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Many queueing systems can be modelled as two-dimensional random walks with reflective boundaries, discrete, continuous or mixed. Stationary probabilities are one of the most sought after statistical quantities in queueing analysis. However, explicit expressions are only available for a very limited number of models. Therefore, tail asymptotic properties become more important, since they provide insightful information on the structure of the tail probabilities, and often lead to approximations, performance bounds, algorithms, among possible other applications. In this survey, we provide key ideas of a kernel method, developed from the classical kernel method in analytic combinatorics, for studying so-called exact tail asymptotic properties in stationary probabilities for this type of random walk.

In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the N-policy under two information levels, respectively, are investigated. We assume that there is no waiting area in front of the server and an arriving customer is served immediately if the server is idle; otherwise (the server is either busy or on a vacation) it has to leave the system to join a virtual retrial orbit waiting for retrials according to the FCFS rules. After a service completion, if the system is not empty, the server becomes idle, available for serving the next customer, either a new arrival or a retried customer from the virtual retrial orbit; otherwise (if the system is empty), the server starts a vacation. Upon the completion of a vacation, the server is reactivated only if it finds at least N customers in the virtual orbit; otherwise, the server continues another vacation. We study this model at two levels of information, respectively. For each level of information, we obtain both equilibrium and optimal balking strategies of customers, and make corresponding numerical comparisons. Through Particle Swarm Optimization (PSO) algorithm, we explore the impact of parameters on the equilibrium and social optimal thresholds, and obtain the trend in changes, as a function of system parameters, for the optimal social welfare, which provides guiding significance for social planners. Finally, by comparing the social welfare under two information levels, we find that whether the system information should be disclosed to customers depends on how to maintain the growth of social welfare.

In the literature, retrial queues with batch arrivals and heavy-tailed service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The equivalence theorem provides the distribution (or tail) equivalence between the total number of customers in the system for the retrial queue and the total number of customers in the corresponding standard (non-retrial) queue. In this paper, under the assumption of regularly varying tails, we eliminate this condition by allowing that the service time can be either heavier or lighter than the batch size. The main contribution made in this paper is an asymptotic characterization of the difference between two tail probabilities: the probability of the total number of customers in the system for the MX/G/1 retrial queue and the probability of the total number of customers in the corresponding standard (non-retrial) queue.

Background The Chinese native Diqing Tibetan pig has a long history of domestication and is distributed in the southernmost region of China compared to other Tibetan breeds. In this study, we performed whole-genome sequencing of the Diqing Tibetan pigs. By integrating previously published data, we explored the genetic structure, population diversity, and genetic introgression from commercial European pigs and Southern Chinese domestic pigs into Diqing Tibetan pigs. We further examined the potential genetic influences of European pig introgression and inferred the historical events of admixture with Southern Chinese breeds. Results Our analysis revealed various instances of population admixture between Diqing Tibetan pigs and European pigs, as well as redundant introgression from South Chinese pigs when compared to other Tibetan pig populations. The introgression from European pigs significantly increased the population diversity in Diqing Tibetan pigs, which may influence fertility. Additionally, the introgression from European pigs affected the proportion of introgression from Southern Chinese pigs, with the most pronounced effect near the PSCK2 gene, which is associated with body size. Regarding ancestral genetic components from Southern Chinese pigs, we discovered a significant level of redundant proportion in Diqing Tibetan pigs compared to other Tibetan breeds. This admixture may have occurred at multiple time points from different breeds, with the Diannan small ear breed in Yunnan Province of China potentially serving as a recent primary contributor to the introgression into Diqing Tibetan breed. Conclusion Our study reveals that the Diqing Tibetan breed has been shaped by admixture from European and multiple Southern Chinese sources, where European introgression increased diversity and reshaped Southern ancestry, while Southern introgression itself derives from distinct Southern Chinese pig breeds.

