Recent papers have shown that Π∞k = 1 P(k) = limm→∞ (P(m) ... P(1)) exists whenever the sequence of stochastic matrices {P(k)}∞k = 1 exhibits convergence to an aperiodic matrix P with a single subchain (closed, irreducible set of states). We show how the limit matrix depends upon P(1).
For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation.
We examine the relative effects of several service order disciplines on important operating characteristics of queues in which customers request a random number of servers. This class of queues is characterized by customers who cannot begin service until all required servers are available. We show that for many systems in this class, it is possible to define a new service order disciplien which is more efficient than FIFO with respect to one or more measures such as expected waiting time, probability of delay, etc.
Subjects at four age levels (kindergarten, fourth grade, eighth grade, and college) made preference judgments for a set of consumer products varying on four dimensions. Though product preferences reflected independently assessed dimension ratings, subjects had preferences on more dimensions than they took into account in the product ratings. Not until late adolescence did subjects integrate their preferences on two or more dimensions.
Several propositions concerning the effect of individual, product class, and task-related factors on information-acquisition strategies were formulated and tested. Marked differences were found for subjects at different socioeconomic levels. A new scheme for analyzing information-acquisition sequence data was developed and employed.
We consider the Policy Iteration Algorithm for undiscounted Markov Renewal Programs. Previous specifications of the policy evaluation part of this algorithm all required the analysis of the chain structure for each policy generated. The purpose of this paper is to provide a unique specification of the value sectors as well as an anticycling rule which avoids parsing the transition probability matrices into their subchains.
This paper considers two-person zero-sum sequential games with finite state and action spaces. We consider the pair of functional equations (f.e.) that arises in the undiscounted infinite stage model, and show that a certain class of successive approximation schemes is guaranteed to converge to a solution pair whenever an equilibrium policy with respect to the average return per unit time criterion (AEP) exists. Existence of the latter thus implies the existence of a solution to this pair of f.e. whereas the converse implication is shown only to hold under special circumstances.
This paper examines the hypothesis that the expected rate of return to speculation in the forward foreign exchange market is zero; that is, the logarithm of the forward exchange rate is the market's conditional expectation of the logarithm of the future spot rate. A new computationally tractable econometric methodology for examining restrictions on a k-step-ahead forecasting equation is employed. Using data sampled more finely than the forecast interval, we are able to reject the simple market efficiency hypothesis for exchange rates from the 1970s and the 1920s.