Generalized Processor Sharing Research Articles

On-Demand Centralized Resource Allocation for IoT Applications: AI-Enabled Benchmark

The development of emerging information technologies, such as the Internet of Things (IoT), edge computing, and blockchain, has triggered a significant increase in IoT application services and data volume. Ensuring satisfactory service quality for diverse IoT application services based on limited network resources has become an urgent issue. Generalized processor sharing (GPS), functioning as a central resource scheduling mechanism guiding differentiated services, stands as a key technology for implementing on-demand resource allocation. The performance prediction of GPS is a crucial step that aims to capture the actual allocated resources using various queue metrics. Some methods (mainly analytical methods) have attempted to establish upper and lower bounds or approximate solutions. Recently, artificial intelligence (AI) methods, such as deep learning, have been designed to assess performance under self-similar traffic. However, the proposed methods in the literature have been developed for specific traffic scenarios with predefined constraints, thus limiting their real-world applicability. Furthermore, the absence of a benchmark in the literature leads to an unfair performance prediction comparison. To address the drawbacks in the literature, an AI-enabled performance benchmark with comprehensive traffic-oriented experiments showcasing the performance of existing methods is presented. Specifically, three types of methods are employed: traditional approximate analytical methods, traditional machine learning-based methods, and deep learning-based methods. Following that, various traffic flows with different settings are collected, and intricate experimental analyses at both the feature and method levels under different traffic conditions are conducted. Finally, insights from the experimental analysis that may be beneficial for the future performance prediction of GPS are derived.

Processor Sharing Queues With Impatient Customers and State-Dependent Rates

We study queues with impatient customers and Processor Sharing (PS) discipline as well as other variants of PS discipline, namely, Discriminatory Processor Sharing (DPS) and Generalized Processor Sharing (GPS) disciplines, where customers have deadlines until the end of service (DES). Customers arrive according to a state-dependent Poisson process and have general impatience. Customers have exponential service times with state-dependent service rates. Analytical methods based on simple Markov chains are given for the performance analysis of such queues. The principal measures of performance are the steady-state probability of missing deadline and the steady-state probability of blocking. Similar results are obtained for related queues with Random Order Service (ROS) discipline where customers have deadlines until the beginning of service (DBS). In view of a lack of exact analytical results for First Come First Served (FCFS) queues with state-dependent rates, a highly accurate approximation method is also given for these latter queues. The efficacy and accuracy of the approach are illustrated by some numerical examples and simulation experiments.

Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.

Individual Service Curves for Bandwidth-Sharing Policies Using Network Calculus

Bandwidth-sharing policies guarantee a proportion of the service offered by a server to each class of traffic. These policies include GPS (Generalized Processor Sharing) and DRR (Deficit Round Robin). In this letter, we compute service curves for each class of traffic for such scheduling policies using network calculus. These individual service curves take into account the characteristics of the cross-traffic and thus improve the state-of-the-art performance bounds like delay or backlog.

Modeling and Performance Assessment of Dynamic Rate Adaptation for M2M Communications

With the advance of Internet of Things and the support of a diverse array of smart-world applications, the number of Machine-to-Machine (M2M) devices has continued to grow at an accelerated rate. This significant and unchecked increase poses enormous challenges to both M2M infrastructure and the coexistence of M2M applications. In this paper, we model the traffic arrival patterns of time-driven, event-driven and loop-driven M2M applications, and propose a novel dynamic rate adaptation (DRA) scheme to obtain an optimized service rate distribution among a mixture of diverse M2M applications. DRA introduces real-time monitoring of M2M traffic arrival rate, building on which a service rate distribution between M2M applications can be incrementally adjusted moment to moment, through the use of the mean value theorem of integrals (MVTI) and generalized processor sharing (GPS). Via a combination of both theoretical analysis and extensive performance evaluation, we have validated the effectiveness of our proposed DRA scheme. Our experimental results demonstrate that DRA can significantly improve M2M communications performance with respect to throughput, delay, and energy consumption. In addition, we extend our proposed DRA scheme from the perspective of Device-to-Device (D2D) communications and further discuss the resilience of DRA.

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.

