機率研討會

主講者: Professor Ronald W. Wolff (University of California, Berkeley)
講題: Little’s Law when the Average Waiting Time is Infinite
時間: 2013-03-04 (Mon.)  14:30 -
地點: 數學所 722 研討室 (台大院區)
Abstract: One version of Little’s Law is a relation between averages along a sample path. There are two others in a stochastic setting; they readily extend to the case where the average waiting time is infinite. We investigate conditions for the sample-path version of this case to hold. Published proofs assume our equation holds. It is only sufficient. We present examples of what may happen when our equation does not hold, including one that may be new where the average waiting time is infinite and the average number of customers in the system is ?nite. We obtain a sufficient condition called “weakly FIFO” that is weaker than our equation, and through truncation, a necessary and sufficient condition. We show that the equation is sufficient but not necessary for the departure rate to be equal to the arrival rate.
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