This paper introduces delta-continuous functions in interval-valued neutrosophic soft topological spaces and investigates their fundamental properties. Additionally, delta-irresolute functions are introduced within the same framework. The relationships between these functions and existing function classes are explored. Several theorems, accompanied by illustrative examples, are provided to support the theoretical findings. The study also includes an application of the proposed concepts to distance and similarity measures.
We consider a queueing system that utilizes a single server to manage product flow through bulk and overload service modes, depending on queue length. Balking occurs when the queue length reaches 'N'. After completion of service, products undergo quality inspection, with defective products sent for rework based on specific probabilities. If the product is non-defective, the server continues processing until the queue length exceeds a certain threshold; beyond this point, the server is either routed back to bulk service or directed to an overload service. Also, the server goes into a vacation mode when the queue size is below a certain limit to ensure that resources are well utilized. Through steady-state analysis using the supplementary variable technique, key performance metrics and stability conditions were determined. Cost functions are established for the concerned model. The results, supported by illustrative numerical data, shed light on the effectiveness of the proposed model.
To analyze a bulk queueing system with server-controlled admission for reservice, low-batch service, multiple vacation and set-up time. The study explores how the server dynamically adjusts between low-batch and bulk services based on the queue size. After completing a bulk service, the departing batch may request reservice with a certain probability. However, accepting the request is not mandatory, and the server admits it with some probability. Whenever the queue becomes empty, whether after reservicing, completing service with no reservice request, or ending the low-batch service, the server enters a random-length vacation. If the queue still has less than 'a' customers after the vacation, the server goes on another vacation. This will continue until at least 'a' customers are waiting. Once the vacation is over, if there are at least 'a' customers, the server requires set-up time to restart service. The probability-generating function (PGF) is derived using the SVT and LST techniques to obtain the steady-state solution. Key performance metrics of the queueing model are analyzed for various server states by leveraging the properties of the probability-generating function. The proposed model provides insights into server behavior, facilitating the reduction of queue length, waiting time, busy period, and TAC while enhancing idle time in a bulk queueing system.
In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and accurate. The method is then used to sample from diffusions whose transition densities are unknown in closed form. This work has its applications in population genetics; accordingly, we sample paths of the Wright-Fisher diffusions that have a bounded drift.
This paper introduces a new stationary first-order autoregressive integer-valued process with a marginal distribution following the New Discrete Lindley distribution, referred to as NDL-INAR(1). The process is developed to model over-dispersed count time series exhibiting a mixed behavior arising from the combination of multiple distributions. Its statistical properties are thoroughly investigated, and the parameters are estimated using conditional maximum likelihood. The asymptotic properties of the estimators are also analyzed. The performance of the proposed model is evaluated by comparing it with other existing INAR(1) processes through applications to real datasets. Results demonstrate that the NDL-INAR(1) process effectively captures the characteristics of over-dispersed time series and provides improved predictive accuracy in comparison with alternative models. The study highlights the flexibility and applicability of the NDL-INAR(1) process for practical time series modeling of count data in various fields.
