Infinite Buffer Capacity Research Articles

Data Partition and Rate Control for Learning and Energy Efficient Edge Intelligence

The rapid development of artificial intelligence together with the powerful computation capabilities of the advanced edge servers make it possible to deploy learning tasks at the wireless network edge, which is dubbed as edge intelligence (EI). The communication bottleneck between the data resource and the server results in deteriorated learning performance as well as tremendous energy consumption. To tackle this challenge, we explore a new paradigm called learning-and-energy-efficient (LEE) EI, which simultaneously maximizes the learning accuracies and energy efficiencies of multiple tasks via data partition and rate control. Mathematically, this results in a multi-objective optimization problem. Moreover, the continuously varying communication rates introduce infinite variables, which further complicates the problem. To solve this complex problem, we consider the case with infinite server buffer capacity and one-shot data arrival at sensor. First, the number of variables is reduced to a finite level by exploiting the optimality of constant-rate transmission in each epoch. Second, the optimal solution of the multi-objective problem is found by applying the stratified sequencing or merging of objectives. By assuming higher priority of learning efficiency in stratified sequencing, the optimal data partition is derived in closed form by the Lagrange method, while the optimal rate control is proved to have the structure of directional water filling (DWF), based on which a string-pulling (SP) algorithm is proposed to obtain the numerical values. The DWF structure of rate control is also proved to be optimal in merging of objectives, which combines different objectives in a weighted manner. By exploiting the optimal rate changing properties, the SP algorithm is further extended to tackle the more challenging cases with limited server buffer capacity or bursty data arrival at sensor. The performance of the proposed joint data partition and rate control design is examined by extensive experiments based on public datasets.

The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.

Supervised-learning-based approximation method for multi-server queueing networks under different service disciplines with correlated interarrival and service times

ABSTRACT Developing efficient performance evaluation methods is important to design and control complex production systems effectively. We present an approximation method (SLQNA) to predict the performance measures of queueing networks composed of multi-server stations operating under different service disciplines with correlated interarrival and service times with merge, split, and batching blocks separated with infinite capacity buffers. SLQNA yields the mean, coefficient of variation, and first-lag autocorrelation of the inter-departure times and the distribution of the time spent in the block, referred as the cycle time at each block. The method generates the training data by simulating different blocks for different parameters and uses Gaussian Process Regression to predict the inter-departure time and the cycle time distribution characteristics of each block in isolation. The predictions obtained for one block are fed into the next block in the network. The cycle time distributions of the blocks are used to approximate the distribution of the total time spent in the network (total cycle time). This approach eliminates the need to generate new data and train new models for each given network. We present SLQNA as a versatile, accurate, and efficient method to evaluate the cycle time distribution and other performance measures in queueing networks.

CLOUD STORAGE FACILITY AS A FLUID QUEUE CONTROLLED BY MARKOVIAN QUEUE

Cloud storage faces many problems in the storage process which badly affect the system's efficiency. One of the most problems is insufficient buffer space in cloud storage. This means that the packets of data wait to have storage service which may lead to weakness in performance evaluation of the system. The storage process is considered a stochastic process in which we can determine the probability distribution of the buffer occupancy and the buffer content and predict the performance behavior of the system at any time. This paper modulates a cloud storage facility as a fluid queue controlled by Markovian queue. This queue has infinite buffer capacity which determined by the M/M/1/N queue with constant arrival and service rates. We obtain the analytical solution of the distribution of the buffer occupancy. Moreover, several performance measures and numerical results are given which illustrate the effectiveness of the proposed model.

Open Problem—Load Balancing Using Delayed Information

Load-balancing algorithms are important for efficiently routing jobs in systems of parallel queues; however, there has been relatively little attention devoted to developing algorithms in the presence of messaging and/or routing delays. Given a system of parallel queues with infinite capacity buffers; first-come, first-serve service discipline; and a single stream of incoming jobs that are routed by a dispatcher upon arrival, it has been shown that join the shortest queue (JSQ) satisfies certain optimality properties, including minimizing mean wait time when the job sizes are exponentially distributed ( Winston 1977 , Ephremides et al. 1980 ) and state space collapse of the queue lengths under heavy traffic scaling for general service distributions ( Reiman 1984 ). However, implementation of JSQ uses up-to-date information about the state of the buffers, which requires instantaneous exchange of multiple messages between the dispatcher and the queues. This challenge has led to the development of efficient algorithms that require fewer messages, including join the shortest of d queues (JSQ(d); Vvedenskaya et al. 1996 , Mitzenmacher 2001 ), join the idle queue (JIQ; Badonnel and Burgess 2008 , Lu et al. 2011 ), and persistent idle load distribution (PILD; Atar et al. 2019a , b ); see van der Boor et al. (2018) for a survey of some recent results in the many-server limit. Although these algorithms do not use full information about the system, they still use up-to-date information about the state of some of the queues. Because of the physical separation between the dispatcher and the queues, processing effects, or periodic updates from the queues, the dispatcher may have access only to information about the delayed states of the queues. (There may also be routing delays because of the time it takes a job to travel between the dispatcher and its assigned server, for which these algorithms also do not account.) In such settings, it has been shown that JSQ can perform quite poorly and lead to sustained oscillations in queue lengths ( Mitzenmacher 2000 ).

