Tandem Queueing Model Research Articles

Towards Impact of Chunk-Level Characteristics on Mobile Live Streaming Performance

Today, mobile live streaming is gaining a rapid growth in use, which refers to watching the media content recorded and broadcast in real time on mobile devices. In live streaming process, each video segment must go through recording, encoding, uploading, transcoding, publishing, downloading, decoding before playback. The ingest algorithm inside the streamer decides the upload bitrate, while the adaptive bitrate (ABR) algorithm inside the player determines the download bitrate. Thanks to the chunked CMAF standard, each segment is split into smaller chunks that can be independently encoded, transferred, decoded and played. It is of great help to quantify the impact of chunk-level characteristics on mobile live streaming performance. In this paper, we establish a tandem queuing model to describe the whole streaming system. Based on the model, we respectively characterize rebuffering probability, rebuffering count, streaming latency, and average bitrate, analyzing the impact of chunk upload and download rates, upload and download time variances, startup threshold and chunk length on them. From analysis results, we propose insights and recommendations for bitrate adaptation in mobile live streaming and design simple heuristic ingest and ABR algorithms leveraging them. Extensive simulations verify the insights as well as effectiveness of designed algorithms.

A two server tandem queueing model with Markovian arrival process, phase type service, working vacation, feedback, re-service, unreliable server, interrupted closedown and customers intolerance.

A two server tandem queueing model with Markovian arrival process, phase type service, working vacation, feedback, re-service, unreliable server, interrupted closedown and customers intolerance.

Coordinating Vehicle Platoons for Highway Bottleneck Decongestion and Throughput Improvement

Truck platooning is a technology that is expected to become widespread in the coming years. Apart from the numerous benefits that it brings, its potential effects on the overall traffic situation need to be studied further, especially at bottlenecks and ramps. Assuming we can control the platoons from the infrastructure, they can be used as controlled moving bottlenecks, actuating control actions on the rest of the traffic, and potentially improving the throughput of the whole system. In this work, we use a tandem queueing model with moving bottlenecks as a prediction model to calculate control actions for the platoons. We use platoon speeds and formations as control inputs, and design a control law for throughput improvement of a highway section with a stationary bottleneck. By postponing and shaping the inflow to the bottleneck, we are able to avoid capacity drop, which significantly reduces the total time spent of all vehicles. We derived the estimated improvement in throughput that is achieved by applying the proposed control law, and tested it in a simulation study, with multi-class cell transmission model with platoons used as the simulation model, finding that the median delay of all vehicles is reduced by 75.6% compared to the uncontrolled case. Notably, although they are slowed down while actuating control actions, platooned vehicles experience less delay compared to the uncontrolled case, since they avoid going through congestion at the bottleneck.

Модель оценки сквозной задержки пакетов для цепочки NFV узлов в сетях пятого поколения

It is expected that future communication networks will provide configurable delay-sensitive types of services (for example, streaming video, machine interaction). To support a variety of applications and use cases of servers providing various functions, you can use network function virtualization (NFV), which will be able to provide flexible implementation and placement of configuration of the necessary network functions. This article analyzes the end-to-end packet latency (E2E) for multiple traffic flows passing through the chain of embedded virtual network functions (VNF) in fifth-generation communication networks (5G). The Dominant of Generalized Resource Processing (DR-GPS) is used to distribute computing resources and transfer data between threads in each node of Network Function Virtualization (NFV) to achieve equitable distribution and utilization of available resources. The tandem queuing model is designed for incoming packets combined in several streams passing through the NFV node and its outgoing transmission channel. To analyze manageability, we separate packet processing (and transmission) of various streams in the simulation and determine the average packet processing and transmission rates of each stream as approximate service speeds.

