V-uniform ergodicity for fluid queues

In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.

Basic Limit Theorems for Light Traffic Queues &Their Applications

In this paper, we study some basic limit theorems characterizing the stationary behavior of light traffic queuing systems. Beginning with limit theorems for the simple M/M/1 queuing system, we demonstrate the methodology for applying these theorems for the benefit of service systems. The limit theorems studied here are dominant in the literature. Our contribution is primarily on the analysis leading to the application of these theorems in various problem situations for better operations. Relevant Examples are included to aid the application of the results studied in this work.

A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units

We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.

Variability Analysis for a Two-station Queueing Network in Heavy Traffic with Arrival Processes Driven by Queues

The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.

A Maintenance Service Improvement Approach Based on Queue Networks: Application

The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.

Analysis of Queues in a Random Environment with Impatient Customers

We study M/M/c queues(c = 1, 1 < c < ∞ and c = ∞) in a Markovian environment with impatient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain.When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

Tail Asymptotics of Two Parallel Queues with Transfers of Customers

This paper studies a system consisting of two parallel queues with transfers of customers.In the system,one queue is called main queue and the other one is called auxiliary queue.The main queue is monitored at exponential time instances.At a monitoring instant,if the number of customers in main queue reaches L(>K),a batch of L−K customers is transferred from the main queue to the auxiliary queue,and if the number of customers in main queue is less than or equal to K,the transfers will not happen.For this system,by using a Foster-Lyapunov type condition,we establish a sufficient stability condition.Then,we provide a sufficient condition under which,for any fixed number of customers in the auxiliary queue,the stationary probability of the number of customers in the main queue has an exact geometric tail asymptotic as the number of customers in main queue increases to infinity.Finally,we give some numerical results to illustrate the impact of some critical model parameters on the decay rate.

Python Server Page Performance Analysis and Modeling

Today, in the field of computer networks, new services have been developed on the Internet or intranets, including the mail server, database management, sounds, videos and the web server itself Apache. The number of solutions for this server is therefore growing continuously, these services are becoming more and more complex and expensive, without being able to fulfill the needs of the users. The absence of benchmarks for websites with dynamic content is the major obstacle to research in this area. These users place high demands on the speed of access to information on the Internet. This is why the performance of the web server is critically important. Several factors influence performance, such as server execution speed, network saturation on the internet or intranet, increased response time, and throughputs. By measuring these factors, we propose a performance evaluation strategy for servers that allows us to determine the actual performance of different servers in terms of user satisfaction. Furthermore, we identified performance characteristics such as throughput, resource utilization, and response time of a system through measurement and modeling by simulation. Finally, we present a simple queue model of an Apache web server, which reasonably represents the behavior of a saturated web server using the Simulink model in Matlab (Matrix Laboratory) and also incorporates sporadic incoming traffic. We obtain server performance metrics such as average response time and throughput through simulations. Compared to other models, our model is conceptually straightforward. The model has been validated through measurements and simulations during the tests that we conducted.

Multi-class dynamic network traffic flow propagation model with physical queues

This paper proposes an improved multi-class dynamic network traffic flow propagation model with a consideration of physical queues. Each link is divided into two areas: Free flow area and queue area. The vehicles of the same class are assumed to satisfy the first-in-first-out(FIFO) principle on the whole link, and the vehicles of the different classes also follow FIFO in the queue area but not in the free flow area. To characterize this phenomenon by numerical methods, the improved model is directly formulated in discrete time space. Numerical examples are developed to illustrate the unrealistic flows of the existing model and the performance of the improved model. This analysis can more realistically capture the traffic flow propagation, such as interactions between multi-class traffic flows, and the dynamic traffic interactions across multiple links.

Equilibrium Joining Strategies in the M/M/1 Queues with Setup Times under N-Policy

This paper carries out a game-theoretic analysis of a single-server queueing system with setup times under N-policy by considering both the partially observable and the partially unobservable information scenarios. The server switches off whenever the system becomes empty, and is resumed when the number of customers reaches a certain threshold value. Customers decide whether to join or to balk the system upon arrival based on their available information. The equilibrium joining strategy of customers as well as the systemzs performance measures are derived under different information levels. We find that both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors exist in our system. Numerical results show that the social welfare is unimodal in the threshold, and is decreasing in the waiting cost.

