Concept explainers
a)
To determine: Utilization rate for the system.
Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.
b)
To determine: The average waiting time for units in each category.
Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.
c)
To determine: The average number of customers in each class that are waiting for service.
Introduction: Poisson distribution is utilized to ascertain the probability of an occasion happening over a specific time period or interval. The interval can be one of time, zone, volume or separation. The probability of an event happening is discovered utilizing the equation in the Poisson distribution.
Want to see the full answer?
Check out a sample textbook solutionChapter 18 Solutions
EBK OPERATIONS MANAGEMENT
- In the library, students arrive randomly at the help desk, which is staffed by 4 employees (all of them answer inquiries from students). The time required for inquiry varies from student to student. Arrivals have been found to follow a Poisson process (i.e., exponentially distributed inter-arrival times), and the service times follow an exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 13 students per hour. What is the utilization of the help desk? Note: 1. Provide your answer as a percentage, but do not include the % mark. 2. Keep two decimal places. For example, if your result is 35.126%, enter 35.13.arrow_forwardAt a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a haircut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chairarrow_forward4.) The DMV Licensing 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. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?arrow_forward
- A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find The probability of there being no customer in the system The average number of customers in the system iii. Average number of customers waiting to be served iv. Average time a customer spends in the system v. Average waiting time for a customerarrow_forward. A manager must determine requirements for waiting space for customers. A priority system isused to process customers, who are assigned to one of two classes when they enter the processingcenter. The highest-priority class has an arrival rate of four per hour; the other class has an arrivalrate of two per hour. Both can be described as Poisson-distributed. There are two servers, andeach can process customers in an average of 15 minutes.a. What is the system utilization?b. Determine the number of customers of each class that are waiting for service.c. Determine the average waiting time for each class.d. If the manager could alter the assignment rules so that arrival rates of the two classes wereboth 3/hour, what would be the revised average waiting time for each priority class?arrow_forwardThe Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of l = 3 per day (approximately Poisson in nature). The crew can service an average of m = 8 machines per day, with a repair time distribution that resembles the exponential distribution. (a) What is the utilization rate of this service system? (b) What is the average downtime for a machine that is broken? (c) How many machines are waiting to be serviced at any given time? (d) What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,