Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following: i. Average number of units in the system ii. Average waiting time iii. Average length of queue iv. Probability that a customer arriving at the pump will have to wait v. The utilization factor for the pump unit vi. Probability that the number of customers in the system is 2.

Q: The expected total time in the system. b. The expected time each customer has to wait. c. The…

A: As per Bartleby guidelines, we can only solve the first three subparts of one question at a…

Q: a. What is the utilization? (Round your answer to 3 decimal places.) Utilzation b. What is the…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Determine the average time customers spend at the machine, including waiting in line and completing…

A: Arrival rate = 1 customer every 2 minutesService rate = 1 customer takes 99 seconds

Q: In a queueing system, customers arrive once every 4 minutes (standard deviation = 7) and services…

A: Queuing systems are basic mathematical models that are used to explain traffic bottlenecks. A…

Q: Consider a two-channel waiting line with Poisson arrivals and exponential service times. The…

A: The answer is as below

Q: b. Determine the average time customers spend in the system. (Do not round intermediate…

A: A discrete probability distribution that shows the likelihood of an event within a specified time is…

Q: a. What is the utilization? Utilization b. What is the expected number of customers in the system…

A: As per Bartleby guidelines, we can only solve the first three subparts of one question at a…

Q: Capacity utilization of the teller. Average number of cars in the waiting line Average number in the…

A: Arrival rateA15.00Service rateS20.00

Q: A server operates with 75 percent utilization. The average processing time istwo minutes and the…

A: Utilization of Server = ρ=0.75 Average processing time = 2 minutes Service rate = μ = 12×60 = 30…

Q: At a particular service operation, customers form a single queue that operates on a first-come,…

A: Given Arrival rate, λ = 12 per hour Service rate, μ = 15 per hour

Q: Suppose that arrivals are distributed according to the Poisson distribution with a mean of 0.2 unit…

A: Given data, Arrival rate, = 0.2 per period Service rate, = 4 periods = 0.25 per period Number of…

Q: a. What is the average length of the waiting line? (Round your answer to 2 decimal places.)   b.…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: a. The average number of customers in the system. b. The average time a customer spends waiting in…

A: Given that: Arrival rate (lambda) 20 customers per hr Service rate (mu)  30 customers per hr

Q: In waiting line management, system performance measures include which of the following: I. an…

A: In the waiting line management, system performance measures include- II. the average number of…

Q: In a queueing system, customers arrive once every 6 seconds (standard deviation = 5) and services…

A: Given data  Arrival rate  λ=16 Service rate  μ=15 Coefficient of variations of the arrival time…

Q: In an M/MA queueing system, the arrival rate is 4 customers per hour and the service rate is 6…

A: Note:  We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: For the first four minutes of the day, the arrival rate at the gas station is 50 vehicles per…

A: Arrival rate a = 50 vehicles per min Service rate s = 44 vehicles per min There are 50-44 = 6…

Q: In an M/MA queueing system, the arrival rate is 7 customers per hour and the service rate is 12…

A: MM1 is technical Queueing system which is  based  on the probability where arrivals are determined…

Q: 7. What is the difference between Balking and Reneging?

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Note: Formulas to solve the following problems are given in the class and example problems were…

A: Arrival rate λ = 603                           =20 per hour Service rate μ = 602.4…

Q: In an M/MA queueing system, the arrival rate is 8 customers per hour and the service rate is 11…

A: Given data  Arrival rate of clients (λ) = 8 customer per hour  Service rate of clients (μ) = 11…

Q: a. What is λ? b. What is μ? c. Find probability of no units in the system.

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Customers enter the camera department of a store at an average rate of six per hour. The department…

A: The given problem corresponds to the M/M/1 queuing model which is a single-server queuing system…

Q: A request for assistance at the reference desk at a library is submitted at an average rate of 9 per…

A: Given Information: Arrival Rate (λ) = 9 customers per hour Service time = 6 minutes per customer…

Q: In a queueing system, customers arrive once every 5 minutes (standard deviation = 7) and services…

A:

Q: Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is…

A: A)Identify the queueing model:The queueing model identified using the given situation is M/M/1…

Q: Emergency medical personnel are standing outside the HyVee grocery store and taking the temperature…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Answer the following questions. Answers are listed at the end of this section.1. The queuing models…

A: Note: I have answered for 1 to 3 questions. Kindly post the remaining questions separately. 1) First…

Q: on process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of…

A: Mean arrival rate(λ)=0.5 per minutesThe service time(μ)=1.5 per minutes

Q: Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the…

A:

Q: Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per…

A: The correct solution of the given statement is in Step 2.

Q: A new shopping mall is considering setting up an information desk manned by one employee. Based upon…

A: I will determine the total expected cost over an 8-hour day, the related answer is presented below,

Q: What is the expected average number of snowplows in the garage (waiting for repair and being…

A: Arrival rate is Poisson distribution and service rate is exponential. Arrival rate λ = 5 per…

Q: Christmas Airlines is reviewing its check-in procedures in anticipation of college students…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution.…

A: Queuing theory is a mathematical theory of representing data, where the company has arrival rate,…

Q: A proposal has been presented to the government of Newfoundland and Labrador that would build a new…

A: Highway length = 16 kmsTotal toll booths= 7Arrival rate of cutomers ,  = 9 per minuteService time in…

Q: Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The…

A: Given:Arrival rate (A)3Service rate (S)5number of servers (C)1

Q: A horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes…

A: Service waiting time refers to the duration a person or customer has to wait before receiving a…

Q: A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall.…

A: The M/M/1 queueing system simulates the behaviour of a single-server queue with exponentially…

Inventory Management

The supply chain is crucial to a firm's operations as it manages the inflow and outflow of products that are manufactured from the initial stage to the end product. It also considers the raw materials needed at different stages of production and when the work is in progress. Inventory management functions consist of ordering, storing, and procuring the organization's inventory like raw materials, factors, and finished products. It's also used for controlling the number of products for trade and helps manage the organization's inventory and stock. Inventory Management has been defined as having the right inventory, of the right volume, at the right cost.