Egg-laying performance is of great economic importance in poultry, but the underlying genetic mechanisms are still elusive. In this work, we conduct a multi-omics and multi-tissue integrative study in hens with distinct egg production, to detect the hub candidate genes and construct hub molecular networks contributing to egg-laying phenotypic differences. We identifiy three hub candidate genes as egg-laying facilitators: TFPI2 , which promotes the GnRH secretion in hypothalamic neuron cells; CAMK2D , which promotes the FSHβ and LHβ secretion in pituitary cells; and OSTN , which promotes granulosa cell proliferation and the synthesis of sex steroid hormones. We reveal key endocrine factors involving egg production by inter-tissue crosstalk analysis, and demonstrate that both a hepatokine, APOA4, and an adipokine, ANGPTL2, could increase egg production by inter-tissue communication with hypothalamic-pituitary-ovarian axis. Together, These results reveal the molecular mechanisms of multi-tissue coordinative regulation of chicken egg-laying performance and provide key insights to avian reproductive regulation. Egg-laying performance is an important phenotype for breeding chicken. Here, the authors explore the regulatory networks driving phenotypic differences in egg-laying, and identify laying-related variants and endocrine factors.

Background Genetic resources are essential components of biodiversity. As national strategy, the conservation of genetic resources is crucial not only for biodiversity but also for sustainable agriculture and cultural heritage. However, the exact origin of most local breeds remains unclear at the genomic level. The conservation efforts are becoming more challenging as local breeds are currently experiencing genetic drift and admixture, which may be further complicated by historical hybridizations. A typical example is the Beijing-You chicken, a local breed renowned for its excellent meat flavor and unique appearance. With a relatively recent history (~ 300 years), it displays mixed phenotypes which may have resulted from genomic admixture, with its exact origin yet to be determined. Results Through comprehensive genomic similarity analysis, we identified 12 genetic donor breeds for the Beijing-You chicken and quantified their genetic contributions, with the highest ancestry proportion coming from Henan chickens. The local ancestry components and genomic structure analyses of the Beijing-You chicken suggest recent hybridization in the formation of this breed. Furthermore, we innovatively used ancestry components as new material for genetic evaluation and selection signature detection, demonstrating that conservation efforts over the past decade have been effective. Analysis of selection signatures revealed genes and regions associated with polydactyly, egg production, intramuscular fat, and spermatogenesis. Conclusions By integrating various analytical strategies, we developed a novel framework for genetic traceability and evaluation. Our results highlight the effectiveness of ancestry components in genetic assessment and offer valuable insights for the conservation, improvement, and sustainable utilization of local breeds.

Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: retrial queueing systems with priority. This type of queueing system is important in various applications, including telecommunication and computer management networks with big data. The system considered here receives two types of customers, of which Type-1 customers (in a queue) have non-pre-emptive priority to receive service over Type-2 customers (in an orbit). For this type of system, we propose an exhaustive version of the stochastic decomposition approach, which is one of the main contributions made in this paper, for the purpose of studying asymptotic behaviour of the tail probability of the number of customers in the steady state for this retrial queue with two types of customers. Under the assumption that the service times of Type-1 customers have a regularly varying tail and the service times of Type-2 customers have a tail lighter than Type-1 customers, we obtain tail asymptotic properties for the numbers of customers in the queue and in the orbit, respectively, conditioning on the server’s status, in terms of the exhaustive stochastic decomposition results. These tail asymptotic results are new, which is another main contribution made in this paper. Tail asymptotic properties are very important, not only on their own merits but also often as key tools for approximating performance metrics and constructing numerical algorithms.

A system of interacting multi-class finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-color nodes. The interactions are local and described through local empirical measures. Two levels of heterogeneity are considered: between and within the blocks where the nodes are labeled into two types. The central nodes are those connected only to nodes from the same block, whereas the peripheral nodes are connected to both nodes from the same block and nodes from other blocks. Limits of such systems as the number of nodes tends to infinity are investigated. In particular, under specific regularity conditions, propagation of chaos and the law of large numbers are established in a multi-population setting. Moreover, it is shown that, as the number of nodes goes to infinity, the behavior of the system can be represented by the solution of a McKean–Vlasov system. Then, we prove large deviations principles for the vectors of empirical measures and the empirical processes, which extends the classical results of Dawson and Gärtner (Stochastics 20, 1987) and Léonard (Ann. Inst. H. Poincaré Prob. Statist. 31, 1995).