Comparisons of Exhaustive and Nonexhaustive M/M/l/N Queues with Working Vacation and Threshold Policy

This paper compares the performance of exhaustive and nonexhaustive M/M/l/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exist in the system, and turns to normal service until the number of customers achieves a threshold. However, in a nonexhaustive queue, the server switches service rate between a low and a high value depending on system congestion. To get equilibrium arrival rate of customers and social welfare for the two types of queues, we first derive queue length distributions and expected busy circle. Then, by making sensitivity analysis of busy circle, system cost, arrival rate and optimal social welfare, we find that customers tend to join exhaustive queues instead of nonexhaustive queues, and the optimal threshold in an exhaustive queue is probably inconsistent with the one in a nonexhaustive queue. Moreover, in general, whet her to consider system cost or not in social welfare will obviously affect the tendencies of optimal arrival rate and optimal social welfare with the threshold and system capacity for the two types of queues, especially for the nonexhaustive queues, and then affect the final decisions of social planner or system manager.

AN ALGORITHM PROPOSED FOR BUSY-PERIOD SUBCOMPONENT ANALYSIS OF BULK QUEUES

This paper presents an algorthmic procedure for a busy-period subcomponent analysis of bulkqueues. A component of interest for many server queues is the period t_k to reduce congestion froma level k to level k-1. For an M(x)/M/c system with the possibility of total or partial rejection ofbatches, it is demonstrated that the expected length of busy periods, the proportion of delayed batchand the steady state queue length probabilities can be easily obtained. The procedure is based on thenested partial sums and monotonic properties of expected lengths of the busy periods.

Moderate deviation for maximum likelihood estimators from single server queues

Consider a single server queueing model which is observed over a continuous time interval(0,T],where T is determined by a suitable stopping rule.Let θ be the unknown parameter for the arrival process and θT be the maximum likelihood estimator of θ.The main goal of this paper is to obtain a moderate deviation result of the maximum likelihood estimator for the single server queueing model under certain regular conditions.

OPTIMAL CONTROL FOR A TANDEM NETWORK OF QUEUES WITH BLOCKING

e consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.

Secure and Optimal LOADng Routing for IoT with Composite RoutingMetric

Security is the one of the major challenges for routing the data between the source and destination in an Internet of Things(IoT)network.To overcome this challenge,a secure Lightweight On-demand Ad hoc Distancevector—Next Generation(LOADng)Routing Protocol is proposed in this paper.As the LOADng protocol is the second version of Ad Hoc On-Demand Distance Vector(AODV)protocol,it retains most of the basic functionality and characteristics of AODV.During the route discovery process,the cyclic shift transposition algorithm(CSTA)is used to encrypt the control packets of the LOADng protocol to improve its security.CSTA approach only derives transposition and substitution without product cipher with respect to input data.Besides this,for choosing the best probable path between the source and destination,routing metrics such as link quality Indicator(LQI),hop count(HC)and queue length(QL)are included in the control packets.The data is then securely sent using CSTA using the optimal secure path selected.Experimental Results depict that the proposed secure and optimal LOADng(SO-LOADng)using CSTA encryption obtains better throughput,delivery ratio encryption time and decryption time than the existing state-ofart approaches.

A Fully Adaptive Active Queue Management Method for Congestion Prevention at the Router Buffer

Active queue management(AQM)methods manage the queued packets at the router buffer,prevent buffer congestion,and stabilize the network performance.The bursty nature of the traffic passing by the network routers and the slake behavior of the existing AQM methods leads to unnecessary packet dropping.This paper proposes a fully adaptive active queue management(AAQM)method to maintain stable network performance,avoid congestion and packet loss,and eliminate unnecessary packet dropping.The proposed AAQM method is based on load and queue length indicators and uses an adaptive mechanism to adjust the dropping probability based on the buffer status.The proposed AAQM method adapts to single and multiclass traffic models.Extensive simulation results over two types of traffic showed that the proposed method achieved the best results compared to the existing methods,including Random Early Detection(RED),BLUE,Effective RED(ERED),Fuzzy RED(FRED),Fuzzy Gentle RED(FGRED),and Fuzzy BLUE(FBLUE).The proposed and compared methods achieved similar results with low or moderate traffic load.However,under high traffic load,the proposed AAQM method achieved the best rate of zero loss,similar to BLUE,compared to 0.01 for RED,0.27 for ERED,0.04 for FRED,0.12 for FGRED,and 0.44 for FBLUE.For throughput,the proposed AAQM method achieved the highest rate of 0.54,surpassing the BLUE method’s throughput of 0.43.For delay,the proposed AAQM method achieved the second-best delay of 28.51,while the BLUE method achieved the best delay of 13.18;however,the BLUE results are insufficient because of the low throughput.Consequently,the proposed AAQM method outperformed the compared methods with its superior throughput and acceptable delay.

