Suppose that 8 customers per hour arrive at a bank during the 11a-1p. "lunch-hour", period. It is observed that there are, on average, 6 customers in the bank during this same "lunch-hour" period. Which of the following statements are true assuming the system is in steady- state during that period? (Hint: What law govern's the behavior of systems in "steady-state"?) O The average customer spends 45 minutes in the bank. O The bank must have at least 2 bank tellers. There is always a line of customers waiting during the 11a-1p period. O The average service time (not including waiting) at the bank is 3/4 of an hour. O Exactly two answers are correct. O None of the answers are correct.
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- 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.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.48. Ships arrive at a port facility at an average rate of twoships every three days. On average, it takes a single crewone day to unload a ship. Assume that interarrival andservice times are exponential. The shipping companyowns the port facility as well as the ships using that facility. The companyestimates that it costs $1000 per dayfor each day that a ship spends in port. The crew servicing the ships consists of 100 workers, each of whom ispaid an average of $30 per day. A consultant has recommended that the shipping company hire an additional40 workers and split the employees into two equal-sizecrews of 70 each. This would give each crew an averageunloading or loading time of 1.5 days. Which crew arrangement would you recommend to the company?
- A firm is engaged in both shipping and receiving activities. The management is always interested in improving the efficiency of new innovations in loading and unloading procedures. The arrival distribution of trucks is found to be Poisson with arrival rate of 3 trucks per The service time distribution is exponential with unloading rate of 4 trucks per hour. Determine (i) expected number of trucks in the queue, hour. (ii) expected waiting time of the truck in the queue, (iii) probability that the loading and unloading dock and workers will be idle, (iv) what reductions in waiting time are possible if loading and unloading is standardised?(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?A bank official finds that the length of time customers wait to be served by teller are approximately normally distributed with a mean of 5 minutes and a standard deviation of 3 minutes. What probability that a customer has to wait for at least 6.7 minutes?
- Please do not give solution in image formate thanku. We consider a level-2 IT service desk with 2 staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment is fulfilled? (Show all the formulas and computations - since Lq (avg number of jobs in queue) is complex to calculate assume that it is = 1.02 (requests).)In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 2 seconds (standard deviation = 4.3). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the queue (in seconds)? secondsPlease do not give solution in image format thanku 1. In a queueing system, customers arrive once every 4 seconds (standard deviation = 4) and services take 3 seconds (standard deviation = 5.1). What is the average time a customer wiill spend in the system (in seconds)?
- At the SuperSpeedy drive-through the time between consecutive customerarrivals has a mean of 50 seconds and a standard deviation of 30 seconds. Thereare two servers whose service time averages 80 seconds with a standard deviationof 20 seconds. Assume that no customers leave the drive-through after entry.b. What is the average time a customer spends at the drive-through? What fractionof that is waiting in the queue?In queuing theory and modeling, if 1/μ represents mean service time. Whatdoes μ represent? Service rateInterarrival time Arrival rate NoneIn a queueing system, customers arrive once every 6 seconds (standard deviation = 5) and services take 5 seconds (standard deviation = 4). (Do nót round intermediate calculations. Round your answer to three decimal places.) customers What is the average number of customers in the queue?