Consider a system with three parallel servers. Job arrivals arePoisson distributed at the rate of eight per hour unless all threeservers are busy. Since there is no waiting space, the arrival rateis zero if all servers a busy. Normally, each server has servicetime that is exponentially distributed with mean 20 minutes.However, if all three servers are busy the servers speed up sothat mean service time is 15 minutes. Find the steady stateprobability for each system state.

The considered system has parallel servers.Job arrivals have a Poisson distribution with the rate…

Answered: Consider a system with three parallel…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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4. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85.B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.D) The probability of surviving 1 year after being diagnosed with a slow-progressing form of…
A burger joint has on average 9 customers arriving per hour. There is only one employee serving customers and she takes about 4 minutes on average to serve a customer. The burger joint is open 10 hours per day and makes a profit of $10 for each burger sold. The staff has a pay rate of $20/hour. Assume a Poisson distribution on the arrival rate of customers and exponential distribution on the service time of the employee. Q. If customers do not want to spend more than 6 minutes in the burger joint (including waiting and service), how much potential profit would the joint lose per day?
A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of five per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. a. Calculate the percentage utilization of the graduate student. (Round your answer to 1 decimal place.) b. Calculate the average number of students in the system, including the graduate student service desk. (Round your answer to 1 decimal place.) c. Calculate the average time in the system. (Round your answer to 1 decimal place.) d. Calculate the probability of four or more students being in line or being served. (Round your intermediate calculations to 3 decimal places and final answer to…
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. T.... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, than 0.05. It be unusual to observe two components fail, since the probability that two components fail,, is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) O Time Remaining: 02:29:14 Next Left Raht
Moore’s portable X-ray equipment repair service shop receives an average of 6 portable X-ray sets per 8-hour day to be repaired. Moore would like to be able to tell his customers that they can expect one day service. What average repair time per set will the repair shop have to achieve to provide 1-day service on average? Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.
116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that…
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A disk drive has a constant failure rate and an MTTF of 5000 hr. (a) What will the probability of failure be for one year of operation? (b) What will the probability of failure be for one year of operation if two of the drives are placed in active parallel and the failures are independent? (d) What will the probability of failure be for one year of operation if the system si changed to standby model. (e) Describe the effect on the MTTF with a switching failure probability of 0.05. () What would be change in MTTF if the probability of failure of standby unit is 10 percent of the failure of the primary unit in the standby mode?
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Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (c) What is the average time spent in the shop?
The arrival of customers to a small local food restaurant may be modeled by a Poisson process with rate of 1 per 15 min period. Assume customer will only arrive if there is at least one customer present. Each customer on average stays for a time exponentially distributed with mean 20 minutes. This is modeled as a birth-death process. (i) Compute the probability that the capacity of 20 will be reached if we start with 5 customers.

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