Memetic algorithm for solving flexible flow-shop scheduling problems with dynamic transport waiting times

Flexible flow-shop scheduling with dynamic transport waiting times (FFSPDW) is a typical flow shop scheduling problem in smart manufacturing system. In this problem, jobs need to be transported by transporters like AGV (Automated Guided Vehicle) to next stage after processing. During transportation, waiting time dynamically occurs for both jobs and transporters, and finally contributes to makespan. The waiting times are conditioned by buffer capacity, machine allocations and production sequence. In order to minimize makespan with consideration of dynamic waiting times, we proposed a waiting time calculation approach to evaluate waiting time and makespan. This approach considers two situations: infinite buffer capacity and zero buffer capacity. Further, we developed a memetic algorithm integrated with waiting time calculation approach to solve FFSPDW. Finally, we verified the algorithm parameters via analysis of variance. Computational results show that the proposed memetic algorithm is able to reach high quality solutions with short computation time. Consequently, the proposed approach is suitable for solving industrial FFSPDW problems.

A RANDOM ACCESS G-NETWORK: STABILITY, STABLE THROUGHPUT, AND QUEUEING ANALYSIS

The effect of signals on stability, stable throughput region, and delay in a two-user slotted ALOHA-based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model security attacks, expiration of deadlines, or other malfunctions, and introduce load balancing among highly interacting queues. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a non-homogeneous Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the expected number of buffered packets at user queues is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.

Efficient parallel tabu search for the blocking job shop scheduling problem

The Blocking Job Shop Scheduling (BJSS) is an NP-hard scheduling problem. It is obtained from the classical job shop scheduling problem by replacing the infinite buffer capacity constraint by a zero buffer capacity which introduces the blocking constraint. This constraint affects deeply the ability of meta-heuristics to find good solutions due to the low ratio of feasible to explored solutions. In this paper, we discuss the parallelization of the Tabu Search algorithm (TS) which represents one of the most widely used heuristics. Applying the classical TS neighborhood to the BJSS problem produces infeasible solutions in 98% of cases which leads to waste a valuable time in exploring infeasible solutions. For this reason, the use of a feasibility recovery strategy is unavoidable; however, the recovery step slows down considerably the TS algorithm. Therefore, incurring a huge time to explore a small area in the search space. To overcome this drawback and to accelerate the TS algorithm, we propose in this paper parallel multi-start TS approaches where several processes explore simultaneously the search space. Our parallelization exploits a cluster-based architecture with 512 CPU-cores. The obtained results show the positive impact of our proposed parallelization on the solution quality. Moreover, combining both the parallelism and the recovery strategy allowed us to improve the best result in the literature for a large number of known benchmarks.

Age of information performance of multiaccess strategies with packet management

We consider a system consisting of N source nodes communicating with a common receiver. Each source node has a buffer of infinite capacity to store incoming bursty traffic in the form of status updates transmitted in packets, which should maintain the status information at the receiver fresh. Packets waiting for transmission can be discarded to avoid wasting network resources for the transmission of stale information. We investigate the age of information (AoI) performance of the system under scheduled and random access. Moreover, we present analysis of the AoI with and without packet management at the transmission queue of the source nodes, where as packet management we consider the capability to replace unserved packets at the queue whenever newer ones arrive. Finally, we provide simulation results that illustrate the impact of the network operating parameters on the age performance of the different access protocols.

