(This is not related to the previous question). The average arrival rate is 4/hour (Poisson) and the average service rate is 6/hour (negative exponential) and one server. Determine the following: Average number in the line and average number in the system? Average wait time in the line average wait time in the system? System Utilization Probability of 3 or more in the system
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- The Universal Manufacturing Company produces a particular product in an assembly-line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, on average, according to an exponential distribution. The machine operator can process an average of 10 parts per hour (Poisson distributed). Determine the average number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the machine is idle. The management of Universal Manufacturing Company likes to have its operators working 90% of the time. What must the assembly line arrival rate be in order for the operators to be as busy as management would like?at the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel address. the arrival rate at the sorting machines is at the rate of 100 per hour following Poisson distribution. the machine sorts at the constant rate of 150 per hour.a. what is the utilization rate of system? b. what is the average number of packages waiting to be sorted? c. what is the average number of packages in the sorting system? d. how long must the average package wait until it gets sorted? e. what would Lq and wq be if the service rate were exponential, not constant?The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the average time a cab must wait for a fare?
- Bank with 2 tellers. Customers arrive at a rate 80 per hour and wait in a single line. Average time to serve is 1.2 minutes per customer What is the expected number of customers present in the bank? = What is the expected length of time a customer spends in the bank? = What is the fraction of time any specific teller is idle? = probability that the system is empty + 0.5(probability that the system has 1 customerAn average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.Moore, Aiken, and Payne is a critical care dental clinic serving the emergency needs of the general public on a first-come, first-served basis. The clinic has five dental chairs, three of which are currently staffed by a dentist. Patients in distress arrive at the rate of five per hour, according to a Poisson distribution, and do not balk or renege. The average time required for an emergency treatment is 30 minutes, according to an exponential distribution. Use POM for Windows or OM Explorer to answerthe following questions:a. If the clinic manager would like to ensure that patients do not spend more than 15 minutes on average waiting to see the dentist, are three dentists on staff adequate? If not, how many more dentists are required? b. From the current state of three dentists on staff, what is the change in each of the following operating characteristics when a fourth dentist is placed on staff:▪ Average utilization▪ Average number of customers in line▪ Average number of customers…
- A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find The probability of there being no customer in the system The average number of customers in the system iii. Average number of customers waiting to be served iv. Average time a customer spends in the system v. Average waiting time for a customerStudents arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?