Performance evaluation of a discrete-time Geo[X]/G/1 retrial queue with general retrial times

AbstractWe consider a discrete-time Geo[X]/G/1 retrial queue with general retrial times. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. The present model is proved to have a stochastic decomposition law. Hence, a measure of the proximity between the distributions of the system size in the present model and the corresponding one without retrials is derived. A set of numerical results is presented with a focus on the effect of batch arrivals and general retrial times on the system performance. It appears that it is the mean batch size (and not the batch size distribution) that has the main effect on the system performance. Moreover, increasing the mean batch size is shown to have a noticeable effect on the size of the stability region. Finally, geometric retrial times are shown to have an overall better performance compared with two other distributions

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Estimating the minimum delay optimal cycle length based on a time-dependent delay formula

For fixed time traffic signal control, the well-known Webster’s formula is widely used to estimate the minimum delay optimal cycle length. However, this formula overestimates the cycle length for high degrees of saturation. In this paper, we propose two regression formulas for estimating the minimum delay optimal cycle length based on a time-dependent delay formula as used in the Canadian Capacity Guide and the Highway Capacity Manual (HCM). For this purpose, we develop a search algorithm to determine the minimum delay optimal cycle length required for the regression analysis. Numerical results show that the proposed formulas give a better estimation for the optimal cycle length at high intersection flow ratios compared to Webster’s formula

Hybrid feedback-based access scheme for cognitive radio systems

[abstract not available

Reactive spectrum handoff combined with random target channel selection in cognitive radio networks with prioritized secondary users

Cognitive radio aims at improving spectrum utilization by allowing secondary users to access primary user’s spectrum. The delay time of secondary users due to multiple interruptions from primary users is considered a crucial issue. In this work, to reduce secondary user delay time, we propose a mixed preemptive/non-preemptive resume priority model where secondary user priority increases with each interruption by the primary user. We consider reactive spectrum handoff combined with random target channel selection for the case of all-busy channels. We derive closed form expressions of the average cumulative delay time and the extended data delivery time for each secondary user class. Numerical results show that the proposed approach reduces the secondary user delay time per class compared to other models in case of light loaded networks. Keywords: Cognitive radio, Spectrum handoff, Queueing theory, Priority scheme