We consider a priority queueing system where a single processor serves k classes of packets that are generated randomly following Poisson processes. Our objective is to compute the expected Peak Age of Information (PAoI) under various scenarios. In particular, we consider two situations where the buffer size at each queue is one and infinite, and in the infinite buffer size case we consider First Come First Serve (FCFS) and Last Come First Serve (LCFS) as service disciplines. For the system with buffer size one at each queue, we derive PAoI exactly for the case of exponential service time and bounds (which are excellent approximations) for the case of general service time, with small k. For the system with infinite buffer size, we provide closed-form expressions of PAoI for both FCFS and LCFS where service time is general and k could be large. Using those results we investigated the effect of ordering of priorities and service disciplines for the various scenarios. We perform extensive numerical studies to validate our results and develop insights. Keywords— Age of Information, Priority Queues, Performance Analysis.

Whether government‐based forms of food assistance such as theSupplementalNutritionAssistanceProgram (SNAP), communal efforts including food pantries, aid from friends and family, or alternative means such as gardening are the appropriate means to reduce the prevalence of household food insecurity is a continuous source of policy contention. To inform this debate, we examine the relative importance of these forms of food assistance and acquisition to a sample ofU.S. older adults from the 2010BrazosValleyHealth Assessment of centralTexas households that have been stratified by income eligibility forSNAP, low‐incomeSNAPineligibility, and above low income status. To identify how membership in these socioeconomic groups constrains household capacity to acquire sufficient food to maintain an adequate and healthy diet, we explore the varied associations of assets received from government; communal and intimate social networks; and alternative food sources such as gardening, hunting, and fishing with household food security across socioeconomic status, while examining the importance of place of residence on the use of capital assets.SNAPparticipation was the only specific capital asset associated with all levels of food insecurity for bothSNAP‐eligible and ineligible low‐income groups, thus emphasizing the continued importance of food assistance among poverty‐level older adults.

Many countries have implemented different carbon reduction policies to achieve carbon neutrality in the current century. As one of the popular policies, the cap-and-trade policy provides carbon emission quotas for power generation companies. Each company must carefully determine its energy production based on the carbon emission quota and renewable uncertainty. This paper analyzes the cooperation among different power generation companies using the coalitional game theory. Power generation companies can form a union to share the total carbon emission quotas to maximize their total profit. We show the optimality of the grand coalition by proving that the profit function is superadditive. This result highlights the benefits of cooperation. Besides, we propose a profit allocation mechanism that allocates the total profit to different power generation companies. Furthermore, we prove that the proposed profit allocation mechanism is in the core of the coalitional game such that no group of power generation companies has any incentives to leave the grand coalition. We design a smart contract to enable power generation companies to form a coalition. We further implement the smart contract on the Ethereum platform to validate its effectiveness. Numerical studies have been conducted to validate the established theoretical results.

In this research, we study the information freshness in M/G/1 queueing system with a single buffer and the server taking multiple vacations. This system has wide applications in communication systems. We aim to evaluate the information freshness in this system with both i.i.d. and non-i.i.d. vacations under three different scheduling policies, namely Conventional Buffer System (CBS), Buffer Relaxation System (BRS), and Conventional Buffer System with Preemption in Service (CBS-P). For the systems with i.i.d. vacations, we derive the closed-form expressions of information freshness metrics such as the expected Age of Information (AoI), the expected Peak Age of Information (PAoI), and the variance of peak age under each policy. For systems with non-i.i.d. vacations, we use the polling system as an example and provide the closed-form expression of its PAoI under each policy. We explore the conditions under which one of these policies has advantages over the others for each information freshness metric. We further perform numerical studies to validate our results and develop insights.