Statistics II20805 marksNumerical: Poisson process queuingCounting process
Customers of certain Internet service provider connect to the internet at the average rate of 10 new connections per minute. Connections are modelle by binomial counting process. a. What frame length gives the probability 0.1 of an arrival during given frame? b. Find the mean and variance for the nu
Customers of certain Internet service provider connect to the internet at the average rate of 10 new connections per minute. Connections are modelle by binomial counting process. a. What frame length gives the probability 0.1 of an arrival during given frame? b. Find the mean and variance for the number of seconds between two consecutive connections. [5]
- Arrival rate: $\lambdaA = 10$ connections per minute - Process model: Binomial counting process - Part (a): required frame probability $p = 0.1$ - Part (b): find mean and variance of inter-arrival time in seconds Convert rate to seconds for consistency: $$\lambdaA = 10 \text{ per minute} = \fra...