Individual Queues Research Articles

An investigation into the optimal allocation of resources for China's universities to participate in global education governance based on queuing theory

Abstract Queuing theory is used to classify the regularity of educational resource allocation by hierarchy in this paper. The Poisson distribution is used to label the resource queue interval parameters to obtain the expected value of individual queues. The average delay of each class of packets can be reasonably predicted by concatenating individual resources using the Lagrange multiplier algorithm. The load balancing algorithm in each queueing series calculates the average arrival rate of task requests to achieve an optimal model design. The results show that, under the guidance of queuing theory, the coefficient of variance in the participation of Chinese university students in global education governance is reduced by 0.25% on average, and the average of comprehensive efficiency reaches about 1.01%, which realizes the optimal and reasonable allocation of resources.

Lyapunov optimized energy-efficient dynamic offloading with queue length constraints

With the advent of the Internet of Things (IoT), more computation-intensive applications are migrated to IoT devices. Whereas the battery with limited capacity and the processor with low computing power become the bottlenecks that limit its further development. Mobile edge computing (MEC) provides a promising solution to break through the bottlenecks. Many effective methods are proposed to guide how to offload tasks from IoT devices to MEC to enhance the computing capacity and prolong the battery life of devices. This paper investigates the task offloading problem for a multi-device single-MEC system whose status, such as task arrival rate and channel state, is dynamically changing over time and aims at minimizing the energy consumption of devices and maintaining the system stability in the long term. This problem requires lots of future information about the system, which brings a challenge since it is difficult to obtain future information. Moreover, to improve the system performance with respect to task response time, we define an individual queue length threshold for each IoT device such that the queue length of each device can stabilize around the predefined threshold. To address this problem, we first construct a virtual queue for each device to transform the queue length threshold constraint into the virtual queue stability constraint. Secondly, applying the Lyapunov optimization method, the original problem, which requires future system information, is transformed into a problem that only depends on the information of the current time. Thirdly, a dynamic energy-efficient task offloading algorithm is proposed to optimize the time-average energy consumption while maintaining the queue length constraint. This algorithm generates the offloading decision in real-time without requiring system statistical information. Lastly, simulations are conducted to analyze the effect of different parameters on performance. A group of comparisons are given, showing that the task queue length under the proposed method can be controlled effectively compared with the existing studies.

PROBE VEHICLE LANE IDENTIFICATION AT SIGNALIZED INTERSECTION USING SUPPORT VECTOR MACHINE METHOD

Transportation problems in Indonesia, especially in urban areas, can be solved by applying Intelligent Transportation Systems (ITS), one of which is by using a Global Positioning System (GPS) based probe vehicle system. This system is growing because smartphones can be used as instruments for investigators' vehicles. This system provides information on the location and speed of all investigator vehicles every second, making it possible to estimate the real time traffic condition on a road segment passed by the probe vehicle. The implementation of this system in the city of Manado can help improve traffic conditions because so many motorists carry smartphones while driving. However, the problem is that the GPS on this smartphone has a low accuracy of 3 to 15 meters, so this GPS data cannot be used to solve transportation problems at the micro level such as at intersections. The purpose of this study was to obtain a method for identifying probe vehicle lanes through GPS data from smartphones. The steps in achieving the research goal are 1) building a microscopic transportation model using software to obtain data 2) building a data processing algorithm for vehicle lane identification using traffic flow theory and machine learning methods which in this case is Support Vector Machine, and 3) perform model validation. The results showed that the individual queue shock wave from each probe vehicle could be used to identify the lane of the probe vehicle. This study also confirms that the Support Vector Machine method can be used to predict the lane position of the probe vehicle.

Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling

We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the complete resource pooling condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of linear combinations of queue lengths in heavy traffic. We showcase the generality of our result by presenting various stochastic networks as corollaries, each of which is a contribution by itself. In particular, we study the input-queued switch with correlated arrivals, and we show that, if the state space collapses to a full-dimensional subspace, the correlation among the arrival processes does not matter in heavy traffic. We exemplify this last case with a parallel-server system, an [Formula: see text]-system, and an ad hoc wireless network. Whereas these results are obtained using the drift method, we additionally present a negative result showing a limitation of the drift method. We show that it is not possible to obtain the individual queue lengths using the drift method with polynomial test functions. We do this by presenting an alternate view of the drift method in terms of a system of linear equations, and we use this system of equations to obtain bounds on arbitrary linear combinations of the queue lengths.

A novel four‐tier software‐defined network architecture for scalable secure routing and load balancing

SummarySoftware‐defined networking is an emerging paradigm for supporting flexible network management. In the traditional architecture for a software‐defined network (SDN), the controller commonly uses a general routing algorithm such as Open Shortest Path First (OSPF), which chooses the shortest path for communication. This may cause the largest amount of network traffic, especially in large‐scale environments. In this paper, we present the design for a novel SDN‐based four‐tier architecture for scalable secure routing and load balancing. In Tier 1, user authentication is conducted using elliptic curve cryptography (ECC); this avoids unnecessary loads from unauthorized users. In Tier 2, packet classification is performed based on the packet characteristics using the fuzzy analytical hierarchy process (fuzzy AHP), and packets are placed into three individual queues. In Tier 3, scalable secure routing is achieved by selecting the optimal path using the improved particle swarm optimization and ant colony optimization algorithms. With these optimization algorithms, we can adaptively change the number of users, the number of switches, and other parameters. In Tier 4, the recommended secure cluster (multicontroller) management is accomplished using an algorithm that employs modified k‐means clustering and a recurrent neural network. Deep reinforcement learning (DRL) is also proposed for updating the controller information. Experimental results are analyzed using the OMNeT++ network simulator, and the evaluated performance displayed improvement over a variety of existing methods in terms of response time (50% to 60%), load (55%), execution time (3.2%), throughput (9.8%), packet loss rate (1.02%), end‐to‐end delay (50%), and bandwidth consumption (45%).

Learning traffic correlations in multi-class queueing systems by sampling queue lengths, with routing applications

We consider a system of parallel single-server queues. Work of different classes arrives as correlated Gaussian processes with known drifts but unknown covariance matrix Σ, and it is deterministically routed to the different queues according to some routing matrix.We first provide a procedure to estimate Σ based on the empirical large deviations behavior of the individual queues, for a finite set of routing matrices, and prove that the resulting estimate is asymptotically consistent under minimal technical conditions. We also introduce a more efficient procedure to estimate Σ based on the empirical large deviation behavior of linear combinations of queues, for a single routing matrix, and prove that the resulting estimate is asymptotically consistent under some technical conditions. We establish, however, that in specific cases the latter approach cannot be used due to an inherent loss of information produced by the dynamics of the queues.Finally, given a well-behaved cost function on the steady-state marginal queue lengths, we show how our procedures can be used to obtain an asymptotically consistent estimator for the cost under any routing matrix, and identify an optimal one.

Scaling limits for closed product-form queueing networks

We consider a general class of closed product-form queueing networks, consisting of single-server queues and infinite-server queues. Even if a network is of product-form type, performance evaluation tends to be difficult due to the potentially large state space and the dependence between the individual queues. To remedy this, we analyze the model in a Halfin–Whitt inspired scaling regime, where we jointly blow up the traffic loads of all queues and the number of customers in the network. This leads to a closed-form limiting stationary distribution, which provides intuition on the impact of the dependence between the queues on the network’s behavior. We assess the practical applicability of our results through a series of numerical experiments, which illustrate the convergence and show how the scaling parameters can be chosen to obtain accurate approximations.

Evaluating the Bank Queuing Systems by Fuzzy Logic

Various models are used in the banking system to organize the queue structure of customers' banking transactions. The average waiting time for a customer in the queue generally varies depending on whether bank customer or not and the customer score it has. Different uncertain parameters are used to determine the individual queue group and average waiting time in bank queuing systems. This paper proposes a fuzzy logic-based approach in bank queuing systems. In this study, individual bank queue group and average waiting times are determined according to the number of waiting customers, customer score and credit score parameters. In addition, identification number is a determining factor for the priority of transactions in bank queuing systems. People who are not customers of the bank often have longer waiting times. As a new approach to the working structure of bank queuing systems, this study also suggests that non-bank customers should be given priority sequence numbers according to their credit scores.