Two-machine hybrid flowshop scheduling with identical jobs: Solution algorithms and analysis of hybrid benefits

We study two-machine hybrid flowshop scheduling with identical jobs. Each job consists of two tasks, namely a flexible task and a fixed task. The flexible task can be processed on either machine, while the fixed task must be processed on the second machine. The fixed task can only be processed after the flexible task is finished. Due to different technological capabilities of the two machines, the flexible task has different processing times on the two machines. Our goal is to find a schedule that minimises the makespan. We consider two variants of the problem, namely no buffer and infinite buffer capacity between the two machines. We present constant-time solution algorithms for both variants. In addition, analysing the relationship between the hybrid benefits and performance difference between the two machines, we find that, for the infinite-buffer case, increasing the technological level of the second machine does not necessarily increase the hybrid benefits.

Performance Analysis of Cloud Computing Center with Queueing Model

Cloud computing is a novel raising computing resource allocation. Successful development of cloud computing paradigm necessitates explicit performance evaluation of cloud data centers. The computing resource allocation and performance managing have been one of the most important septets of cloud computing. In this paper, we consider the cloud center as a queuing system with single task arrivals and a task request buffer of infinite capacity. We assess the performance of queuing system by using an analytical model and solve it to obtain important performance factors like mean number of tasks in the system. Using this model in order to evaluate the performance analysis of cloud server farms and obtained solved it to obtain accurate estimation of complete probability distribution of the request response time and other paramount performance indicators.

Optimality of the fastest available server policy

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labeled FAS, is optimal among nonidling policies in queueing models with multiple independent Markov-modulated Poisson arrival processes and heterogeneous parallel exponential servers with server-dependent service rates. The criteria are to minimize the long-run average cost per unit time and the expected present value of the costs. We obtain results for loss and delay queueing models with finite- or infinite-capacity buffers under a first-come-first-served priority scheme. We analyze the robustness of the cost structure assumptions that are invoked in the proof of FAS optimality.

On the Stability of Static Poisson Networks Under Random Access

We investigate the stable packet arrival rate region of a discrete-time slotted random access network, where the sources are distributed as a Poisson point process. Each of the sources in the network has a destination at a given distance and a buffer of infinite capacity. The network is assumed to be random but static, i.e., the sources and the destinations are placed randomly and remain static during all the time slots. We employ tools from queueing theory as well as point process theory to study the stability of this system using the concept of dominance. The problem is an instance of the interacting queues problem, further complicated by the Poisson spatial distribution. We obtain sufficient conditions and necessary conditions for stability. Numerical results show that the gap between the sufficient conditions and the necessary conditions is small when the access probability, the density of transmitters, or the SINR threshold is small. The results also reveal that a slight change of the arrival rate may greatly affect the fraction of unstable queues in the network.

A MARKOVIAN ANALYSIS OF IEEE 802.11 BROADCAST TRANSMISSION NETWORKS WITH BUFFERING

The purpose of this paper is to analyze the so-called back-off technique of the IEEE 802.11 protocol in broadcast mode with waiting queues. In contrast to existing models, packets arriving when a station (or node) is in back-off state are not discarded, but are stored in a buffer of infinite capacity. As in previous studies, the key point of our analysis hinges on the assumption that the time on the channel is viewed as a random succession of transmission slots (whose duration corresponds to the length of a packet) and mini-slots during which the back-off of the station is decremented. These events occur independently, with given probabilities. The state of a node is represented by a two-dimensional Markov chain in discrete-time, formed by the back-off counter and the number of packets at the station. Two models are proposed both of which are shown to cope reasonably well with the physical principles of the protocol. The stability (ergodicity) conditions are obtained and interpreted in terms of maximum throughput. Several approximations related to these models are also discussed.

Estimation of Network Disordering Effects by In-depth Analysis of the Resequencing Buffer Contents in Steady-state

The paper is devoted to the analytic analysis of resequencing issue, which is common in packet networks, using queueing-theoretic approach. The authors propose the mathematical model, which describes the simplest setting of packet resequencing, but which allows one to make the first step in the in-depth-analysis of the queues dynamics in the resequencing buffer. Specifically consideration is given to N-server queueing system (N > 3) with single infinite capacity buffer and resequencing, which may serve as a model of packet reordering in packet networks. Customers arrive at the system according to Poisson flow, occupy one place in the buffer and receive service from one of the servers, which is exponentially distributed with the same parameter. The order of customers upon arrival has to be preserved upon departure. Customers, which violated the order are kept in resequencing buffer which also has infinite capacity. It is shown that the resequencing buffer can be considered as consisting of n, 1 ≤ n ≤ N −1, interconnected queues, depending on the number of busy servers, with i-th queue containing customers, which have to wait for i service completions before they can leave the system. Recursive algorithm for computation of the joint stationary distribution of the number of customers in the buffer and servers, and each queue in resequencing buffer are being obtained. Numerical examples, which show the dynamics of the characteristics of the queues in resequencing buffer are given.

