Modelling Traffic Loading on the Lion's Gate Bridge Idea: want to know how strong bridge needs to be. Compute: load x such that Expected time to first exceedance of load x is 100 years. Method uses: 1) modelling assumptions. 2) conservative modelling; to
Models for coin tossing Toss coin n times. On trial k write down a 1 for heads and 0 for tails. Typical outcome is = (1, . . . , n) a sequence of zeros and ones. Example: n = 3 gives 8 possible outcomes = cfw_(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1
Queuing Theory Ingredients of Queuing Problem: 1: Queue input process. 2: Number of servers 3: Queue discipline: first come first serve? last in first out? pre-emptive priorities? 4: Service time distribution. Example: Imagine customers arriving at a faci
Renewal Theory
Basic idea: study processes where after random time everything starts over at the beginning.
Example: M/G/1 queue starts over every time
the queue empties.
Begin with renewal process:
Have counting process N (t).
Times between arrivals are
Markov Chains Stochastic process: family cfw_Xi; i I of rvs I the index set. Often I R, e.g. [0, ), [0, 1] Z or N. Continuous time: I is an interval Discrete time: I Z. Generally all Xn take values in state space S. In following S is a nite or countable s