Priority Queue

THEOPHILUS AGAMA A. An addition chain of length h that leads to a number n is a sequence of positive integers s_0 = 1, s_1 = 2,. .. , s_h = n such that s_i = s_j + s_k (i > j ≥ k) for each 1 ≤ i ≤ h. A Brauer addition chain is the one where j = i-1 for each 1 ≤ i ≤ h. Let l(•) and l* (•) denote the minimal length of an addition chain and the Brauer addition chain, respectively, that leads to an integer •. Applying probabilistic methods to the iterated factor method, we show that l(2 n-1) ≤ n-1 + l(n) for almost all positive integers n as n-→ ∞.

We continue the renormalized-tail program initiated in \cite{AbuGhuwaleh2026}. For an analytic power series

\[

f(z)=\sum_{n\ge 0} a_n z^n, \qquad a_n
eq 0,

\]

the normalized Taylor tails

\[

T_n^f(w):=\sum_{k\ge 0}\frac{a_{n+k}}{a_n}w^k

\]

form the renormalization orbit studied in \cite{AbuGhuwaleh2026}. That paper established the universal geometric limit profile and the first two asymptotic fingerprints of the orbit. Here we prove the full higher-order hierarchy. Assuming

\[

\frac{a_{n+1}}{a_n}=\rho\left(1+\frac{\beta_1}{n}+\frac{\beta_2}{n^2}+\cdots+\frac{\beta_m}{n^m}+\cO(n^{-m-\eta})\right),

\qquad \rho\in\C^\times,\ \eta>0,

\]

we show that for every fixed $s\in(0,1)$,

\[

T_n^f(w)=\frac{1}{1-\rho w}+\sum_{j=1}^m \frac{P_j(\rho w;\beta_1,\dots,\beta_j)}{n^j}+o(n^{-m})

\]

uniformly on $\{|\rho w|\le s\}$. Each $P_j$ is a universal rational function depending only on $(\beta_1,\dots,\beta_j)$, and we give a constructive recursive algorithm for all of them via logarithmic cumulants, Faulhaber sums, and Newton interpolation. The hierarchy is triangular: the coefficient $\beta_j$ is recovered directly from the linear term of $P_j$. In particular, the first two fingerprints from \cite{AbuGhuwaleh2026} are recovered as the cases $m=1,2$, while the higher-order terms are new. We also compute the third and fourth fingerprints explicitly and derive the resulting hierarchy for algebraic singularities.

In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.

Abstract: "Computer systems depend on high priority background processes to provide both reliability and security. This is especially true in multiserver systems where many such background processes are required for data coherence, fault detection, intrusion detection, etc. From a user's perspective, it is important to understand the effect that these many classes of high priority, backround tasks have on the performance of lower priority user-level tasks. We model this situation as an M/GI/k queue with m preemptive-resume priority classes, presenting the first analysis of this system with more than two priority classes under a general phase-type service distribution. (Prior analyses of the M/GI/k with more than two priority classes are approximations that, we show, can be highly inaccurate.) Our analytical method is very different from the prior literature: it combines the technique of dimensionality reduction [10] with Neuts' technique for determining busy periods in ...

The paper we present here introduces a new priority mechanism in discrete-time queueing systems. It is a milder form of priority when compared to HoL priority, but it favors customers of one type over the other when compared to regular FCFS. It also provides an answer to the starvation problem that occurs in HoL priority systems. In this new priority mechanism, customers of different priority classes entering the system during the same time slot are served in order of their respective priority class-hence the name slot-bound priority. Customers entering during different slots are served on an FCFS basis. We consider two customer classes pertaining to two levels of priority such that type-1 customers are served before type-2 customers that enter the system during the same slot. A general independent arrival process and generally distributed service times are assumed. Expressions for the probability generating function PGF of the system content number of type-j customers, j 1, 2 in regime are obtained using a slot-to-slot analysis. The first moments are calculated, as well as an approximation for the probability mass functions associated with the found PGFs. Lastly, some examples allow us some deeper insight into the inner workings of the slot-bound priority mechanism.

In an attempt to meet the stringent time constraints of real time flows, several scheduling algorithms have been proposed in the literature. Among such algorithms, the so-called EDF algorithm is widely known for its optimal management of flows with strict time constraints, when compared with the standard FIFO algorithm. But still, EDF is complex and expensive as far as implementation is concerned. As a main contribution in this paper, we therefore propose a hybrid EDF/FIFO queue management approach, which consists of a short EDF queue completed by a FIFO queue. This approach allows reducing EDF’s implementation complexity while making efficient use of its optimal flow management. Our simulation results underscore the main interest behind this proposal.

