Service times Poisson arrivals at rate n Service time has arbitrary distribution with given E[X] and E[X2I Service times are independent and identically distributed (ID) Independent of arrival times E[service time]=1/u Single Server queue
An interesting property of an M/M/ 1 queue, which greatly simplifies combining these queues into a network, is the surprising fact that the output of an M/M/ queue with arrival rate is a Poisson process of rate This is part of Burke's theorem, which follows from reversibility A Markov chain has the property that P[future present, past] P[future present] Conditional on the present state, future states and past states are independent
Carrier Sense Multiple Access(CSMA) In certain situations nodes can hear each other by listening to the channel “Carrier Sensing CSMA: Polite version of Aloha Nodes listen to the channel before they start transmission Channel idle=> Transmit Channel busy = Wait (join backlog) When do backlogged nodes transmit? When channel becomes idle backlogged nodes attempt transmission with probability q=1 Persistent protocol, q=1 Non-persistent protocol,< 1
