THE JOINT ARRIVAL AND DEPARTURE PROCESS FOR THE M/M/l QUEUE

We consider the M/M/1-queue and derive an explicit expression for the joint distribution of the number of arrivals and the number of departures in [0, t), given the number of customers initially present. The derivation is almost purely combinatorial, it avoids the use of generating functions, and immediately yields a simple probabilistic interpretation of the result.     

Exact finite sample properties of double k-class estimators in simultaneous equations

In our earlier paper [Srivastava, Agnihotri and Dwivedi (1980)] the dominance of double k-class over k-class with respect to exact mean squared error matrix criteria is established. It is observed that given a member of k-class, one can pick up a member of double k-class that will provide an improved estimator of the coefficients. This result prompted us to study the exact finite sample properties of the double k-class estimator. For this, we have considered a structural equation containing two endogenous variables and have investigated the properties of double k-class estimators of the coefficients of explanatory endogenous variables assuming characterizing scalars to be non-stochastic.     

Productive behavior through the life course: An essay on the quality of life

Present patterns of productive activity are neither well recognized, optimal for society, nor in accordance with individual prefence. Although a great deal of attention has been given to meeting people's needs for income, medical care, and other services, the quality of their lives must also be defined by what they do for themselves and for others. In discovering present patterns of productive activity throughout the life course and optimizing those patterns, we will raise the quality of American life. To accomplish this task, two great changes are needed: we must recognize the full range of productive activities throughout the life course and give people the opportunity to modify the allocation of paid employment.     

Unionism and the public sector

It is incorrect and misleading to speak of unionization as a ‘human right’. The only human right is ‘self-ownership’, i.e. to pursue goals with one's own abilities but with no force or fraud against others. Government cannot dispense rights, only privileges and protections to some at the expense of others. A minimal degree of coercion exercised by government is unavoidable. But labor unions are not governments. Government has granted significant privileges to unions in the private sector, but such are not appropriate for public sector unions.     

Improving perishable product inventory management using goal programming

The multiple objectives of perishable product inventory management are examined in this paper. These objectives include: (1) satisfying demand by carrying sufficient inventories, (2) holding down inventory carrying costs, (3) keeping the amount of product spoilage (outdating) at an acceptable level, and (4) maintaining quality by using the product while it is still fresh, and (5) keeping the cost of rotation low. Some of the above objectives are in conflict. Thus, certain redistribution policies may help attain one or more of these objectives to a greater extent. Redistribution involves the transfer of the product from outlets where demand is low to outlets where demand is high. A goal programming model for solving redistribution problems is presented. An example is provided and sensitivity analysis is performed in order to determine when redistribution is advantageous. Applicability of the model is discussed.     

The entropies: Some roots of ambiguity

Entropy concepts have developed in four general contexts—thermodynamics, communication theory, statistical information theory and social and life sciences. These concepts have five distinct mathematical forms. Ambiguity and complexity in utilization of the concept has been heightened by this multi-faceted heritage. Effective utilization may be strengthened by a sharper articulation of entropy through combinations of literal, mathematical and graphical modes of expression. Geography and planning as user disciplines have important responsibilities in enhancing cross-disciplinary communication of this important adisciplinary concept. Implications of these arguments for the social sciences include the need for caution in drawing social analogies from the ambiguous entropy concepts of statistical mechanics; and an indication of the potential benefits of social science models based on the unambiguous entropic constructs of statistical information theory.     

Localized externalities,contagious processes and the deterioration of urban housing: An empirical analysis

Housing deterioration can develop in spatial-temporal patterns which are compatible with the operation of localized externalities if deteriorated structures exert negative effects on the condition of nearby structures or if structures are affected by unfavorable conditions which are endemic to entire neighborhoods. The pattern of housing deterioration in space and time is examined, using a time series of housing condemnations for Indianapolis. A non-linear logit model with a spatial-temporal lag structure is used to analyze the association between the occurence of new condemnations and the location of existing condemned structures. The model predicts the probability that a housing condemnation occurs within a given time period as a function of the numbers of condemned structures in the same area and adjoining areas at the beginning of the time period. The size of the areas is flexible and an appropriate scale for the process is identified by varying the size of the areas.     

Analytic derivation of sociometric dimensions

Dimensional analysis has been defined variously as the synthesis of dimensionless variables and as a way of spatially representing data. While in sociometrics, one may not be able to devise models resembling those of the physical sciences because of the complexity of many social situations, one may in some cases successfully apply the techniques of classic dimensional analysis and get empirically valid results. More often we derive with analytic methods from the social sciences different kinds of dimensional frameworks in which to represent data. This paper will compare these approaches to the study of relationships and give examples of where each might be appropriate. Finally, a classification of the analytical methods will be presented.