On the adequacy of pseudo-random number generators (or: How big a period do we need?)
Generating pseudo-random number sequences is central to discrete-event computer simulations. Traditionally, generators are used only after they have passed several statistical tests. We propose a new, easy-to-implement test of randomness based upon the '...
Finding duplicate rows in a linear programming model
We present an algorithm for identifying and disposing of duplicate rows in an LP matrix - that is, rows which are identical except for a scalar multiplier. This algorithm is a useful tool for debugging models as well as a means of improving efficiency. ...
Linear programming formulations of Markov decision processes
We give a new derivation of the linear program corresponding to a Markov Decision Process (MDP) in steady state, which seeks to minimize discounted total expected cost. We use this derivation to show, very directly, the known relationship between this ...
A new condition for the existence of optimal stationary policies in average cost Markov decision processes
Discrete time countable state Markov decision processes with finite decision sets and bounded costs are considered. Conditions are given under which an unbounded solution to the average cost optimality equation exists and yields an optimal stationary ...
A simple technique in Markovian control with applications to resource allocation in communication networks
The purpose of this note is to demonstrate that for semi-Markov decision problems with exponentially distributed transition times considerable computational improvements on the value-iteration algorithm can be obtained. This can be achieved by the ...
Control of arrivals and departures in a state-dependent input-output system
At each decision epoch, an offer for a unit to either enter or leave a system is received. These offers arrive according to a Poisson process. With each offer is associated a value revealed upon the arrival of the offer. The distribution of the value of ...
The efficiency of control variates in multiresponse simulation
When control variates are applied to a simulation with multiple responses some of the potential effeciency improvement is lost if the optimal control coefficients must be estimated. To quantify this phenomenon, we formulate a variance ratio and a loss ...
On the continued Erlang loss function
We prove two fundamental results in teletraffic theory. The first is the frequently conjectured convexity of the analytic continuation B(x, a) of the classical Erlang loss function as a function of x, x >= 0. The second is the uniqueness of the solution ...
Quadratic functions with exponential number of local maxima
We construct a quadratic function x, with n x k variables, k >= 2, and exhibit 2^n vertices of the unit hypercube over which f takes distinct values and where each vertex is a strong local maximum of f in the continuous sense as well as in a discrete ...
On constrained maxima of convex functions
This paper states and proves Kuhn-Tucker necessary conditions for a maximum point of a convex function subject to convex constraints. Also presented are conditions which imply that the optimal policy set of this type program is a continuous point-to-set ...