On the equivalence between multiclass processor sharing and random order scheduling policies

Consider a single server system serving a multiclass population. Some popular scheduling policies for such system are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processor sharing (GPS) and weighted fair queueing (WFQ). In this paper, we propose two classes of policies, namely MPS (multiclass processor sharing) and MROS (multiclass random order service), that generalize the four policies mentioned above. For the special case when the multiclass population arrive according to Poisson processes and have independent and exponential service requirement with parameter ?, we show that the tail of the sojourn time distribution for a class i customer in a system with the MPS policy is a constant multiple of the tail of the waiting time distribution of a class i customer in a system with the MROS policy. This result implies that for a class i customer, the tail of the sojourn time distribution in a system with the DPS (GPS) scheduling policy is a constant multiple of the tail of the waiting time distribution in a system with the DROS (respectively WFQ) policy.

Calculation of the performance region of an easy-to-optimize alternative for Generalized Processor Sharing

Service differentiation is a basic requirement in every modern queueing system with multiple classes of customers. In this paper, we look at Hierarchical Generalized Processor Sharing (H-GPS), which is a discrete-time hierarchically-structured implementation of the well-known idealized Generalized Processor Sharing (GPS) scheduling discipline. We prove that, for three classes, H-GPS can be configured to obtain any performance possible by other scheduling mechanisms, such as priority queueing or GPS. The hierarchical nature of a H-GPS system, however, has the major advantage that optimization is easier and more intuitive. To this end, we also present an algorithm to calculate the configuration parameters for H-GPS given a certain performance objective.

Lévy-driven GPS queues with heavy-tailed input

In this paper, we derive exact large buffer asymptotics for a two-class generalized processor sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed Levy processes. Four scenarios need to be distinguished, which differ in terms of (i) the level of heavy-tailedness of the driving Levy processes as well as (ii) the values of the corresponding mean rates relative to the GPS weights. The derived results are illustrated by two important special cases, in which the queues' inputs are modeled by heavy-tailed compound Poisson processes and by $$\alpha $$ź-stable Levy motions.

QoS routing with worst-case delay constraints: Models, algorithms and performance analysis

In a network where weighted fair-queueing schedulers are used at each link, a flow is guaranteed an end-to-end worst-case delays which depends on the rate reserved for it at each link it traverses. Therefore, it is possible to compute resource-constrained paths that meet target delay constraints, and optimize some key performance metrics (e.g., minimize the overall reserved rate, maximize the remaining capacity at bottleneck links, etc.). Despite the large amount of literature that has appeared on weighted fair-queueing schedulers since the mid ’90s, this has so far been done only for a single type of scheduler, probably because the complexity of solving the problem in general appeared forbidding. In this paper, we formulate and solve the optimal path computation and resource allocation problem for a broad category of weighted fair-queueing schedulers, from those emulating a Generalized Processor Sharing fluid server to variants of Deficit Round Robin. We classify schedulers according to their latency expressions, and show that a significant divide exists between those where routing a new flow affects the performance of existing flows, and those for which this do not happen. For the former, explicit admission control constraints are required to ensure that existing flows still meet their deadline afterwards. However, despite this major difference and the differences among categories of schedulers, the problem can always be formulated as a Mixed-Integer Second-Order Cone problem (MI-SOCP), and be solved at optimality in split-second times even in fairly large networks.

On the optimization of two-class work-conserving parameterized scheduling policies

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented \(c\mu \)-rule is a special case of our framework.

Modelling and Analysis of an Integrated Scheduling Scheme with Heterogeneous LRD and SRD Traffic

Multimedia applications in wireless networks are usually categorized into various classes according to their traffic patterns and differentiated Quality-of-Service (QoS) requirements. The traffic of heterogeneous multimedia applications often exhibits Long-Range Dependent (LRD) and Short-Range Dependent (SRD) properties, respectively. The integrated scheduling scheme that combines Priority Queuing (PQ) and Generalized Processor Sharing (GPS) within a hierarchical structure, referred to as PQ-GPS, has been identified as an efficient mechanism for QoS differentiation in wireless networks and attracted significant research efforts. However, due to the high complexity and interdependent relationship among traffic flows, modelling of the integrated scheduling scheme poses great challenges. To address this challenging and important research problem, we develop an original analytical model for PQ-GPS systems under heterogeneous LRD and SRD traffic. A cost-effective flow decomposition approach is proposed to equivalently divide the integrated scheduling system into a group of Single-Server Single-Queue (SSSQ) systems. The expressions for calculating the queue length distribution and loss probability of individual traffic flows are further derived. After validating its accuracy, the developed model is adopted as an efficient performance tool to investigate the important issues of resource allocation and call admission control in the integrated scheduling system under QoS constraints.