Analytical Performance Models for NoCs with Multiple Priority Traffic Classes

Networks-on-chip (NoCs) have become the standard for interconnect solutions in industrial designs ranging from client CPUs to many-core chip-multiprocessors. Since NoCs play a vital role in system performance and power consumption, pre-silicon evaluation environments include cycle-accurate NoC simulators. Long simulations increase the execution time of evaluation frameworks, which are already notoriously slow, and prohibit design-space exploration. Existing analytical NoC models, which assume fair arbitration, cannot replace these simulations since industrial NoCs typically employ priority schedulers and multiple priority classes. To address this limitation, we propose a systematic approach to construct priority-aware analytical performance models using micro-architecture specifications and input traffic. Our approach decomposes the given NoC into individual queues with modified service time to enable accurate and scalable latency computations. Specifically, we introduce novel transformations along with an algorithm that iteratively applies these transformations to decompose the queuing system. Experimental evaluations using real architectures and applications show high accuracy of 97% and up to 2.5× speedup in full-system simulation.

ДОСЛІДЖЕННЯ МЕТОДУ АКТИВНОГО УПРАВЛІННЯ ЧЕРГАМИ НА ІНТЕРФЕЙСАХ МАРШРУТИЗАТОРІВ ТЕЛЕКОМУНІКАЦІЙНИХ МЕРЕЖ

У роботі представлено результати дослідження методу активного управління чергами на інтерфейсах маршрутизаторів телекомунікаційних мереж. Основу запропонованого методу складають оптимізаційні моделі погодженого розв’язання задач агрегації та розподілу потоків пакетів за сформованими на інтерфейсі маршрутизатора чергами (управління перевантаженням); розподілу пропускної здатності інтерфейсу маршрутизатора між сформованими чергами (розподіл канального ресурсу); та забезпечення завчасного обмеження інтенсивності потоків пакетів, що надходять на вхід інтерфейсу маршрутизатора (активне управління чергами). Проаналізовано вплив класів потоків та черг, виду критеріїв оптимальності та множника балансування на характер отриманих рішень та ефективність роботи інтерфейсу.

Performance of large-scale polling systems with branching-type and limited service

Motivated by emerging Internet-of-Things (IoT) applications and smart building environments, we analyze the performance of large-scale symmetric polling systems where the number of queues grows large. We consider a scenario in which the total arrival rate is kept fixed and the individual switch-over time and service time distributions remain the same. This asymptotic regime leads to cycles of infinite length and queue lengths with non-trivial distributions. We show that for most traditional service policies the scaled cycle times converge to a deterministic value in the limit, which in turn implies that the queue lengths at the various nodes become asymptotically independent. Using these insights, we find that the behavior of individual queues simplifies to that of a discrete-time bulk service queue in the limit, so that the marginal queue length and waiting-time distributions become considerably easier to analyze. Additionally, we propose a new flexible k-limited service discipline aimed at striking a good balance between short mean queue lengths and predictable cycle times for deadline-critical applications.

Rate control under heavy traffic with strategic servers

We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with its queue to minimize its expected cost. The rates and the cost functions in addition to depending on the control action, can depend, in a symmetric fashion, on the size of the individual queue and the empirical measure of the states of all queues in the system. In order to determine an approximate Nash equilibrium for this finite player game, we construct a Lasry–Lions-type mean-field game (MFG) for certain reflected diffusions that governs the limiting behavior. Under conditions, we establish the convergence of the Nash-equilibrium value for the finite size queuing system to the value of the MFG.

