1. Given the following values: Compute the following values: i) Average waiting time ii) Probability (wait) iii) Probability of Idle Server iv) Average service time(minutes) Total Number of customers = 20 Total Idle time of server = 14 Total run time of simulation = 86 Number of customers who wait = 11 Total service time=68 Total time customer wait in the queue = 30
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- Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.Assume that during minute t (the current minute isminute 1), the following sequence of events occurs: (1) Atthe beginning of the minute, xt customers arrive at the cashregister; (2) the store manager decides how many cashregisters should be operated during the current minute;(3) if s cash registers are operated and i customers arepresent (including the current minute’s arrivals), c(s, i)customers complete service; and (4) the next minute begins.A cost of 10¢ is assessed for each minute a customerspends waiting to check out (this time includes checkouttime). Assume that it costs c(s) cents to operate s cashregisters for 1 minute. Formulate a dynamic programmingrecursion that minimizes the sum of holding and servicecosts during the next 60 minutes. Assume that before thefirst minute’s arrivals, no customers are present and thatholding cost is assessed at the end of each minute.Proctoring Enabled: Chapter 12 Computer Simulati. O Save & Exit Submit Saved Help You have determined that waiting times at a toll booth are uniformly distributed over the interval 50 to 110 seconds. Your simulation generates the following random numbers. Complete the table with the waiting time associated with each random number. (Round your answers to the nearest whole number.) Random Number Waiting Time 0,64 0.87 0.57 Mc Graw Hill Next < Prev 5 of 5 ASUS
- Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.Saved Help Save & Exit Submit octoring Enabled: Chapter 11 Queuing Models Exercises On a toll road, there are 5 lanes for drivers to pay their toll. Customer arrival times are random, with a general independent distribution. Service times are constant, with a degenerate distribution. What is the proper description for this queueing system? Proper description < Prev 3 of 5 Next Mc Graw Hill 3.The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.
- * 08 HI FL R %S4 LLI %#3 50 For the first two hours of the day, the arrival rate at the donut shop is 10 customers per hour. The donut shop is capable of serving 8 customers per hour. Assume that the system is empty at the start and that no customer who arrives leaves without being served. (Round your answer to 2 decimal places.) What is the average wait time for customers during this time period (in hours)? unoy nces Mc Graw Wellington Paranormal Stars and Pahkitew Island RESTAURANT Restaurant: Scissor Seven My 600-lb Life The Afterparty Pam & Tommy As We See It 8,425 MAR étv A 644 DD F7 F12 F8 F10 F3 F 4 F5 93 %23 5 delet 9 7. 2. } P. 1 B. W N alt 38 command MOSISO command(Random variables) Prove that the mean and standard deviation of the exponential distribution are equal (Queueing Theory) The time between failures of the kencore refridgerator is known to be exponential with mean values 9000 hours (about 1 year of operation), and the company issues a 1 year warranty on the refridgerator. what are the chances that the breakdown repair will be covered by the warranty?Please do not give solution in image format thanku A takeaway café has an average rate of customer arrival of 6 per hour. The café uses two service counters and both counters take 6 minutes to serve each customer. Assuming Poisson arrivals and exponential service, what is the average number of customers waiting in a queue? a. 1.000 b. 0.059 c. 0.600 d. 0.333 e. None of the other answers is correct Feedback
- (Please do not give solution in image format thanku) A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in 3 minutes. Customer arrivals at the machine are Poisson distributed, with an average of 15 customers an hour. Relevant formulas to analyze this M/M/1 model are available in your textbook. What percent of the time is this machine idle? 25% 0% 75% 50% 100%Analyze the following queueing management sysytem 1- traffic intensity of 0.3 in queueing system 2- The average time spends in the system =0.036 3-The average number of the customer in the system 0.43Describe at least 4 operating characteristics you can determine by performing queue analysis. What is the purpose of doing queue analysis to the business owner, i.e., what are possible actions (at least 2) that a business owner or manager might want to take, once the operating characteristics are understood?