Queue Content Research Articles

Analysis of Discrete-Time Queues with Branching Arrivals

We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply π-thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes.

Predictive Lossless Queue for Extremely Large Dataset Transfer in Markov Communication Systems

In this paper, a parametric prediction model is proposed for a queuing system driven by the Markov process. The aim of the model is to minimize the packet loss caused by time dependency characterized by the queue tail being too long, resulting in a time-out during the transfer of a large dataset. The proposed technique requires the key parameters influencing the queue content to be determined prior to its occupation regardless of the server capacity definition, using Bayesian inference. The subsequent time elapsing between the arrival and departure of a packet in the system is given, as well as the system load. This queue content planning is considered as the Markov birth-death chain; a type of discretization that characterizes almost all queuing systems, leading to an exponential queue, and captured herein using beta distribution. The inference results obtained using this exponential queue indicate that the queue with predictive parameters employing beta distribution, even when dealing with a loss system queue, involves less transition time and a greater load than a queue with coarse parameters; hence, preventing a long tail in the queue which is the cause of packet loss.

Reachability Problems on Reliable and Lossy Queue Automata

We study the reachability problem for queue automata and lossy queue automata. Concretely, we consider the set of queue contents which are forwards resp. backwards reachable from a given set of queue contents. Here, we prove the preservation of regularity if the queue automaton loops through some special sets of transformation sequences. This is a generalization of the results by Boigelot et al. and Abdulla et al. regarding queue automata looping through a single sequence of transformations. We also prove that our construction is possible in polynomial time.

On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation

This article considers a single server, infinite buffer, bulk service Poisson queue with single and multiple vacation. The customers are served in batches following ‘general bulk service’ (GBS) rule. The customers are arriving according to the Poisson process, and the service time of the batches follows an exponential distribution. Using bivariate probability generating function (PGF) method the steady-state joint distributions of the queue content and server content (when server is busy), and joint distribution of the queue content and type of the vacation taken by the server (when server is in vacation) have been obtained. Here by the ‘type of the vacation’ we mean the queue length at vacation initiation epoch. The information about these joint distributions may help in increasing the system performance. Finally, several numerical examples are carried out using MAPLE software to verify the analytical results.

Minimizing CPU Utilization Requirements to Monitor an ATLAS Data Transfer System

The ATLAS experiment at LHC will use a PC-based read-out component called FELIX to connect its front-end electronics to the Data Acquisition System. FELIX translates custom front-end protocols to Ethernet and vice versa. Currently, FELIX makes use of parallel multi-threading to achieve the data rate requirements. In order to establish the FELIX operation conditions, monitoring of its parameters is necessary. This includes, but is not limited to, data counters and rates as well as compute resource utilisation. However, for these statistics to be of practical use, the parallel threads are required to intercommunicate. The FELIX monitoring implementation prior to this research utilized thread-safe queues to which data was pushed from the parallel threads. A central thread would extract and combine the queue contents. Enabling statistics would deteriorate the throughput to less than a fifth of the baseline performance. To minimize this performance hit to the greatest extent, we take advantage of the CPU's microarchitecture features and reduce concurrency. The focus is on hardware-supported atomic operations. When a thread performs an atomic operation, the other threads see it as happening instantaneously. They are used to complement and/or replace parallel computing lock mechanisms. The aforementioned queue system gets replaced with sets of C/C++ atomic variables and corresponding atomic functions, hereinafter referred to as atomics. Three implementations are tested. Implementation I has one set of atomic variables being updated by all the parallel threads. Implementation II has a set of atomic variables for every thread. These sets are periodically accumulated by a central thread. Implementation III is the same as implementation II, but appropriate measures are taken to eliminate any concurrency implications. The compiler used during the measurements is GCC, which supports the hardware (microarchitecture) optimizations for atomics. Implementations I and II resulted in negligible differences compared to the original one. Some benchmarks even show deterioration of the performance. Implementation III (concurrency & cache optimized) yields results with a performance improvement of up to six-fold increase compared to the original implementation. Achieved throughput is significantly closer to what is desirable. Similar structured software applications could benefit from the results of this research, especially Implementation III. The results presented demonstrate that atomics can be useful for efficient computations in a multi-threaded environment. However, from the results, it is clear that concurrency, cache invalidation and proper usage of the system's microarchitecture needs to be taken into account in this programming model. The paper details the challenges of properly using atomics and how they are overcome in the implementation of the FELIX monitoring system.