Analytical approximations to predict order picking times at a warehouse

The primary objective of this research was to develop analytical approximations to predict the time taken to complete a customer order in a warehouse. The problem under study was modelled as a network of queues and the parametric decomposition approach was adopted to develop the approximations. Under this method, the queuing network is decomposed into individual queues allowing to analyse single (i.e., customer order processing, pallet building, and re-pick process) and fork-join stations (i.e., order picking with synchronisation constraints) within the same framework. Analytical formulations to estimate order picking times were developed and compared with equivalent simulation models to estimate the accuracy of the formulations. Appropriate correction terms were also developed to bridge the gap between the analytical approximations and the simulation models. The experimental study conducted indicates that the analytical approximations along with the correction terms can serve as a good estimate for the order picking times in a warehouse.

Limit Theorems for Queueing Systems with Various Service Disciplines in Heavy-Traffic Conditions

In this paper a multi-server queueing system with regenerative input flow and independent service times with finite means is studied. We consider queueing systems with various disciplines of the service performance: systems with a common queue and systems with individual queues in front of the servers. In the second case an arrived customer chooses one of the servers in accordance with a certain rule and stays in the chosen queue up to the moment of its departure from the system. We define some classes of disciplines and analyze the asymptotical behavior of a multi-server queueing system in a heavy-traffic situation (traffic rate ρ ≥ 1). The main result of this work is limit theorems concerning the weak convergence of scaled processes of waiting time and queue length to the process of the Brownian motion for the case ρ > 1 and its absolute value for the case ρ = 1.

Priority Queue Based Reactive Buffer Management Policy for Delay Tolerant Network under City Based Environments.

Delay Tolerant Network (DTN) multi-copy routing protocols are privileged to create and transmit multiple copies of each message that causes congestion and some messages are dropped. This process is known as reactive drop because messages were dropped re-actively to overcome buffer overflows. The existing reactive buffer management policies apply a single metric to drop source, relay and destine messages. Hereby, selection to drop a message is dubious because each message as source, relay or destine may have consumed dissimilar magnitude of network resources. Similarly, DTN has included time to live (ttl) parameter which defines lifetime of message. Hence, when ttl expires then message is automatically destroyed from relay nodes. However, time-to-live (ttl) is not applicable on messages reached at their destinations. Moreover, nodes keep replicating messages till ttl expires even-though large number of messages has already been dispersed. In this paper, we have proposed Priority Queue Based Reactive Buffer Management Policy (PQB-R) for DTN under City Based Environments. The PQB-R classifies buffered messages into source, relay and destine queues. Moreover, separate drop metric has been applied on individual queue. The experiment results prove that proposed PQB-R has reduced number of messages transmissions, message drop and increases delivery ratio.

A Novel Computer Simulation of the Mind Using Buddhist Theories

We explore whether a body of knowledge for the mind based on ancient Buddhist psychology is computer programmable and could add value to the field of computational cognitive science. This system composed of the mechanics of human consciousness and cognitive processes is appealing because of its root in meditation, a rare non-intrusive method to examining the mind. In this paper, we design and develop a computer program that embodies the key components of the system, including consciousness, mental states, sense-based and mind-based cognitive processes in the Python programming language. By utilizing timed events, individual queues for each of the five senses that are regulated by a central queue for the brain, feature and object memory, and a concurrent sense and mind architecture, our prototype simulates a tick’s life cycle to depict its population growth curve as it learns to survive by refining its choices under varying arrival frequency of prey. The program could be of interest to artificial intelligence and robotics as it offers an alternative way to modeling and mimicking human cognition

Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks

This paper proposes an analytical model to approximate the transient aggregate joint queue-length distribution of tandem finite (space) capacity Markovian networks. The methodology combines ideas from transient aggregation-disaggregation techniques as well as transient network decomposition methods. The complexity of the proposed method is linear in the number of queues and is independent of the space capacities of the individual queues. This makes it a suitable approach for the analysis of large-scale networks. The transient joint distributions are validated versus simulation estimates. The model is then used to describe urban traffic dynamics and to address a dynamic traffic signal control problem. The signal plan analysis shows the added value of using joint distributional information, and more generally spatial-temporal between-link dependency information, to enhance urban traffic operations. The online appendix is available at https://doi.org/10.1287/trsc.2015.0629 .