The calibration method of a tandem queueing model with PH service time using NS-3 simulation of a multihop wireless network

End-to-end delay is one of the key characteristics of communication network performance. This characteristic determines the possibility of using the network for various delay-critical applications like voice or video transmission. One of the widely used approaches to estimating delays is the use of the queuing theory. According to this approach, a telecommunication network is modeled using a multiphase queuing system. Communication channels are modeled using service devices, and the incoming traffic is modeled with random distributions of the inter-arrival intervals between packets. The accuracy of this network model directly depends on how well the service time distributions are chosen. These distributions must consider the specifics of complex telecommunication protocols, size distributions of the transmitted packets, and, in case of wireless channels, the rate of collisions and retransmissions. The paper presents a study of the accuracy of estimates of end-to-end delays in a multi-hop wireless network using a queuing network with a phase-type (PH) service time distributions. To calibrate the model, PH distributions are found using the moments-matching method based on sample data on the duration of packet transmission in IEEE 802.11 channels. This sample data was obtained using a simulation model written in NS-3, taking into account the features of the IEEE 802.11 protocol and the presence of collisions in the network. To evaluate the accuracy, end-to-end delays are calculated using the queuing network and the wireless network simulation model. It is shown that it is possible to obtain reasonably accurate estimates for small networks, but with an increase in the size of the network, the accuracy decreases. In conclusion, recommendations are given to improve the accuracy of modeling.

Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System

In this paper, a new blocked tandem queueing model is given and analysed. The arrival process to this queueing model is Poisson with parameter λ. There is one service unit at the first stage of the system, and the service time of this unit is exponentially distributed with $μ_1$ parameter. There are two parallel service units at the second stage, and the service time of these service units are exponentially distributed with parameters $μ_2$ and $μ_3$. No queue is allowed at the first stage of the system. Upon completing service at the first stage, a customer proceeds to the second stage if at least one of the service units at the second stage is available. If both service units at the second stage are busy, the customer blocks the service unit at the first stage, which results in loss. The most important measure of performance of this queueing system is the loss probability $π_{loss}$. First of all, the state probabilities of the system are obtained and then using these probabilities, the steady-state distribution of the system is obtained. Transition probabilities of the system are calculated by using steady-state probabilities, and finally an equation is obtained for $π_{loss}$ in terms of transition probabilities. Furthermore, another measure of performance, the mean number of customers, is obtained in terms of transition probabilities. Since the Equation for $π_{loss}$ is very complex, a numerical method is used to calculate the minimum $π_{loss}$ probabilities. After numerical optimal $π_{loss}$ calculations, a simulation of the queueing system is done, and it is seen that the obtained numerical $π_{loss}$ values tend to simulation results.

Delay Analysis in IoT Sensor Networks.

Internet of Things (IoT) devices, particularly those used for sensor networks, are often latency-sensitive devices. The topology of the sensor network largely depends on the overall system application. Various configurations include linear, star, hierarchical and mesh in 2D or 3D deployments. Other applications include underwater communication with high attenuation of radio waves, disaster relief networks, rural networking, environmental monitoring networks, and vehicular networks. These networks all share the same characteristics, including link latency, latency variation (jitter), and tail latency. Achieving a predictable performance is critical for many interactive and latency-sensitive applications. In this paper, a two-stage tandem queuing model is developed to estimate the average end-to-end latency and predict the latency variation in closed forms. This model also provides a feedback mechanism to investigate other major performance metrics, such as utilization, and the optimal number of computing units needed in a single cluster. The model is applied for two classes of networks, namely, Edge Sensor Networks (ESNs) and Data Center Networks (DCNs). While the proposed model is theoretically derived from a queuing-based model, the simulation results of various network topologies and under different traffic conditions prove the accuracy of our model.