A unified algorithm for finite and infinite buffer content distribution of Markov fluid models

This paper is interested in the asymptotic distribution of fluid models with finite or infinite buffer capacity. The probability distribution of the buffer content is controlled by a linear differential system with specific boundary conditions. All earlier methods are forced to test the singularity of the drift matrix before starting any computation. Also, the finite and infinite buffer capacity cases are treated differently. Our approach leads to a unified algorithm which is able to compute simultaneously the buffer workload distribution for finite and infinite buffer capacity without looking into the drift matrix singularity. The proposed method is not spectral and it is based on the uniformization technique. An example of a video traffic is firstly modeled by a Markovian fluid and secondly analyzed.

Optimality of the Fastest Available Server Policy

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labelled FAS, is optimal among non-idling policies in queuing models with multiple independent Markov-modulated Poisson arrival processes and heterogeneous parallel exponential servers with server-dependent service rates. The criteria are to minimize the long-run average cost per unit time and the expected present value of the costs. We obtain results for loss and delay queuing models with finite- or infinite-capacity buffers under a first-come-first serve priority scheme. We analyze the robustness of the cost structure assumptions that are invoked in the proof of FAS optimality.

Queueing Characteristics of the Best Effort Network Coding Strategy

Asynchronous network coding has the potential to improve wireless network performance compared with simple routing. However, to achieve the maximum network coding gain, the encoding node consumes a few computing and storage resources that may be unaffordable for wireless sensor networks such as CubeSats. An analogous threshold strategy, called best effort network coding (BENC), which requires only minimal storage resources and no computing resources, is investigated in this paper as an efficient and convenient method of network coding. In this strategy, a new packet arrival evicts the head packet when the queue is full to avoid excessively long waits. Moreover, in contrast to other methods that require a queue for each flow, the BENC uses only one queue for the two coded flows. In addition, the problem of time interval distribution for the output flow, which combines two independent flows, is investigated, and the network coding gain is then analyzed. While the maximum coding gain requires infinite buffer capacity under two independent Poisson arrivals with the same transmission rates, the calculation results show that the BENC needs only 4 buffers to achieve 90% of the maximum coding gain and can reach 99% of the maximum coding gain using 50 buffers. These results are verified by numerical simulations.

STRATEGIC DYNAMIC JOCKEYING BETWEEN TWO PARALLEL QUEUES

Consider a two-station, heterogeneous parallel queueing system in which each station operates as an independent M/M/1 queue with its own infinite-capacity buffer. The input to the system is a Poisson process that splits among the two stations according to a Bernoulli splitting mechanism. However, upon arrival, a strategic customer initially joins one of the queues selectively and decides at subsequent arrival and departure epochs whether to jockey (or switch queues) with the aim of reducing her own sojourn time. There is a holding cost per unit time, and jockeying incurs a fixed non-negative cost while placing the customer at the end of the other queue. We examine individually optimal joining and jockeying policies that minimize the strategic customer's total expected discounted (or undiscounted) costs over finite and infinite time horizons. The main results reveal that, if the strategic customer is in station 1 with ℓ customers in front of her, and q1 and q2 customers in stations 1 and 2, respectively (excluding herself), then the incentive to jockey increases as either ℓ increases or q2 decreases. Numerical examples reveal that it may not be optimal to join, and/or jockey to, the station with the shortest queue or the fastest server.

Scheduling in two-machine robotic cells with a self-buffered robot

ABSTRACTThis study considers a production cell consisting of two machines and a material handling robot. The robot has a buffer space that moves with it. Identical parts are to be produced repetitively in this flowshop environment. The problem is to determine the cyclic schedule of the robot moves that maximizes the throughput rate. After developing the necessary framework to analyze such cells, we separately consider the single-, double-, and infinite-capacity buffer cases. For single- and double-capacity cases, consistent with the literature, we consider one-unit cycles that produce a single part in one repetition. We compare these cycles with each other and determine the set of undominated cycles. For the single-capacity case, we determine the parameter regions where each cycle is optimal, whereas for the double-capacity case, we determine efficient cycles and their worst-case performance bounds. For the infinite-capacity buffer case, we define a new class of cycles that better utilizes the benefits of the buffer space. We derive all such cycles and determine the set of undominated ones.We perform a computational study where we investigate the benefits of robots with a buffer space and the effects of the size of the buffer space on the performance. We compare the performances of self-buffered robots, dual-gripper robots, and robots with swap ability.