Economics Insights @ CBS

In recent years, there has been a surge of research into methods for estimating derivatives of performance measures from sample paths of stochastic systems. In the case of queueing systems, typical performance measures are mean queue lengths, throughputs, etc., and the derivatives estimated are with respect to system parameters, such as parameters of service and interarrival time distributions. Derivative estimates potentially offer a general means of optimizing performance, and are useful in sensitivity analysis.

In many important combinatorial optimization problems, such as bin packing, allocating customer classes to queueing facilities, vehicle routing, multi-item inventory replenishment and combined routing/inventory control, an optimal partition into groups needs to be determined for a finite collection of objects; each is characterized by a single attribute. The cost is often separable in the groups and the group cost often depends on the cardinality and some aggregate measure of the attributes, such as the sum or the maximum element.

We empirically explore the accuracy of an easily computed approximation for long run, average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. The pointwise stationary approximation is computed by integrating over time (that is taking the expectation of) the formula for the stationary performance measure with the arrival rate that applies at each point in time.

Monetary models based on cash-in-advance constraints make strong predictions about the stochastic properties of endogeneous variables such as the velocity of circulation of money, the rate of inflation, and real and nominal interest rates. We develop numerical methods to understand these predictions because the models cannot be characterized analytically. We calibrate some cash-in-advance models using driving processes estimated from U. S. time-series data to generate model predictions that are compared to sample statistics.

A conceptual model is developed that describes the relationships among consumer values, utility, and ownership of durables. These relationships are tested empirically using data on a variety of discretionary durables collected from a sample of 735 adults. Results support the model structure and suggest that augmenting the List of Values (Kahle 1983) with a measure of materialism improves prediction of value-related consumer behavior.