Methodology and Computing in Applied Probability最新文献

For a one-dimensional Wiener process with stochastic resetting (mathcal{X}(t)), obtained from an underlying Wiener process X(t), we study the statistical properties of its first-passage time through zero, when starting from (X>0,) and its first-passage area, that is the random area enclosed between the time axis and the path of the process (mathcal{X} (t)) up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.

An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the population paradox occurs when the population of a state increases but its allocated number of seats decreases. The Balinski-Young impossibility theorem showed that there is no deterministic apportionment method that can avoid the violation of the quota rule and doesn’t have both the Alabama and the population paradoxes. In this paper, we propose a randomized apportionment method as a stochastic solution to the Balinski-Young impossibility.

On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.

Waiting is a major factor influencing the perception of delay-sensitive customers in the service industry. In the process of queueing, some customers often have a psychological expectation of waiting time in the face of uncertain delay information, so that customer service utility depends not only on the actual waiting time, but also on the relative amount of the actual waiting time and the psychological expectation of waiting time. Therefore, this paper investigates how the reference time effect affects heterogeneous customers' queueing decisions and service system efficiency measures (system throughput and social welfare) in an M/G/1 queue with limited service resources and capacity. The results show that the equilibrium joining probability of customers, the system throughput and social welfare are relatively higher as the proportion of customers with high tolerance levels in the queue increases. In addition, the maintenance of customer homogeneity is better for the improvement of service resource utilization, while the maintenance of customer heterogeneity is better for social welfare. As the psychological expected waiting time increases, the equilibrium joining probability of potential customers and the system throughput increase, while the equilibrium joining probability of existing customers decreases, and the social welfare shows a non-monotonic trend of first decreasing and then increasing. The equilibrium queueing strategies for each type of customer and the service system efficiency measures are not monotonic with the change of the reference time effect parameter. Finally, the optimal social welfare is increasing with respect to the degree of reference time effect and the psychological expectation of waiting time.