Joint DNN Partition Deployment and Resource Allocation for Delay-Sensitive Deep Learning Inference in IoT

Nowadays, the widely used Internet-of-Things (IoT) mobile devices (MDs) generate huge volumes of data, which need analyzing and extracting accurate information in real time by compute-intensive deep learning (DL) inference tasks. Due to its multilayer structure, the deep neural network (DNN) is appropriate for the mobile-edge computing (MEC) environment, and the DL tasks can be offloaded to DNN partitions deployed in MEC servers (MECSs) for speed-up inference. In this article, we first assume the arrival process of DL tasks as Poisson distribution and develop a tandem queueing model to evaluate the end-to-end (E2E) inference delay of DL tasks in multiple DNN partitions. To minimize the E2E delay, we develop a joint optimization problem model of partition deployment and resource allocation in MECSs (JPDRA). Since the JPDRA is a mixed-integer nonlinear programming (MINLP) problem, we decompose the original problem into a computing resource allocation (CRA) problem with fixed partition deployment decision and a DNN partition deployment (DPD) problem that optimizes the optimal-delay function related to the CRA problem. Next, we design a CRA algorithm based on Markov approximation and a low-complexity DPD algorithm to obtain the near-optimal solution in the polynomial time. The simulation results demonstrate that the proposed algorithms are more efficient and can reduce the average E2E delay by 25.7% with better convergence performance.

Modeling and Performance Analysis for Satellite Data Relay Networks Using Two-Dimensional Markov-Modulated Process

Satellite Data Relay Networks (SDRNs) play an important role in the data relay from User Satellites (USs) to ground stations by Tracking Data Relay Satellites (TDRSs). For better exploitation of SDRNs, the development of the systematic model and accurate system analysis is essential. To describe the end-to-end data transmission in SDRNs, we construct an MMOO/MMSP/1/K-G/G/1 tandem queuing model where the two parts depict the traffic arrival and transmission service of USs and TDRSs, respectively. Because the active and inactive periods of the data transmission are determined by the visibility between two satellites, classical buffer state based vacation policies become imprecise. Moreover, these two kinds of periods appear alternatively and their duration varies over time so that it is hard to model such intermittent transmission by existing service models. To overcome these difficulties, we propose a Markov Chain Monte Carlo based Markov Modulated Service Process (MMSP) which can tightly match the distributions of the active and inactive periods. In this process, we propose two algorithms to calculate the service state transition probability and the number of the sub-states in each service state, respectively, which guarantees the alternative transition between the active and inactive states as well as the sojourn time spent in each state. For the quality of service analysis, we find the different features of the queue variation under different arrival and service rate conditions. By separately calculating the related mean queue lengths and emergence probabilities, we first derive the expressions of the system loss probability, mean queue length, and mean delay. Finally, we conduct numerous simulations to verify the accuracy of our system model and performance evaluation, which provides the guidance to the buffer design and transmission resource allocation.

Prediction of Two-Node Tandem Queue with Feedback Having State and Time Dependent Service Rates

Queuing networks are current area of great research and application interest, in view of their increased applicability in - modelling manufacturing facilities and computer/communication networks, production and assembly lines, hospitals, transport systems, banks and so forth. The present paper develops and analyses a tandem queuing model having two nodes with feedback. Such type of model finds its application in many fields, e.g. telecommunication, inventory, hospitals, traffic control and so on. For example, in hospitals, a patient first visits the doctor and goes through a series of examinations, after which he revisits the doctor for medication. The inter-arrival time is exponentially distributed, whereas the service rate for each node depends on the aggregate of customers in the respective queues and thus follows non-homogeneous Poisson process. After constructing the difference –differential equations, and using PGF technique, we have obtained the joint probability distribution for queue size. Some key measures such as the “average number of customers in queue”, “utilization time of each queue”, “average waiting time in each queue” are computed.

Multi Node Tandem Queuing Model with Binomial Bulk Size Distribution Having Load Dependent Service

In this article we study a multi node tandem queuing model consisting of K-nodes in which the customers arriving in batches to the first queue and after receiving service they will be directed with some node specific probability to join any one of the (K-1) parallel queues which are connected to first queue in series and exit from the system after getting service. It is assumed that the arrival and service completions follow Poisson processes and service rates depend on number of customers in the queue connected to it. Here the bulk arrivals are assumed to be Binomially distributed. Using difference differential equations the joint probability function is derived and performance measures such as average number of customers, waiting time of customer, throughput of each service station, utilization of each server, variance of number of customers in each queue are derived explicitly. A numerical illustration is provided to understand the theoretical results. Sensitivity analysis of the system behavior with regards to the arrival rates and load dependent service distribution parameters is carried out. A comparison between transient and study state behavior is also done .