On finite-buffer batch-size-dependent bulk service queue with queue-length dependent vacation

ABSTRACT This paper considers a single server finite-buffer batch-size-dependent bulk service queue with queue-length dependent vacation. Customers arrive at the system according to the Poisson process and are served in batches of maximum size ‘b’ with a minimum threshold value ‘a’ following the ‘general bulk service’ rule. The service time distribution is assumed to be of general type which modulates depending on serving batch size. The server is allowed to take vacation, either single or multiple vacations, whenever permissible numbers of customers are not found in the queue at the beginning of the service. The vacation time distribution is assumed to be of general type and dynamically changes depending on the queue content at vacation initiation epoch. We use the supplementary variable and the embedded Markov chain techniques to obtain the steady-state joint distribution of the queue content service batch size, queue content and type of vacation taken by the server at various epochs. Several numerical results are presented at the end to bring out the qualitative aspect of the model, which reveals the fact that queue-length dependent vacation further reduces congestion in the batch-size-dependent bulk service queues.

Dynamic bandwidth allocation algorithms for improved throughput and latency performance in CDMA-based next-generation ethernet passive optical networks

In this paper, we propose new scheduling algorithms to improve the performance of the code division multiple access (CDMA) enabled next generation ethernet passive optical networks (NG-EPON). The original dynamic bandwidth allocation (DBA) scheme based on a round robin scheduling algorithm was originally proposed for the first generation CDMA based EPON where the network throughput and delay requirements per optical network unit (ONU) are relatively moderate. On the other hand, in the NG-EPON standard, the network capacity is increased up to 100 Gb/s and stringent requirements are applied to the packet delay. For this reason, in this work, we propose new scheduling algorithms for NG-EPON to assign a grant size on each upstream CDMA code in order to guarantee the newly required network throughput and delay performance. The first DBA algorithm is the first in first out (FIFO) algorithm in which the ONU requests are ordered in terms of their request arrival time. The second scheme is the reservation pattern (RP) algorithm in which each ONU starts transmitting its queue content in its reserved pattern of subcycles following a pre-defined pattern. The performances of the newly proposed algorithms are evaluated and compared. Results show that both newly proposed scheduling schemes can significantly improve the network performance in terms of the packet delay, jitter, and throughput. In addition, the results are compared to many dynamic wavelength and bandwidth allocation (DWBA) algorithms. The results show that the performances are comparable and that CDMA can be a good alternative for WDM for multi-channels based NG-EPON.

A procedure to approximate the mean queue content in a discrete-time generalized processor sharing queue with Bernoulli arrivals

Generalized Processor Sharing is a notoriously hard model to analyze. In earlier work we derived an iterative procedure to calculate coefficients for a power series of the joint probability generating function of the stationary queue content. This procedure posed computational limitations on the possible number of coefficients calculable for the performance measures, such as mean queue content. In this paper, we propose a direct approach and derive a procedure to directly calculate the power series for these performance measures, thus eliminating the problems associated with the probability generating function. The result is a procedure of complexity O(N3) to calculate the first N coefficients of the mean queue content. Finally, the approximations are compared and validated with simulations.

Internet Provisioning in VANETs: Performance Modeling of Drive-Thru Scenarios

Drive-thru-Internet is a scenario in cooperative intelligent transportation systems (C-ITSs), where a road-side unit (RSU) provides multimedia services to vehicles that pass by. Performance of the drive-thru-Internet depends on various factors, including data traffic intensity, vehicle traffic density, and radio-link quality within the coverage area of the RSU, and must be evaluated at the stage of system design in order to fulfill the quality-of-service requirements of the customers in C-ITS. In this paper, we present an analytical framework that models downlink traffic in a drive-thru-Internet scenario by means of a multidimensional Markov process: the packet arrivals in the RSU buffer constitute Poisson processes and the transmission times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we use iterative perturbation techniques to calculate the stationary distribution of the Markov chain. Our numerical results reveal that the proposed approach yields accurate estimates of various performance metrics, such as the mean queue content and the mean packet delay for a wide range of workloads.