Exploiting Intra-Request Slack to Improve SSD Performance

With Solid State Disks (SSDs) offering high degrees of parallelism, SSD controllers place data and direct requests to exploit the maximum offered hardware parallelism. In the quest to maximize parallelism and utilization, sub-requests of a request that are directed to different flash chips by the scheduler can experience differential wait times since their individual queues are not coordinated and load balanced at all times. Since the macro request is considered complete only when its last sub-request completes, some of its sub-requests that complete earlier have to necessarily wait for this last sub-request. This paper opens the door to a new class of schedulers to leverage such slack between sub-requests in order to improve response times. Specifically, the paper presents the design and implementation of a slack-enabled re-ordering scheduler, called Slacker , for sub-requests issued to each flash chip. Layered under a modern SSD request scheduler, Slacker estimates the slack of each incoming sub-request to a flash chip and allows them to jump ahead of existing sub-requests with sufficient slack so as to not detrimentally impact their response times. Slacker is simple to implement and imposes only marginal additions to the hardware. Using a spectrum of 21 workloads with diverse read-write characteristics, we show that Slacker provides as much as 19.5%, 13% and 14.5% improvement in response times, with average improvements of 12%, 6.5% and 8.5%, for write-intensive, read-intensive and read-write balanced workloads, respectively.

Exploiting Intra-Request Slack to Improve SSD Performance

With Solid State Disks (SSDs) offering high degrees of parallelism, SSD controllers place data and direct requests to exploit the maximum offered hardware parallelism. In the quest to maximize parallelism and utilization, sub-requests of a request that are directed to different flash chips by the scheduler can experience differential wait times since their individual queues are not coordinated and load balanced at all times. Since the macro request is considered complete only when its last sub-request completes, some of its sub-requests that complete earlier have to necessarily wait for this last sub-request. This paper opens the door to a new class of schedulers to leverage such slack between sub-requests in order to improve response times. Specifically, the paper presents the design and implementation of a slack-enabled re-ordering scheduler, called Slacker , for sub-requests issued to each flash chip. Layered under a modern SSD request scheduler, Slacker estimates the slack of each incoming sub-request to a flash chip and allows them to jump ahead of existing sub-requests with sufficient slack so as to not detrimentally impact their response times. Slacker is simple to implement and imposes only marginal additions to the hardware. Using a spectrum of 21 workloads with diverse read-write characteristics, we show that Slacker provides as much as 19.5%, 13% and 14.5% improvement in response times, with average improvements of 12%, 6.5% and 8.5%, for write-intensive, read-intensive and read-write balanced workloads, respectively.

On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach

This paper is motivated by recent results in the design of signal plans for Manhattan that highlight the importance of providing signal control algorithms with an analytical description of between-link dependencies. This is particularly important for congested networks prone to the occurrence of spillbacks. This paper formulates a probabilistic network model that proposes an aggregate description of the queue-length, and then approximates the joint aggregate queue-length distribution of subnetworks. The goal is to model between-queue dependencies beyond first-order moments, yet to do so in a tractable manner such that these techniques can be used for optimization purposes.This paper models an urban road network as a finite space capacity Markovian queueing network. Exact evaluation of the stationary joint queue-length distribution of such a network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the network state space, which is exponential in the number of queues. This paper proposes to address the dimensionality issue by: 1) describing the state of the network aggregately, and 2) decomposing the network into overlapping subnetworks. We propose an analytical approximation of the stationary aggregate joint queue-length distribution of a subnetwork. The model consists of a system of nonlinear equations with a dimension that is linear, instead of exponential, in the number of queues and that is independent of the space capacity of the individual queues. The method is derived for tandem Markovian finite capacity queueing networks. The proposed model is computationally tractable and scalable, it can be efficiently used for the higher-order distributional analysis of large-scale networks. The model is validated versus simulation estimates and versus other decomposition methods. We then use it to address an urban traffic control problem. We show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested urban networks.