Modeling multi-stage healthcare systems with service interactions under blocking for bed allocation

Balancing bed allocation is a critical but cumbersome decision-making process in hospitals due to limited capacity, fluctuations in the rate of patient arrival and service interactions among various units; typically, this will cause blockages in multi-stage healthcare services. Accurately estimating the blocking probability is an important task in order to improve the performance of healthcare systems. Early studies assumed either unlimited bed capacity or no service interaction among units. In this study, we consider the correlation between the blockage and service time of the subsequent stage and apply a multi-stage tandem-queuing model with limited bed capacity and service interactions to model healthcare systems. We develop two effective heuristics to estimate the patient-blocking probability, which are then used to develop an integrated mathematical model for bed allocation. We collect real-world data from a tertiary hospital in China to delineate the effect of service interactions while estimating the blocking probability and use non-parametric rank-sum tests to verify and compare the relative performances of the proposed model against two popular heuristics. Our comparative results illustrate that the proposed model is as accurate as simulations. We also observe that increasing the number of beds during the first stage is more effective in reducing blockage than doing so later in case of a limited number of beds.

End-to-End Delay Modeling for Embedded VNF Chains in 5G Core Networks

In this paper, an analytical end-to-end (E2E) packet delay modeling is established for multiple traffic flows traversing an embedded virtual network function (VNF) chain in fifth generation communication networks. The dominant-resource generalized processing sharing is employed to allocate both computing and transmission resources among flows at each network function virtualization (NFV) node to achieve dominant-resource fair allocation and high resource utilization. A tandem queueing model is developed to characterize packets of multiple flows passing through an NFV node and its outgoing transmission link. For analysis tractability, we decouple packet processing (and transmission) of different flows in the modeling and determine average packet processing and transmission rates of each flow as approximated service rates. An M/D/1 queueing model is developed to calculate packet delay for each flow at the first NFV node. Based on the analysis of packet interarrival time at the subsequent NFV node, we adopt an M/D/1 queueing model as an approximation to evaluate the average packet delay for each flow at each subsequent NFV node. The queueing model is proved to achieve more accurate delay evaluation than that using a G/D/1 queueing model. Packet transmission delay on each embedded virtual link between consecutive NFV nodes is also derived for E2E delay calculation. Extensive simulation results demonstrate the accuracy of our proposed E2E packet delay modeling, upon which delay-aware VNF chain embedding can be achieved.

On two node tandem queueing model with time dependent service rates

Queueing is a phenomenon associated with congestion. For controlling congestion and to utilize the resources optimally the queueing models are developed. In queueing models, it is customary to consider that the arrival and service processes are stable and follows a Poisson process. But in many systems the service process is time dependent and it can be well characterized by non-homogeneous Poisson process. This paper introduces a tandem queueing model with non-homogeneous Poisson service process. The system performance is analysed by deriving the system performance measure such as, average content of the queues, average waiting time of a customer in the queue and in the system, the throughput of transmitters, and the variance of the number of customers in the system. The effect of various changes in parameter on the system performance measures is carried through sensitivity analysis. It is observed that the time dependent service rate has significant influence on the system performance measures. This model can accurately predict the performance measures, when the service rates are time dependent. Several of the earlier models become particular cases of this model.

