Trucks come to a facility to pick up final goods for delivery to far-off markets. They must join a waiting line when they arrive and are served on an FCFS basis. Ten trucks come per hour, whereas fifteen trucks are loaded per hour. The fact that loading is exponentially distributed and arrivals are Poisson distributed are also a given. Transporters have expressed dissatisfaction about the approximately 12-hour wait time for their trucks at the factory. (A) Verify the validity of the complaint. (B) What is the probability that the loaders are idle?

Trucks come to a facility to pick up final goods for delivery to far-off markets. They must join a waiting line when they arrive and are served on an FCFS basis. Ten trucks come per hour, whereas fifteen trucks are loaded per hour. The fact that loading is exponentially distributed and arrivals are Poisson distributed are also a given. Transporters have expressed dissatisfaction about the approximately 12-hour wait time for their trucks at the factory. (A) Verify the validity of the complaint. (B) What is the probability that the loaders are idle?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has two screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival rate is 4.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. The facility manager's goal is to limit the average number of passengers waiting in line to 8 or fewer. How many screening stations must be…
An entrepreneur opened a small hardware store in a street mall. During the first few weeks, business was slow, with the store averaging only one customer arrived every 15 minutes. Assume that the random arrival of customers is Poisson distributed. What is the probability that at least two customers arrive during a one-hour period?
All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 3 passengers per minute. On Monday morning the arrival rate is 5.2 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 2 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. The facility manager's goal is to limit the average number of passengers waiting in line to 7 or fewer. How many screening stations must…
The 30 management professors at Omega University find out that telephone calls made to their offices are not being picked up. A call-forwarding system redirects calls to the management office after the fourth ring. A department office assistant answers the telephone and takes messages.An average of 90 telephone calls per hour is placed to the management faculty, and each telephone call consumes about one minute of the assistant’s time. The calls arrive to a Poisson distribution, as shown in Figure (a), with an average of 1.5 calls per minute. Because the professors spend much of their time in class and in conferences, there is only a 40 percent chance that they will pick up a call themselves, as shown in Figure (b). If two or more telephone calls are forwarded to the office during the same minute, only the first call will be answered.a. Without using simulation, make a preliminary guess of what proportion of the time the assistant will be on the telephone and what proportion of the…
All airplane passengers at the Lake City Regional Airport must pass through a security screening area before proceeding to the boarding area. The airport has three screening stations available, and the facility manager must decide how many to have open at any particular time. The service rate for processing passengers at each screening station is 4 passengers per minute. On Monday morning the arrival rate is 7.8 passengers per minute. Assume that processing times at each screening station follow an exponential distribution and that arrivals follow a Poisson distribution. When the security level is raised to high, the service rate for processing passengers is reduced to 3 passengers per minute at each screening station. Suppose the security level is raised to high on Monday morning. Note: Use P0 values from Table 11.4 to answer the questions below. The facility manager's goal is to limit the average number of passengers waiting in line to 8 or fewer. How many screening stations must…
The manager of a grocery store in the retirement community of Sunnyville is interested in providing good service to the senior citizens who shop in her store. Currently, the store has a separate checkout counter for senior citizens. On average, 30 senior citizens per hour arrive at the counter, according to a Poisson distribution, and are served at an average rate of 35 customers per hour, with exponential service times. Find the following operatingcharacteristics:a. Probability of zero customers in the systemb. Average utilization of the checkout clerkc. Average number of customers in the systemd. Average number of customers in linee. Average time spent in the systemf. Average waiting time in line
The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive?
A mail order company receives a steady supply of orders by telephone. The manager records the number of calls received per day over a period of 3 months and found that it can be modeled via Poisson distribution with mean 8 orders per week (note: They only work 5 days in a week).
A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the milk from this herd. The farmer estimates that there’s a 10% chance of a cow grazing on some of the flavorful weeds. (a) Under these conditions, what is the probability that none of the 12 animals in this herd ate the tasty weeds? (b) Does the Poisson model give a good estimate of the probability that no animal ate the weed?
On weekdays during the academic year, the number of telephone calls at the main University call center follows a Poisson Point Process with a mean of 4 calls per minute.
Suppose you manage the demand for a towing company in Little Rock which follows a poisson process. On a usual day your company gets 4 requests for towing services. What is the probability you will get 0 or 1 request a day? What is the mean, variance, and standard deviation for the numberof calls your company gets?
Would you expect the Poisson distribution to be a good approximation of a. Runners crossing the finish line in the Boston Marathon? b. Arrival times of the students in your OSCM class? c. Arrival times of the bus to your stop at school?