Current standards reserve one bit in the ATM cell header to indicate loss priority. When congestion oc- curs ai a queue lower priority cells can be discarded in order to insure a smaller cell loss rate for higher priority cells. Strategies for determining which cells to discard are termed space priority buffer manage- ment schemes. In ihis paper two adjustable

The probability generating function (PGF) of a discrete random variable is a concise way to describe the corresponding probability distribution and facilitate analysis. This paper will revisit and explore certain key properties of the PGFs, focusing on structural properties, moment characterization and stability under convolution. Through applications to distribution generation, branching processes, and queueing models, PGFs are shown to provide clear insight into extinction probabilities and steady-state behavior. The results confirm that probability generating functions provide a coherent and useful framework for both theory and applications in discrete stochastic modelling.

Placement is a critical component of today's physical synthesis flow with tremendous impact on the final performance of VLSI designs. However, it accounts for a significant portion of the overall physical synthesis runtime. With complexity and netlist size of today's VLSI design growing rapidly, clustering for placement can provide an attractive solution to manage affordable placement runtime. Such clustering, however, has to be carefully devised to avoid any adverse impact on the final placement solution quality. In this paper we present a new bottom-up clustering technique, called best-choice, targeted for large-scale placement problems. Our best-choice clustering technique operates directly on a circuit hypergraph and repeatedly clusters the globally best pair of objects. Clustering score manipulation using a priority-queue data structure enables us to identify the best pair of objects whenever clustering is performed. To improve the runtime of priority-queuebased best-choice clustering, we propose a lazy-update technique for faster updates of clustering score with almost no loss of solution quality. We also discuss a number of effective methods for clustering score calculation, balancing cluster sizes, and handling of fixed blocks. The effectiveness of our best-choice clustering methodology is demonstrated by extensive comparisons against other standard clustering techniques such as Edge-Coarsening and First-Choice . All clustering methods are implemented within an industrial placer CPLACE [1] and tested on several industrial benchmarks in a semi-persistent clustering context.

Mobile Ad hoc Network (MANET) is a collection of two or more devices or nodes or terminals with wireless communications and networking capability that communicate with each other without the aid of any centralized administrator a dynamic network consisting of several mobile nodes communicating wirelessly. MANET is an infrastructure less network and each member node is free to move in and out of the network in a random manner. Congestion may occur in any node when data packets travel from source to destination. Controlling congestion is critical to ensure adequate network operation and performance. Due to this mobile nature of the nodes in MANET, the possibility for the network to get congested is high. This may result in isolated nodes and reduced network performance. So in this paper, we proposed to develop a congestion control technique for fault tolerant multicast routing in MANET. In this technique, the congestion probability around the forwarding node is initially estimated and...

The popularity of opportunistic spectrum access (OSA), implemented by cognitive radios (CRs), necessitates that these networks should be able to provide service differentiation for different classes of traffic. One of the classic schemes for such a goal is through priority queueing. As link interruptions in OSA networks are frequent, we discuss in this paper four priority queueing disciplines in the presence of interruptions: preemptive-resume, non-preemptive, exceptional non-preemptive and preemptive in case of occurrence of an interruption. Analytical results, in addition to simulation results to validate their accuracy, are provided.

Although many efficient image cutout approaches have been proposed, it is still a challenge to cut out foreground objects from a video clip because of the costs of time and memory consumption and the difficulty in maintaining temporal coherence for the cutout results. In this paper, we propose a novel and efficient video cutout approach by extending a multilevel banded image segmentation method to video cutout. In our method, the segmentation results are propagated frame by frame at the lowest resolution level based on optical flow, and are refined in image pyramids level by level through banded graph cuts. We construct an adaptive narrow band to ensure that the segmentation result falls exactly into the narrow band during propagation. Experimental results show that the video cutout approach based on adaptive multilevel bands dramatically reduces time and memory costs, and achieves ideal segmentation results. Chen M G, Sui B C, Gao Y, et al. Efficient video cutout based on adaptive multilevel banded method.

