1) What is the sample mean, sample standard deviation, minimum, and maximum of the waiting time in the queue observed for the customers who arrived at, and departed from, the queue during the time interval [100.0, 120.0]?
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- Problem 11-19 (Algorithmic) 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 10 or fewer. How…Chapter 5. (M/M/s/K Model). Leia is responsible for 13 data units in the IT offices in a small business called DataWish. Each data unit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each data unit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per data unit and $800 per…Four trucks, 1, 2, 3, and 4, are waiting on a loading dock at XYZ Company that hasonly a single service bay. The trucks are labeled in the order that they arrived at thedock. Assume the current time is 1:00 P.M. The times required to unload each truck and the times that the goods they contain are due in the plant are given in thefollowing table.Truck Unloading Time (minutes) Time Material Is Due1 20 1:25 P.M.2 14 1:45 P.M.3 35 1:50 P.M.4 10 1:30 P.M.Determine the schedules that result for each of the rules FCFS, SPT, EDD, andCR. In each case compute the mean flow time, average tardiness, and number oftardy jobs.
- Chapter 5. (M/M/s/K Model). Leia is responsible for 12 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 4 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $750 per week per computer and $800 per week of…Consider the Dynamic Program formulation of the n-class optimal booking problem with sequential arrivals. In thisproblem, show some monotonicities of the value function.• Jt(x) − Jt(x − 1) is non-decreasing in t, ∀x.• Jt(x) − Jt(x − 1) is non-increasing in x, ∀t.Consider that the second property implies the first property. To prove the second property, given Dt, consider the discrete concavity of Ht(Dt, x) = max0≤u≤min{Dt,x} (pt)u + Jt−1(x − u) in x, i.e., Ht(Dt, x + 1) − Ht(Dt, x) ≤ Ht(Dt, x) − Ht(Dt, x − 1) for any x ∈ Z+ for any t. Image attatched for clarity.In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.) What is the expected waiting time in the queue(Wq)? (Express the waiting time in hours, round your answer to 3 decimal places.)
- An average of 12 jobs per hour arrive at our departmentalprinter.a Use two different computations (one involving thePoisson and another the exponential random variable) todetermine the probability that no job will arrive duringthe next 15 minutes. b What is the probability that 5 or fewer jobs will ar-rive during the next 30 minutes?Problem#1: Arrivals of a customers to payment counter in a bank follow poisson distribution with an average of 10 per hour. The service time follows negative exponential distribution with an average of 4 minutes.(a) What is the average number of customers in the Queue?(b) The bank will open one or more counter when the waiting time of a customer is at least 10 minutes. By how much the flow of arrivals should increase in order to justify the second counter?9. Mrs. Laila is an academic staff at the Rustaq International Business Administration Department. She has almost 5 years' experience in teaching different courses. In this semester, she has taught the Tourism Information System course which contains different topics. In one topie, the teacher has to conduct a meeting with Omani and non-Omani students by using a video-conferencing method; yet, she does not have any experience on how to manage a conference meeting. Would you be able to help Mrs. Laila by explaining tactics that lead to an effective video-conferencing meeting?
- Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.3. Indicate whether each of the following applications would be suitable for a queue.a. An ailing company wants to evaluate employee records so as to lay off some workerson the basis of service time (the most recently hired employees are laid off first).b. A program is to keep track of patients as they check into a clinic, assigning them todoctors on a first come, first served basis.c. A program to solve a maze is to backtrack to an earlier position (the last place where achoice was made) when a dead-end position is reached.d. An inventory of parts is to be processed by part number.e. An operating system is to process requests for computer resources by allocating theresources in the order in which they are requested.f. A grocery chain wants to run a simulation to see how the average customer wait timewould be affected by changing the number of checkout lines in its stores.g. A dictionary of words used by a spelling checker is to be initialized.h. Customers are to take numbers at a…The VBO grocery store has a checkout counter with a full-time cashier. Customers arrive randomly with an average rate of 20 per hour. The distribution of service time is exponential with an average of 2 minutes. Occasionally, this situation causes a long queue and customer complaints. Since there is no room for another cashier, the manager plans to hire another person to help pack the groceries and reduce the expected service time to 1.5 minutes, still with exponential distribution. The manager wants the percentage of time when there are more than 2 customers at the cash register to be less than 25%. He also wants no more than 5% of customers to have to wait 5 minutes or more before starting service or 7 minutes or more before finishing service. a) Use the formulas from the M/M/1 model to calculate L, Lq, W and Wq, π0, π1 and π2 of the current transaction. What is the probability that there are more than 2 customers at the cash register? (b) Repeat (a) for the helper alternative.