Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

Mitochondrial DAMPs Increase Endothelial Permeability through Neutrophil Dependent and Independent Pathways

Trauma and sepsis can cause acute lung injury (ALI) and Acute Respiratory Distress Syndrome (ARDS) in part by triggering neutrophil (PMN)-mediated increases in endothelial cell (EC) permeability. We had shown that mitochondrial (mt) damage-associated molecular patterns (DAMPs) appear in the blood after injury or shock and activate human PMN. So we now hypothesized that mitochondrial DAMPs (MTD) like mitochondrial DNA (mtDNA) and peptides might play a role in increased EC permeability during systemic inflammation and proceeded to evaluate the underlying mechanisms. MtDNA induced changes in EC permeability occurred in two phases: a brief, PMN-independent ‘spike’ in permeability was followed by a prolonged PMN-dependent increase in permeability. Fragmented mitochondria (MTD) caused PMN-independent increase in EC permeability that were abolished with protease treatment. Exposure to mtDNA caused PMN-EC adherence by activating expression of adherence molecule expression in both cell types. Cellular activation was manifested as an increase in PMN calcium flux and EC MAPK phosphorylation. Permeability and PMN adherence were attenuated by endosomal TLR inhibitors. EC lacked formyl peptide receptors but were nonetheless activated by mt-proteins, showing that non-formylated mt-protein DAMPs can activate EC. Mitochondrial DAMPs can be released into the circulation by many processes that cause cell injury and lead to pathologic endothelial permeability. We show here that mitochondria contain multiple DAMP motifs that can act on EC and/or PMN via multiple pathways. This can enhance PMN adherence to EC, activate PMN-EC interactions and subsequently increase systemic endothelial permeability. Mitochondrial DAMPs may be important therapeutic targets in conditions where inflammation pathologically increases endothelial permeability

Relating the Seemingly Unrelated: Principled Understanding of Generalization for Generative Models in Arithmetic Reasoning Tasks

Large language models (LLMs) have demonstrated impressive versatility across numerous tasks, yet their generalization capabilities remain poorly understood. To investigate these behaviors, arithmetic tasks serve as important venues. In previous studies, seemingly unrelated mysteries still exist -- (1) models with appropriate positional embeddings can correctly perform longer unseen arithmetic operations such as addition, but their effectiveness varies in more complex tasks like multiplication; (2) models perform well for longer unseen cases in modular addition under specific moduli (e.g., modulo 100) but struggle under very close moduli (e.g., modulo 101), regardless of the positional encoding used. We believe previous studies have been treating the symptoms rather than addressing the root cause -- they have paid excessive attention to improving model components, while overlooking the differences in task properties that may be the real drivers. This is confirmed by our unified theoretical framework for different arithmetic scenarios. For example, unlike multiplication, the digital addition task has the property of translation invariance which naturally aligns with the relative positional encoding, and this combination leads to successful generalization of addition to unseen longer domains. The discrepancy in operations modulo 100 and 101 arises from the base. Modulo 100, unlike 101, is compatible with the decimal system (base 10), such that unseen information in digits beyond the units digit and the tens digit is actually not needed for the task. Extensive experiments with GPT-like models validate our theoretical predictions. These findings deepen our understanding of the generalization mechanisms, and facilitate more data-efficient model training and objective-oriented AI alignment

1,4-Bis[(2-ethyl-1H-benzimidazol-1-yl)meth­yl]benzene

In the title mol­ecule, C26H26N4, the central benzene ring forms dihedral angles of 89.9 (2) and 85.4 (2)° with the two benzimidazole rings