Optimal dispatching in a tandem queue

We investigate a Markovian tandem queueing model in which service to the first queue is provided in batches. The main goal is to choose the batch sizes so as to minimize a linear cost function of the mean queue lengths. This model can be formulated as a Markov Decision Process (MDP) for which the optimal strategy has nice structural properties. In principle we can numerically compute the optimal decision in each state, but doing so can be computationally very demanding. A previously obtained approximation is computationally efficient for low and moderate loads, but for high loads also suffers from long computation times. In this paper, we exploit the structure of the optimal strategy and develop heuristic policies motivated by the analysis of a related controlled fluid problem. The fluid approach provides excellent approximations, and thus understanding, of the optimal MDP policy. The computational effort to determine the heuristic policies is much lower and, more importantly, hardly affected by the system load. The heuristic approximations can be extended to models with general service distributions, for which we numerically illustrate the accuracy.

Forked queueing model with load dependent service rate and bulk arrivals

In this paper a forked two-node tandem queueing model with load dependent service rates having bulk arrivals is introduced and analysed under transient and equilibrium conditions. The system performance measures like probability of emptiness of the system, the probabilities of emptiness of marginal queues, the average number of customers in each queue, the average waiting time of the customer in each queue, the throughput of each node, the utility of servers and the variance of the number of customers in each queue are derived and analysed. The sensitivity analysis of a model reveals that the bulk size distribution parameters has a significant influence on system performance measures. Through numerical studies, it is observed that the load dependent service rates can reduce the congestion in queues and mean delay. A comparative study of the model with respect to equilibrium and transient conditions reveal that the time has significant influence on the performance measures. This model also includes some of the earlier models as particular cases for specific values of the parameters.

Jitter analysis of real-time services in IEEE 802.15.4 WSNs and wired IP concatenated networks

It is challenging and significant to explore the impacts of non-real-time services on real-time services from the perspective of jitter. Most of current researches on jitter made too many mathematical hypotheses on networks and traffic. This paper puts forward a tandem queuing model to characterize the real communication scenario where heterogeneous services are served by IEEE 802.15.4 wireless sensor networks (WSNs), and then the packets served successfully are fed to Internet protocol (IP) networks. By analyzing the contention access processes in IEEE 802.15.4 WSNs, the authors derive the departure processes of the two types of services, i.e., the arrival processes of IP networks. The IP network is modeled as a queuing system, in which the real-time service is forwarded accompanied by the non-real-time service. Investigating the jitter of real-time services is intractable. Therefore, this paper abstracts this problem as a dynamic queuing system evolving on a dynamic time interval. Referring the transient analysis method (TAM), this paper obtains the queue length in a random time interval which is scaled by the arrival of real-time services. Queue length evolution is closely connected with the jitter. Benefiting from the derivation in probability generation domain, the jitter of real-time services is obtained.

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACTIn this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 − α − β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.

The Analysis, Optimization, and Simulation of a Two-Stage Tandem Queueing Model with Hyperexponential Service Time at Second Stage

The aim of this paper is to analyze a tandem queueing model with two stages. The arrivals to the first stage are Poisson stream and the service time at this stage is exponential. There is no waiting room at first stage. The service time is hyperexponential and no waiting is allowed at second stage. The transition probabilities and loss probabilities of this model are obtained. In addition, the loss probability at second stage is optimized. Performance measures and the variance of the numbers of customers of this tandem queueing model are found. It is seen that the numbers of customers in first stage and second stage are dependent. Finally we have simulated this queueing model. For different values of parameters, exact values, simulated values, and optimal values of obtained performance measures of this model are numerically shown in tables and graphs.

A Tandem Queueing model for an appointment-based service system

We develop a queueing model for an appointment-based service system that consists of two queues in tandem: the appointment queue followed by the service queue. Customers join the appointment queue when they call for appointments, stay there (not physically) until the appointment time comes, and then leave the appointment queue and may physically join the service queue, and wait there until served, or become a no-show. The probability of becoming a no-show depends on the time spent in the appointment queue. We build a Tandem Queue model that explicitly captures the dependence between these two queues. We then derive several performance measures of interest, such as service utilization and customer long-run average waiting times in both queues. We also develop several approximation methods to compute the long-run average waiting time in the service queue, including one which is particularly useful when service times in that queue are not exponential.