Statistics II20755 marksNumerical: binomial arrival processBernoulli single server queuing process
Jobs are sent to mainframe computer at a rate of 4 jobs per minute. Arrivals are modeled by a binomial process. a. Choose a frame size that makes the probability of a new received during each frame equal to 0.1. b. Using the chosen frame compute the probability of more than 4 jobs received during on
Jobs are sent to mainframe computer at a rate of 4 jobs per minute. Arrivals are modeled by a binomial process. a. Choose a frame size that makes the probability of a new received during each frame equal to 0.1. b. Using the chosen frame compute the probability of more than 4 jobs received during one minute. c. Compute mean and variance of inter arrival time? [5]
- Arrival rate: $\lambda = 4$ jobs per minute - Process type: Binomial (Bernoulli frames) - Target frame probability: $p = 0.1$ --- In a binomial process, arrivals occur one per frame with probability $p$, so the rate is: $$\lambda = \frac{p}{\Delta} \implies \Delta = \frac{p}{\lambda} = \frac{0....