On some queue length controlled stochastic processes

On the Rate of Convergence of Some Stochastic Processes

We present a general technique for obtaining bounds on the deviation of the optimal value of some stochastic combinatorial problems from their mean. As a particular application, we prove an exponential rate of convergence for the length of a shortest path through n random points in the unit square. This strengthens a previous result of Steele [St (1981b)].

Generators of some Non–Commutative Stochastic Processes

A fundamental result of Biane (1998) states that a process with freely independent increments has the Markov property, but that there are two kinds of free Lévy processes: the first kind has stationary increments, while the second kind has stationary transition operators. We show that a process of the first kind (with mean zero and finite variance) has the same transition operators as the free ...

Some Inference Theorems in Stochastic Processes

Variable-Length Extractors: Efficiently Extracting Randomness from Weak Stochastic Processes

The topic of generating random bits from imperfect random sources was studied extensively. Existing work provides solutions that are based on the concept of a fixed-length extractor; namely, an algorithm that gets a fixed number of random bits from a source and generates random bits. Typically, the number of random bits extracted using fixed-length extractors is upperbounded by the min-entropy....

Second Moment of Queue Size with Stationary Arrival Processes and Arbitrary Queue Discipline

In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...