. A facility of m identical machines is sharing a single repair person. The time to repair a failed machine is exponentially distributed with mean 1/λ. A machine, once operational, fails after a time that is exponentially distributed with mean 1/μ. All failure and repair times are independent. (a) Draw state transition diagram (b) Find out expression for the steady-state proportion of time where there is no operational machine.
Answer:
. A facility of m identical machines is sharing a single repair person. The time to...
4. Each time a machine is repaired, it remains up and working for an exponentially distributed time with rate λ. It then fails, and its failure is either of two types. If it is type 1 failure, then the time to repair the machine is exponentially distributed with mean μ1; if it is a type 1 failure, then the time to repair the machine is exponentially distributed with mean μ2. Each failure is, independently of the time it took the...
Problem 2 There are three machines and two mechanics in a factory. The break time of each machine is exponentially distributed with A 1 (per day). The repair time of a broken machine is also exponentially distributed with a mean of 3 hours. (Mechanics work separately) (1). Construct the rate diagram for this queueing system. (be careful about the arrival rate A) (2). Set up the rate balance equations, then solve for pn's. (3). Compute L (4). Compute the actual...
Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a type 1 failure, then the time to repair the machine is exponential with rate μ!, if it is a type 2 failure, then the repair time is exponential with rate H2. Each failure is, independently of the time it took the machine to fail, a...
Homework Assignment 3.5 Summer 2018 Question 3: Continuous-time Markov Chains (a) A facility has three that are identical. Each machine fails independently with an exponential distribution with a rate of 1 every day; repairs on any machine are also exponentially distributed with a rate of 1 every 12 hours. Create a continuous-time Markov chain to model this (identify the rates, and the transition probabilities) (b) Now, assume the facility above has three machines, but one of them is of Type...
(3). How is the steady state probability distribution changed? Problem 2 There are three machines and two mechanics in a factory. The break time of each machine is exponentially distributed with A1 (per day). The repair time of a broken machine is also exponentially distributed with a mean of 3 hours. (Mechanics work separately). (1). Construct the rate diagram for this queueing system. (be careful about the arrival rate An (2). Set up the rate balance equations, then solve for...
Each time a machine is repaired, it remains up for an exponentially distributed time with rate ?. It then fails, and its failure is either of two types: - Each failure is, independently of the time it took the machine to fail, a type 1 failure with probability ? and a type 2 failure with probability 1 − ?. - If it is a type ? failure, the time to repair the machine is exponential with rate ?? , ?...