In this paper, we analyze a two-class single-server preemptive priority queueing system with restricted number of priority customers and catastrophes. The arrivals per class follow the Poisson process with exponentially distributed service times. Customers are served on a first-come, first-served basis within their queue. Explicit expressions for the mean queue length and the joint distribution are derived in the steady-state case for the number of high and low priority customers in the system. The analysis is based on the generating function technique. Also, we study the impact of catastrophe on the system and other performance measures.

Research on the performance of implicit k-heaps has shown that aligning data with cache lines and increasing heap arity are effective techniques for improving the data reference locality of heap operations. The technique of tree blocking has long been used to enhance the data reference locality of tree-based search methods. In this paper we propose c-clustered tree blocking, a new tree blocking method designed to further enhance the data reference locality of implicit k-heap operations. We examine the effect of our method on the performance of a traditional aligned implicit 2-heap using internal memory benchmarks based on the Hold model. Our empirical results, reproduced on four contemporary architectures, show that our method produces speedups of up to 2.0 in either benchmark, while reducing data cache misses by up to 85% and TLB misses by up to 65%. For larger heap arities our method matches the performance of traditional implicit k-heaps while improving page level locality.

Recently, the increasing demand to transfer data through the Internet has pushed the Internet infrastructure to the final edge of the ability of these networks. This high demand causes a deficiency of rapid response to emergencies and disasters to control or reduce the devastating effects of these disasters. As one of the main cornerstones to address the data traffic forwarding issue, the Internet networks need to impose the highest priority on the special networks: Security, Health, and Emergency (SHE) data traffic. These networks work in closed and private domains to serve a group of users for specific tasks. Our novel proposed network flow priority management based on ML and SDN fulfills high control to give the required flow priority to SHE data traffic. The proposal relies on selected header bits from the traffic class field of a packet using the ML to prioritize traffic flows according to the precedence levels by governing the Differentiated Services Code Point (DSCP) bits in keeping with network administrator policies. The proposed network has been evaluated and performed utilizing the MATLAB platform and the Mininet simulator. The results of extensive testing show enhancement by applying our forcing priority algorithm obtained an efficient reduction in queuing delay and lost packets. The average waiting time in queue was reduced by around 61%, and the lost packets hit 0.005% when adopting the SDN-based ML network traffic priority management. warded within packets that pass over Internet infrastructures. 46 SHE networks can exist in two structures: Based stationary 47 infrastructures and Non-stationary infrastructure networks. 48 The stationary infrastructure depends on a fixed groundwork, 49 where links route the data traffic to a base station within 50 predefined paths. It is relatively expensive and cannot be 51 applied in hostile conditions such as proactive catastrophes 52 handling applications (abnormal weather forecasting, earth 53 quacks, volcano). While, the non-stationary network does not 54 depend on fixed network devices, i.e., wireless infrastruc-55 ture networks such as Ad-hoc, security, and health networks. 56 These networks rely on a closed domain structure where the 57 users can only communicate efficiently within this domain. 58 In the case of failure of the non-stationary networks, they 59 could use the Internet links to deliver information but without 60 high priority for their data traffic. To solve the issue of the pri-61 ority of data forwarding over Internet links; this data should 62 take the highest priority by network devices for emergency 63 routing. 64 Our contribution aims to enhance packets traffic forward-65 ing based on SDN and ML in case of failure of the SHE net-66 work through the Internet. We propose novel traffic priority 67 management, the novelty of our proposal relies on selecting 68 specific header bits from the traffic class field rather than 69 checking the whole header bits (320bit). Selecting header 70 bits depends on which one of SHE traffic should be with 71 the highest priority. Controlling the differentiated service and 72 assured forwarding bits in a packet header field forces desired 73 priority for specific traffic. The proposal relies on selected 74 header bits from the traffic class field of a packet using the 75 ML to prioritize traffic flows according to the precedence 76 levels by governing the Differentiated Services Code Point 77 (DSCP) bits in keeping with network administrator policies. 78 The traffic management based on selected bit shows improve-79 ments in several aspects, such as processing time delay, con-80 suming power, and reducing the burden on the server. The rest 81 of the paper is organized as background and related works 82 in section II, the proposed network is described in section 83 III. The SDN controller and the OpenFlow Switch (OFS) are 84 exhibited in section IV, in section V, forced flow priority 85 control is presented. Simulation and performance evaluation 86 are explained in section VI. 87 II. BACKGROUND AND RELATED WORKS 88 In the last two decades, numerous study institutes focused 89 on in-depth research on packet engineering for different net-90 work technologies and topologies. A series of fulfillment has 91 been performed in forwarding and routing protocols, net-92 work traffic classification, and Quality of Service (QoS) [4], 93 [5], [6]. In [7], they presented an ML approach to optimize 94 network performance and attain optimal energy efficiency 95 by applying a Q-learning algorithm. To guarantee the QoS 96

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in the arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario.