Multi-Agent Deep Reinforcement Learning for Cross-Layer Scheduling in Mobile Ad-Hoc Networks

Due to the fading characteristics of wireless channels and the burstiness of data traffic,how to deal with congestion in Ad-hoc networks with effective algorithms is still open and challenging.In this paper,we focus on enabling congestion control to minimize network transmission delays through flexible power control.To effectively solve the congestion problem,we propose a distributed cross-layer scheduling algorithm,which is empowered by graph-based multi-agent deep reinforcement learning.The transmit power is adaptively adjusted in real-time by our algorithm based only on local information(i.e.,channel state information and queue length)and local communication(i.e.,information exchanged with neighbors).Moreover,the training complexity of the algorithm is low due to the regional cooperation based on the graph attention network.In the evaluation,we show that our algorithm can reduce the transmission delay of data flow under severe signal interference and drastically changing channel states,and demonstrate the adaptability and stability in different topologies.The method is general and can be extended to various types of topologies.

Traffic Flow Characteristics in Work Zone and Non-Work Zone Environment and Its Impact on Road Crashes at the Segment Level

This study investigates relationships between congestion and travel time performance metrics and crashes on road segments. The study focuses on work zone routes in Iowa, utilizing 2021 commercially-available probe vehicle data and crash data. Travel time performance metrics were derived from the probe vehicle data, and crash counts were obtained from the crash data. Additional variables included road characteristics (traffic volume, road type, segment length) and a categorical variable for the presence of a work zone. A mixed effect linear regression model was employed to identify relationships between road segment crash counts and the selected performance metrics. This was accomplished for two sets of models that include congestion performance measures at different defining threshold values, along with travel time performance measures. The study results indicate that the congestion indicators, certain travel time performance measures, and traffic counts were statistically significant and positively correlated with crash counts. Indicator variables for rural interstate locations and non-active work zones have a stronger influence on crash count than those for municipal interstate locations and active work zones. These findings can inform decision-makers on work zone safety strategies and crash mitigation planning, especially in high traffic volume areas prone to congestion and queues.

A Spectrum Occupancy Model for Primary Users in Cognitive Radio Systems

There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.

Passengers gathering-scattering analysis at the corners of subway stations

During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess.In this paper,a method of passenger gathering and scattering analysis based on queueing models was proposed to investigate the corner performance in subway stations.Firstly,we constructed a set of state spaces of passenger flow according to passenger density and proposed the state transition model of passenger flow.Moreover,the model of passenger flow blocking and unblocking probability were also presented.Then,to illustrate the validity of the method and model,several passenger gathering-scattering scenarios and were simulated to verify the influence of passenger distribution and facility width on passenger walking,and the blocking probability,throughput,and expected time were also analyzed under various widths of the target corridor and arrival rates.Results showed that the proposed model can reproduce the trend of walking parameters changing and the self-organizing phenomenon of'faster is lower'.With the increase of arrival rates of passengers,walking speeds of passengers decrease and the expected walking time is prolonged,and the blocking probability sharply increased when the arrival rate exceeded 7 peds/s.In addition,with change of width of the target facility,efficiency of capacity of walking circulation facility fluctuated.With the width of the target corridor enlarged by 10%,the steady state of passenger flow was less crowded.Therefore,corridor width is critical to the circulation efficiency of passengers in subway stations.The conclusions will help to develop reasonable passenger flow control plans to ease the jam and keep passengers walking safely.