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The purpose of this paper is to provide delay announcements for call centers with hyperexponential patience modeling. The paper aims to employ a state-dependent Markovian approximation for informing arriving customers about anticipated delay in a real call center.

Motivated by real call center data, the patience distribution is modeled by the hyperexponential distribution and is analyzed by its realistic significance, with and without delay information. Appropriate M/M/s/r+H₂ queueing model is structured, including a voice response system that is employed in practice, and a state-dependent Markovian approximation is applied for computing abandonment. Based on this approximation, a method is proposed for estimating virtual delays, and it is investigated about the problem of announcing virtual delays to customers upon their arrival.

There are two parts of findings from the results obtained from the case study and a numerical study of simulation comparisons. First, using an H₂ distribution for the abandonment distribution is driven by an empirical study which shows its good fit to real-life call center data. Second, simulation experiments indicate that the model and approximation are reasonable, and the state-dependent Markovian approximation works very well for call centers with larger pooling. It is concluded that our approach can be applied in a voice response system of real call centers.

Many results pertain to announcing delay information, customer reactions and links to estimating hyperexponential distribution based on real data that have not been established in previous studies; however, this paper analytically characterizes these performance measures for delay announcements.

In this article, the elementary notions and aggregation operations of single-valued neutrosophic parameterized complex fuzzy hypersoft set (sv-NPCFHSS) are characterized initially. Then by using matrix version of sv-NPCFHSS, a decision-support system is constructed for the evaluation of real estate residential projects by observing various risk factors.

Two approaches are utilized in this research: set-theoretic approach and algorithmic approach. The first approach is used to investigate the notions of sv-NPCFHSS and its some aggregations whereas the second approach is used to propose an algorithm for designing its decision-support system by using the aggregation operations like reduced fuzzy matrix, decision matrix, etc. of sv-NPCFHSS. The adopted algorithm is validated in real estate scenario for the selection of residential project by observing various risk factors to avoid any expected investment loss.

The proposed approach is more flexible and reliable as it copes with the shortcomings of literature on sv-neutrosophic set, sv-neutrosophic soft set and other fuzzy soft set-like structures by considering hypersoft setting, complex setting and neutrosophic setting collectively.

It has limitations for complex intuitionistic fuzzy hypersoft set, complex neutrosophic hypersoft set and other complex neutrosophic hypersoft set-like models.

The scope of this research may cover a wide range of applications in several fields of mathematical sciences like artificial intelligence, optimization, MCDM, theoretical computer science, soft computing, mathematical statistics etc.

The proposed model bears the characteristics of most of the relevant existing fuzzy soft set-like models collectively and fulfills their limitations.