In clustered energy harvesting-cognitive radio sensor networks (EH-CRSNs), reliance on direct links for both EH and data transmission causes distant nodes to deplete energy faster, thereby shortening network lifetime. To address the above issues, this paper integrates an active intelligent reflecting surface (IRS) into EH-CRSNs and proposes a system energy efficiency (EE) maximization-oriented clustering protocol (EEMCP) to achieve a trade-off between network lifetime and monitoring capability. Specifically, by optimizing the reflection coefficient matrix of the active IRS during uplink transmission, the transmission range of cluster heads (CHs) is extended, enabling direct communication with the sink and mitigating data delivery failures caused by the absence of suitable relay nodes in conventional clustered EH-CRSNs. Furthermore, the optimal cluster radius is theoretically derived with the objective of maximizing system EE, thereby constraining local control signaling and intra-cluster communication ranges to reduce energy consumption. High-quality CHs are then selected to form clusters through joint evaluation of node-level communication capacity and channel quality to enhance data transmission performance. Simulations indicate that the EEMCP protocol enables superior system EE, exceeding the peak EE of existing clustering protocols by at least 1.98 times.

In developing countries like India, people are abhorrent towards the public transportation, mainly because of the pitiable service quality and travel delay. Congestion at the intersection is very common these days. In order to improve the public transportation and reduce the congestion, giving priority to the buses at the intersection can be possible approach. In this paper, two different transit priority strategies at an intersection are analyzed and their performance impact is evaluated. The impact of bus priority is measured in terms of reduction in delay of the buses and cars, due to the priority given. The main findings of the study are that the bus priorities are more efficient at high volumes. Transit priority strategies include reservation of existing lane for the buses near the intersection or adding extra lane for the buses and insertion of phase exclusively for the buses in the traffic signal. Micro-simulation tool VISSIM is used to carry out the simulation process. This ...

In the recent years, it has been shown that the behavior of variable bit rate (VBR) video sources cannot be captured by the traditional Markov models since they do not exhibit a long-range dependent (LRD) characteristic which on the contrary is present in video traffic. Since then, a debate has been opened to understand the actual behavior of packet sources and the influence of this fact onto network analysis and network project. In this paper we compare two classes of video models: the first model belongs to a particular class of Markov models: the Hidden Markov Models (HMM), while the second is derived from application of chaotic attractors. The comparison is first related to their accuracy in modeling variable bit rate (VBR) video traffic out of an eventual video server, i.e. at the level of multiple aggregated streams. The two are then used to feed a simulated packet network to investigate whether they allow correct prediction of network performances.

This paper introduces relaxed abduction, a novel non-standard reasoning task for description logics. Although abductive reasoning over description logic knowledge bases has been applied successfully to various information interpretation tasks, it typically fails to provide adequate (or even any) results when confronted with spurious information or incomplete models. Relaxed abduction addresses this flaw by ignoring such pieces of information automatically based on a joint optimization of the sets of explained observations and required assumptions. We present a method to solve relaxed abduction over EL + TBoxes based on the notion of multi-criterion shortest hyperpaths.

The physical activities of a real wireless network are represented by events which are the main components of a discrete event simulation (DES) system and are produced by its event generator during simulation time. Each network service (e.g. voice, data and video) constitutes an event for a particular mobile user. A critical component within the simulation system, called scheduler, runs by selecting the next earliest event, executing it till completion, and returning to execute the next event. Calendar queue is the state of the art implementation of the scheduler among the most popular networking simulation tools such as ns-2. However, Calendar queue time-stamping mechanism presents drawbacks in the case of complex dynamical systems, like wireless networks, where probability of events concurrency is large. In such a case sequential time-stamping of calendar queue scheduling does not reflect real network events occurrence and generation. It should be remarked that there are very few reports if any in the literature concerning research on events scheduling mechanisms in such real time systems. On the other hand, multi-threading technology offers advanced capabilities for modelling concurrent events. The main goal of this paper is to illustrate that multithreading architectures provide the means for designing efficient schedulers in the simulation of wireless networks resource allocation but, also, several critical issues such as deadlocks, synchronization and scheduling must be effectively faced. In this paper, a stable simulation model is presented based on a novel layered thread architecture and on an alternative network event scheduling mechanism, called the Priority Queue (PQ) -Time Division Multiplexing (TDM) Layered Multithreading mechanism, which supports concurrent events as compared to the state of the art approach which supports only sequential events. Moreover, specific drawbacks of the JVM multi-threading platform such as thread execution unpredictability are also faced and presented.

