Suppose that documents are transmitted by a facsimile machine. Assume that the documents arrive at random, 75% of which is of the fixed form with constant transmission (service) time 40 seconds, whereas the rest are exponentially distributed with the mean 2 minutes. 1. How many documents per hour can be transmitted with mean waiting time no greater than 30 seconds? 2. If the number of documents per hour is the same as (1), and if all documents are of the fixed form, how much is the mean waiting time? Please answer both 1 and 2 with a complete step and formula used
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Suppose that documents are transmitted by a facsimile machine. Assume that the documents arrive at random, 75% of which is of the fixed form with constant transmission (service) time 40 seconds, whereas the rest are exponentially distributed with the mean 2 minutes.
1. How many documents per hour can be transmitted with mean waiting time no greater than 30 seconds?
2. If the number of documents per hour is the same as (1), and if all documents are of the fixed form, how much is the mean waiting time?
Please answer both 1 and 2 with a complete step and formula used.
Step by step
Solved in 4 steps
- 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?suppose tht a queueing system has two identical servers, and an exponential service-time distribution with a mean of 1/u=10minutes. furthermore, a customer has just arrived to find two in the system. how long would you expect him to wait before being able to start service? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.10. Customers arrive an average of 8 per hour and an average of 12 customers can be served in an hour. Assume this is an M/M/1 model. (Noteshaper Quick Start #18 - #20) what is the system utilization? what is the average length of the line? what is the average number of customers in the system? what is the average amount of time spent waiting in the line? what is the average amount of time a customer spends in the system? what is the probability of no customers in the system? 11. Customers arrive at a ferry ticket office at the rate of 18 per hour on Monday mornings. This can be described as a M/M/1 model. Selling the tickets and providing general information takes an average of 2 minutes per customer. One ticket agent is on duty on Mondays. (Noteshaper Scenario #34) a. What is the average length of the line on Monday mornings? b. On average, how long does a customer wait to buy a ticket on Monday mornings (in minutes)? c. How long does it take to successfully buy a ticket on Monday…
- (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?Which of the following is false about the Assumptions of queuing model? The waiting space available for customers in the queue is finite. Service discipline followed in FCFS The mean arrival rate is less than the mean service rate O The elapsed time since the start of the queue is sufficiently long so that system in stableWhat do we mean by the term queue discipline?o Queue discipline refers to how people should behave in a queue.o Queue discipline refers to the study of queues and waiting lines.o Queue discipline refers to policies for deciding the order of receiving service byarrivals.o Queue discipline refers to removing customers from a queue when they misbehave.
- Experience the Tour de France (ETF) is a specialty travel agent. It arranges vacations for amateur cyclists who want to experience the Tour de France by riding through one or more stages in the race. It has five people who take calls from clients. Each call lasts on average 25 minutes, with a standard deviation of 50 minutes. A call arrives on average every 20 minutes with a standard deviation of 20 minutes. (Do not round intermediate calculations. Round your answer to two decimal places.) On average, how many minutes does a caller wait before talking to an agent? minutesPlease 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).)Why does a (M/M/2):(GD/5/infinity) queuing system have a steady state regardless of the values of A > 0 and u > 0? O No further calling unit can enter the system when there are 5 in it. O A and u are both positive O The queue is not a Poisson queue. none of the above
- 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"?) The average customer spends 45 minutes in the bank. The bank must have at least 2 bank tellers. There is always a line of customers waiting during the 11a-1p period. The average service time (not including waiting) at the bank is 3/4 of an hour. Exactly two answers are correct. None of the answers are correct.An M/M/1 queueing system has that customers arrive to it at a rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an exponential distribution with parameter 5 per hour. This question will ask you to evaluate two options for designing the server in the system. Both options for the single server provide the same service for the customers in the queueing system but they cost different amounts to implement. In addition, the total costs of the queuing system are the implementation costs plus the customer costs. Currently, the customer costs are $100 per hour per customer in the queueing system. In comparing these options, it costs us $100 per hour per customer in the queueing system. (a) The first option for the server is one that has a service time that follows an exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this system. (b) The second option for the server is one that has a service time that follows an…A data storage system consists of 3 disk drives sharinga common queue. An average of 50 storage requests arriveper second. The average time required to service a requestis .03 second. Assuming that interarrival times and servicetimes are exponential, determine:a The probability that a given disk drive is busyb The probability that no disk drives are busyc The probability that a job will have to waitd The average number of jobs present in the storagesystem