Objective: This activity has the purpose of helping students calculate random va
ID: 3068116 • Letter: O
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Objective: This activity has the purpose of helping students calculate random variable from a Probability Distribution. (Objective 1) Student Instructions: Publish your answer to the question below in the Discreet Simulation Blog. This activity is worth 10 points: 6 points for your answer and 4 points for comments made to your classmates. To obtain the complete points on the Blog you must have at least 3 posts: you must create your post (1) and make at least two (2) comments to your classmates. Visit the posts made by your classmates and make a comment or question to discuss their observations Assuming you are waiting in line for service, for lack of a better example, let say you are at the DMV (Department of Motor and Vehicle), all of the sudden you realize that you have been waiting in line for hours, but you want to plan a game of simulation queue. List the activities that you would do to make the waiting line less boring and also take advantage of the moment to collect information of the all process to eventually create a simulation of this long and boring line?Explanation / Answer
(Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service)
A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.
A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........ Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.
The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.
Suppose a random variable X may take k different values, with the probability that X = xi defined to be P(X = xi) = pi. The probabilities pi must satisfy the following:
1: 0 < pi< 1 for each i
2: p1 + p2 + ... + pk = 1.
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails(assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey.
Let us consider the given simple simulation model. Suppose we have a single-channel queuing (waiting line) system, such as a line at the DMV as given in the question. The time between the arrival of customers is uniformly distributed from 1 to 10 minutes. This is obtained by means of a spinner dial (such as those used in some board games). The time required to service a customer be uniformly distributed between 1 to 6 minutes. A single die can be used to generate service times. The system has two random variables and if a large number of readings need to be generated, a computer is needed for generating the random variables and for doing the bookkeeping. To simulate real-world systems adequately, we must also be able to generate behavioral characteristics that are realistic. For example, the time between arrivals and the service times generated must allow for something other than uniform distribution rounded to the nearest whole number.
A queue provides waiting space for the entities whose movements through the model have been suspended based on the system’s status. An example is a work piece Waiting in turn to be processed on a busy machine. The operands of queue block are Queue ID indicating the name of the queue, Capacity of the queue and the Balk label which is used to direct the entity to an alternative block other than the seize block.
Various scheduling policies can be used at queuing nodes:
First In First Out: Also called first-come, first-served (FCFS), this principle states that customers are served one at a time and that the customer that has been waiting the longest is served first.[19]
Last In First Out: This principle also serves customers one at a time, but the customer with the shortest waiting time will be served first. Also known as a stack.
Processor Sharing: Service capacity is shared equally between customers.[19]
Priority: Customers with high priority are served first. Priority queues can be of two types, non-preemptive (where a job in service cannot be interrupted) and preemptive (where a job in service can be interrupted by a higher-priority job). No work is lost in either model.
Shortest Job First: The next job to be served is the one with the smallest size
Preemptive Shortest Job First: The next job to be served is the one with the original smallest size.
Shortest Remaining Processing Time: The next job to serve is the one with the smallest remaining processing requirement.
Service Facility
Customer’s Behavior Of Waiting:
These are thge information i would collect of all the processes to eventually create a simulation of this long and boring line in the DMV and mske it a less boring.
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