“In a data communication system, several messages that arrive at a node are bund
ID: 3183284 • Letter: #
Question
“In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume that the messages arrive at the node according to a Poisson process with = 30 messages per minute. Five messages are used to form a packet.”
(a) What is the mean time until a packet is formed, that is, until five messages have arrived at the node?
(b) What is the standard deviation of the time until a packet is formed?
(c) What is the probability that a packet is formed in less than 10 seconds?
(d) What is the probability that a packet is formed in less than five seconds?
Explanation / Answer
(a) Mean time or expected time until a packet is formed = 5/ 30 minute = 10 seconds
(b) Standerd Deviation of the time until a packet is formed = sqrt(10 ) = 3.16 ( for a poisson distribution std. dev. = sqrt(mean)
(c) P(t < 10, 10) from Poisson distribution = Poisson (t <10, 10) = 0.458 by poission calculator
(d) P( t< 5, 10) from poisson distribution = Poisson (t <5, 10) = 0.029 by poission calculator
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.