponential). Underthe assumption that the airport has only one checkpoint,answer the following questions:a What is the probability that a passenger will have towait before being checked for weapons?b On the average, how many passengers are waiting in line to enter the checkpoint? 1082 CHAPTER 2 0 Queuing Theoryc On the average, how long will a passenger spend atthe checkpoint?The Shady Farm Milk Company can process milk at a fixed rate of 7500 gallons/hour.The company’s clients request 100,000 gallons of milk over the course of one day. Thisdemand is spread out uniformly from 8 a.m. to 6 p.m. The company starts producing at8 a.m. and continues to work until all of the demand has been satisfied. At noon, howmany gallons of milk are in the queue to be processed?A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour.Determine the arrival rate value , service rate value to be used,time taken by aclient waiting in the queue Determine the client’s average waiting time in the system and Compute the probability that the system is idle; P (idle)
- The time from when a patient is discharged from NorthShore Hospital to the time the discharged patient’s bed isready to be assigned to a new patient is referred to as thebed assignment turnaround time. If the bed turnaroundtime is excessive, it can cause problems with patient flowand delay medical procedures throughout the hospital. Thiscan cause long waiting times for physicians and patientsthus creating customer dissatisfaction. The admissions RNhas assigned a patient care associate to measure the bedturnaround time for a randomly selected bed each morning,afternoon, and evening for 30 days. Following are the bedturnaround time sample observations:a. Develop an x-chart to be used in conjunction with anR-chart using 3 limits to monitor the bed turnaroundtimes and indicate if the process is in control usingthese charts.b. Is the hospital capable of consistently achieving bedturnaround times of 120 minutes 15 minutes withoutimproving the process?The manager of a large group of employees must decidewhether she needs another photocopying machine. Thecost of a machine is $40 per eight-hour day regardlessof whether the machine is in use. On average, fourpeople need to use the copying machine per hour. Eachperson uses the copier for an average of 10 minutes.Interarrival times and copying times are exponentiallydistributed. Employees are paid $8 per hour, and weassume that a waiting cost is incurred when a worker iswaiting in line or is using the copying machine. Howmany copying machines should be rented?One operator loads and unloads a group of five machines. Service time is exponentiallydistributed with a mean of 10 minutes per cycle. Machines run for an average of 70 minutesbetween loading and unloading, and this time is also exponential. Find the following:a. The average number of machines waiting for the operatorb. The expected number of machines runningc. Average downtimed. The probability that a machine will not have to wait for service