On the distribution of an infinite-buffer queueing system with versatile bulk-service rule under batch-size-dependent service policy: M/G^(a,Y)_n/1

Batch-service queues have a wide range of noteworthy applications in wireless telecommunication to deal with the multimedia type of data, manufacturing systems, group testing procedure, etc. The knowledge of both the queue and server content distributions helps the system designer to evaluate the efficiency of the queueing system in a better way. We analyse a single server infinite-buffer batch-size-dependent service queue with Poisson arrival and versatile batch-service rule. Based on supplementary variable technique, a bivariate probability generating function, the entire spectrum of new contributions, of queue content and number in a served batch at departure epoch is derived. Moreover, we perceive the complete queue and server content distribution at departure as well as arbitrary epochs. The utility of analytical results is illustrated by the inclusion of some numerical examples, which also includes the investigation of multiple zeroes.

Taylor-series approximations for queues with arrival correlation

• We propose a queueing model with session-based arrivals, where sessions are not always active. • We analyse the system in the light traffic regime, by Taylor series expansion techniques. • We find explicit expressions for the 3rd order expansions of the first two moments of the queue content. • Combining light and heavy traffic approximations covers a large part of parameter space. • We formally prove the existence of the Taylor series expansions . This paper studies a discrete-time single-server queueing system with correlated arrivals. Arrivals at the queue stem from a number of active sessions, each generating a packet in a slot with a fixed probability q . Since an exact queueing analysis is not feasible for q ≠ 1, we rely on Taylor-series expansions of the joint probability generating functions of the number of active sessions and the queue content around q = 0 . These expansions are then either combined with the known generating function for q = 1 if the system is stable for q = 1 , or with heavy-traffic results if this is not the case. In either case, we obtain expressions for the moments of queue content and packet delay and assess the accuracy of our approximations by a simulation study.

Delay-Based Service Differentiation with Many Servers and Time-Varying Arrival Rates

We study the problem of staffing (specifying a time-varying number of servers) and scheduling (assigning newly idle servers to a waiting customer from one of [Formula: see text] classes) in the many-server V model with class-dependent time-varying arrival rates. In order to stabilize performance at class-dependent delay targets, we propose the blind (model-free) head-of-line delay-ratio (HLDR) scheduling rule, which extends an earlier dynamic-priority rule that exploits the head-of-line delay information. We study the HLDR rule in the quality-and-efficiency-driven many-server heavy-traffic (MSHT) regime. We staff to the MSHT fluid limit plus a control function in the diffusion scale. We establish a MSHT limit for the Markov model, which has dramatic state-space collapse, showing that the targeted ratios are attained asymptotically. In the MSHT limit, meeting staffing goals reduces to a one-dimensional control problem for the aggregate queue content, which may be approximated by recently developed staffing algorithms for time-varying single-class models. Simulation experiments confirm that the overall procedure can be effective, even for non-Markov models. The online appendix is available at https://doi.org/10.1287/stsy.2018.0015 .

Modeling data backups as a batch-service queue with vacations and exhaustive policy

For data backup processes to cloud infrastructure, there is a clean trade off between backing up frequently (improving data safety) and reducing resource usage (power consumption and communication cost). With rapid growth of data storage requirements in recent years, we need to find the right balance between both objectives. To explicitly address this trade off, we model a wide set of exhaustive data backup processes as a general batch service queueing model with multiple vacations and probabilistic restarts.We study this queueing model and establish expressions for its performance measures such as system content and queue content distributions. This analysis aids in computing Quality of Service (QoS) measures of the data backup process such as the fraction of time the backup server is busy, the frequency of new connections and the age of the data at the beginning of a backup period. This enables us to quickly examine the dependence of QoS on the model parameters as well as to compute the optimal parameters in the backup process. We illustrate the latter by defining a particular cost function of a user and by framing an optimization problem.

Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state–space grows exponentially with the number of queues involved. To cope with this inherent state–space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space.

Delay-Aware ABS Adjustment to Support QoS for Real-Time Traffic in LTE-A HetNet

To solve interference in a heterogeneous network, LTE-A uses almost blank subframe (ABS) to improve channel quality of picocells at the expense of macrocell’s transmission. Many studies find the ABS ratio based on user number or traffic load. However, the issue of real-time (RT) packet delay is not well studied. We thus develop a delay-aware ABS adjustment (DA3) method to improve performance and lower packet dropping. DA3 estimates cells’ capacity to decide the ratio, and analyzes queue content to alleviate packet discard. Simulation results show that DA3 increases cells’ goodput while reducing RT packet dropping.