We provide the first analytical expressions for the expected waiting time of highpriority customers in the delayed APQ by exploiting a classical conservation law for work-conserving queues. Additionally, we describe an algorithm to compute the expected waiting times of both low-priority and high-priority customers, which requires only the truncation of sums that converge quickly in our experiments. These insights are used to demonstrate how the accumulation rate and delay level should be chosen by health care practitioners to optimize common key performance indicators (KPIs). In particular, we demonstrate that for certain nontrivial KPIs, an accumulating priority queue with a delay of zero is always preferable. Finally, we present a detailed investigation of the quality of an exponential approximation to the high-priority waiting time distribution, which we use to optimize the choice of queueing parameters with respect to both classes' waiting time distributions.

We provide the first analytical expressions for the expected waiting time of highpriority customers in the delayed APQ by exploiting a classical conservation law for work-conserving queues. Additionally, we describe an algorithm to compute the expected waiting times of both low-priority and high-priority customers, which requires only the truncation of sums that converge quickly in our experiments. These insights are used to demonstrate how the accumulation rate and delay level should be chosen by health care practitioners to optimize common key performance indicators (KPIs). In particular, we demonstrate that for certain nontrivial KPIs, an accumulating priority queue with a delay of zero is always preferable. Finally, we present a detailed investigation of the quality of an exponential approximation to the high-priority waiting time distribution, which we use to optimize the choice of queueing parameters with respect to both classes' waiting time distributions.

We provide the first analytical expressions for the expected waiting time of highpriority customers in the delayed APQ by exploiting a classical conservation law for work-conserving queues. Additionally, we describe an algorithm to compute the expected waiting times of both low-priority and high-priority customers, which requires only the truncation of sums that converge quickly in our experiments. These insights are used to demonstrate how the accumulation rate and delay level should be chosen by health care practitioners to optimize common key performance indicators (KPIs). In particular, we demonstrate that for certain nontrivial KPIs, an accumulating priority queue with a delay of zero is always preferable. Finally, we present a detailed investigation of the quality of an exponential approximation to the high-priority waiting time distribution, which we use to optimize the choice of queueing parameters with respect to both classes' waiting time distributions.

In the early days of the Internet architecture, the most important aim is to transmit data over packet switched networks. The traditional Internet architecture used in these networks lacks quality of service. However, today, as realtime applications increase, it is needed. There are approaches to improving the quality of service using the flow label field in the Internet Protocol version 6 header. In this study, a novel algorithm that uses destination network parameters to reduce queuing and end-to-end delay is created. A round-robin-based time-aware priority queue new model is used within this algorithm. Data packets using this proposed queue are prioritized with metric values of the destination network. In order to provide end-to-end service quality, the prioritization value is used by placing it in the flow label field. For this purpose, a new approach to the use of this field is proposed. Delay, one of the most important factors affecting quality of service, is reduced with the proposed algorithm and flow label usage approach. As a result, the reduction in delay times between 22 and 39 ms resulted in various improvement rates between 16.79% and 35.13%.

We consider an M=G=1 retrial queue with general retrial times where the blocked customers either with probability q join the infinite waiting room (called priority queue) or with complementary probability p leave the service area and enter the retrial group (called orbit) in accordance with an FCFS discipline. We assume that only the customer at the head of the orbit is allowed to retry for service. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of the system size distribution, which generalizes the well-known Pollaczek-Khinchin formula. Also we obtain the stochastic decomposition law and as an application we study the asymptotic behaviour under high rate of retrials. Besides the optimal control of the priority policy is investigated. The results agree with known special cases. Finally, numerical calculations are used to observe system performance.

We present a (non-standard) probabilistic analysis of dynamic data structures whose sizes are considered dynamic random walks. The basic operations (insertion, deletion, positive and negative queries, batched insertion, lazy deletion, etc.) are time-dependent random variables. This model is a (small) step toward the analysis of these structures when the distribution of the set of histories is not uniform. As an illustration, we focus on list structures (linear lists, priority queues, and dictionaries) but the technique is applicable as well to more advanced data structures.