The ticket booth on the Tech campus is operated by oneperson, who is selling tickets for the annual Tech versusState football game on Saturday. The ticket seller can servean average of 12 customers per hour (Poisson distributed);on average, 8 customers arrive to purchase tickets eachhour (Poisson distributed). Determine the average time aticket buyer must wait and the portion of time the ticketseller is busy.

The ticket booth on the Tech campus is operated by oneperson, who is selling tickets for the annual Tech versusState football game on Saturday. The ticket seller can servean average of 12 customers per hour (Poisson distributed);on average, 8 customers arrive to purchase tickets eachhour (Poisson distributed). Determine the average time aticket buyer must wait and the portion of time the ticketseller is busy.

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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The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturday. The ticket seller can serve an average of 12 customers per hour (Poison distributed); on average, 8 customers arrive to purchase tickets each hour (Poison distributed). Determine the average time a ticket buyer must wait and the portion of time the ticket seller is busy.
The Seaboard Shipping Company has a warehouse terminal in Spartanburg, South Carolina. The capacity of each termi-nal dock is three trucks. As trucks enter the terminal, the dri-vers receive numbers, and when one of the three dock spaces becomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, and the unloading and loading times (service times) are expo-nentially distributed. The average arrival rate at the terminal is five trucks per hour, and the average service rate per dockis two trucks per hour (30 minutes per truck).a. Compute L, Lq, W, and Wq. b. The management of the shipping company is consider-ing adding extra employees and equipment to improve the average service time per terminal dock to 25 min-utes per truck. It would cost the company $18,000 per year to achieve this improved service. Managementestimates that it will increase its profit by $750 per yearfor each minute it is able to reduce a truck’s waitingtime.…
Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…
Customers arriving at a service center are assigned to one of three categories, with category 1given the highest priority. Records indicate that an average of nine customers arrive per hour andthat one-third are assigned to each category. There are two servers, and each can process customers at the rate of five per hour. Arrival and service rates can be described by Poisson distributions.a. What is the utilization rate for this system?b. Determine the average waiting time for units in each class.c. Find the average number of customers in each class that are waiting for service
The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve customers on a first-come, first-served basis. Customers arrive at an average rate of fiveper hour, and the stylists spend an average of 35 minutes on each customer Determine the average number of customers in the salon, the average time a customer must wait, and the average number waiting to be served.
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 customer
A student computer laboratory has a single laser printer. Jobs queue up on the printer from thenetwork server in the lab and are completed on a first-come, first-served basis. The averageprinting job requires four minutes, but the times vary considerably. Experience has shown thatthe distribution of times closely follows an exponential distribution. At peak times, about 12students per hour require use of the printer, but the arrival of jobs to the printer can be assumed to occur completely at random.Assuming a peak traffic period, determine the following:a. The average number of jobs in the printer queue.b. The average flow time of a job.
The Minute Stop Market has one pump for gasoline, which can service 10 customers per hour (Poisson distrib-uted). Cars arrive at the pump at a rate of 5 per hour (Poisson distributed). a. Determine the average queue length, the average time acar is in the system, and the average time a car must wait.b. If, during the period from 4:00 P.M. to 5:00 P.M., thearrival rate increases to 12 cars per hour, what will bethe effect on the average queue length?
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.
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the average time a cab must wait for a fare?