Shot-noise fluid queues and infinite-server systems with batch arrivals

We show how a shot-noise fluid queue can be considered as the limiting case of a sequence of infinite-server queues with batch arrivals. The shot-noise queue we consider receives fluid amounts at the arrival times of a (time-inhomogeneous) Poisson process, the sizes of which are governed by some probability distribution that may also depend on time. The continuous rate at which fluid leaves the queue is proportional to the current content of the queue. Thus, intuitively, one can think of drops of fluid arriving in batches, which are taken into service immediately upon arrival, at an exponential service rate.We show how to obtain the partial differential equation for (the Laplace–Stieltjes transform of) the queue content at time t, as well as its solution, from the corresponding infinite-server systems by taking appropriate limits. Also, for the special case of a time-homogeneous arrival process, we show that the scaled number of occupied servers in the infinite-server system converges as a process to the shot-noise queue content, implying that finite-dimensional distributions also converge.

A supply chain management model to optimise the sorting capability of a ‘third party logistics’ distribution centre

In this paper, the process flow within a high-end 3PL distribution centre is studied in order to determine the optimal split between the parcel size categories moved within the system. The article considers the application of an optimisation (MIQP) model with a corresponding discrete event simulation model to validate the authenticity of the solution. The study assumes that the current process flow and layout of the centre remains fixed; the entering and exiting routes to and from the centre and the centre itself are located optimally within the network and the models have base times of one and seven days respectively. Performance measures have been analysed through utilization states of equipment and labour, queue contents versus time and average throughput times of each of the parcel categories. The findings in this paper can create a positive trigger for improvement within the distribution centre as equipment and labour can be downsized to decrease costs and improve safety and benefit the company through the alignment of a network of distribution centres that each applies modified relevant versions of the modelling logic conveyed in this paper.

Performance evaluation and validation of session-expiration scheduling technique for queued CAMs in vehicular ad-hoc networks

The paper proposes a CAM scheduling model, namely Session-Expiration Scheduling (SES), for managing CAMs broadcast over the CCH. The model associates a timestamp with each CAM as it enters the MAC layer of the vehicle so as to facilitate prioritisation to unexpired recent CAMs over outdated CAMs. The expired CAMs at each stage of the model are discarded from the network to avoid dissemination of outdated messages on the CCH. This perhaps provides the network with optimum utilisation of limited bandwidth resources. The performance of the model is analysed in terms of channel utilisation, average waiting time and the average queue content using MATLAB 15. Confidence interval testing along with the statistical hypothesis testing is done to evaluate the accuracy and efficiency of the proposed work. It is evident that our obtained simulation results provide 95% confidence for the proposed model.

Performance evaluation and validation of session-expiration scheduling technique for queued CAMs in vehicular ad-hoc networks

The paper proposes a CAM scheduling model, namely Session-Expiration Scheduling (SES), for managing CAMs broadcast over the CCH. The model associates a timestamp with each CAM as it enters the MAC layer of the vehicle so as to facilitate prioritisation to unexpired recent CAMs over outdated CAMs. The expired CAMs at each stage of the model are discarded from the network to avoid dissemination of outdated messages on the CCH. This perhaps provides the network with optimum utilisation of limited bandwidth resources. The performance of the model is analysed in terms of channel utilisation, average waiting time and the average queue content using MATLAB 15. Confidence interval testing along with the statistical hypothesis testing is done to evaluate the accuracy and efficiency of the proposed work. It is evident that our obtained simulation results provide 95% confidence for the proposed model.

Modeling and analysis of an infinite-buffer batch-arrival queue with batch-size-dependent service: [formula omitted

This paper considers a single-server infinite-buffer queue with batch-arrival, batch-service, and generally distributed batch-size-dependent service time. Based on supplementary variable technique by considering supplementary variable as remaining service time of batch in service, a bivariate probability generating function, the entire spectrum of new contributions, of queue content and number in a served batch at departure epoch is derived. We extract the joint distribution of these quantities and present them in terms of the roots of the associated characteristic equation. In addition, departure epoch probabilities are utilized to obtain joint distribution at arbitrary epoch while the later one are employed to acquire joint distribution at pre-arrival epoch. Finally, some numerical results demonstrate the proposed procedure where occurrence of multiple roots is included. Moreover, some graphical representations show that batch-size-dependent service is more potent as compared to batch-size-independent service.