Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request.
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Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request.
- Find the probability that 10 requests are processed by the server during the first 1 minutes.
- Determine the probability that no request is processed by the server during the first 2 minutes
Determine the average number of requests processed in 2 minutes
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- At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.The average time between the arrivals of the taxis arriving at the airport to pick up passengers has an exponential distribution, with an average of 10 minutes. a) What is the probability that a passenger will wait for the taxi less than 15 minutes? b) What is the probability that a passenger will wait for the taxi between 20 and 30 minutes? Solve using the cumulative distribution function H1Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.5per minute. The average time to handle each is 10seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. a) The probability that the operator is busy = enter your response here (round your response to two decimal places). b) The average time that a caller must wait before reaching the operator = enter your response here minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = enter your response here calls (round your response to two decimal places).
- Telephone calls come into an office at random. The time between calls is the following discrete distribution: Service time Probability 6 .40 7 .30 8 .20 9 .10 When the receptionist is busy, a telephone message tells the caller that the call is important and to please wait on the line until the next reservation agent becomes available. We can assume that customers don’t hang up once they join the call queue. The service time for call follows a normal distribution with a mean of 8 mins and standard deviation of 2.5 mins Simulate the operation of the office telephone system for 1100 customers. Discard the first 100 customers and use data over the next 1000 customers to answer the following questions: What is the average waiting time for customers? What is the utilization of the receptionist? What is the probability that a customer waits for longer than 1 min before their call is answered?Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?