Counterexamples to conjectures on discriminatory processor sharing and generalized processor sharing systems

In this paper, we provide counterexamples to conjectures, made by Verloop, Ayesta, and Borst (2010) [6], on discriminatory processor sharing (DPS) and generalized processor sharing (GPS) systems.

Fourth Stage of Voice Priority Queue for VoIP over WLANs

Voice over Internet Protocol (VoIP) is growing rapidly during this decade. VoIP is seen as a short-term and long-term transmission for voice and audio traffic and is moving on Wireless Local Area Networks (WLANs) based on IEEE 802.11 standards. Currently, packet scheduling algorithms like Weighted Fair Queuing (WFQ), was mainly designed to provide the bandwidth reservation. The Strict Priority (SP) is low-cost to maintain the delay sensitive voice traffic. Also, a number of research scheduling solutions have been proposed like General processor sharing (GPS), Deficit Round Robin (DRR), Contention-Aware Temporally fair Scheduling (CATS). Unfortunately, the current scheduling won’t be able to handle the VoIP packets properly and they have drawbacks over real-time applications. The objective of this research is to propose a Fourth Stage of Voice Priority Queue (VPQ) packet scheduling and algorithm to ensure more throughput, fairness and efficient packet scheduling for VoIP performance of queues and traffics. A new scheduler flexible which is capable of satisfying the VoIP traffic flows. Experimental topologies on NS-2 network simulator were analyzed for voice traffic.

Generalized Processor Sharing with Multiple FBM-based Traffic Arrivals

Generalized Processor Sharing with Multiple FBM-based Traffic Arrivals

Long-range dependence of traffic across schedulers with multiple service classes

Long-range dependence (LRD) is a widely verified property of Internet traffic, which severely impacts network performance yielding longer queuing delays. Moreover, LRD has been demonstrated to be almost ubiquitous and hard to remove or control. In this work, we investigated by extensive simulation the effect of schedulers on traffic LRD. We analyzed the output traffic of single schedulers and chains of schedulers merging LRD flows according to various service policies, viz. plain FIFO, strict-priority, earliest-deadline-first and general processor sharing (GPS). First, we noticed that traffic LRD is not affected much by crossing schedulers, for any service policy, when the merged flow has no LRD. Then, we showed that LRD may also spread across flows with different service priorities, with any service policy except balanced GPS, which ensures complete separation between classes. Finally, we experienced the same phenomenon also along chains of schedulers. These findings may explain, in part, why LRD is so widespread in Internet traffic.

Call Admission Control on Single Node Networks under Output Rate-Controlled Generalized Processor Sharing (ORC-GPS) Scheduler

Multimedia applications such as music or video streaming, video teleconferencing and IP telephony are flourishing in packet-switched networks. Applications that generate such real-time data can have very diverse quality-of-service (QoS) requirements. In order to guarantee diverse QoS requirements, the combined use of a packet scheduling algorithm based on Generalized Processor Sharing (GPS) and leaky bucket traffic regulator is the most successful QoS mechanism. GPS can provide a minimum guaranteed service rate for each session and tight delay bounds for leaky bucket constrained sessions. However, the delay bounds for leaky bucket constrained sessions under GPS are unnecessarily large because each session is served according to its associated constant weight until the session buffer is empty. In order to solve this problem, a scheduling policy called Output Rate-Controlled Generalized Processor Sharing (ORC-GPS) was proposed in [17]. ORC-GPS is a rate-based scheduling like GPS, and controls the service rate in order to lower the delay bounds for leaky bucket constrained sessions. In this paper, we propose a call admission control (CAC) algorithm for ORC-GPS, for leaky-bucket constrained sessions with deterministic delay requirements. This CAC algorithm for ORC-GPS determines the optimal values of parameters of ORC-GPS from the deterministic delay requirements of the sessions. In numerical experiments, we compare the CAC algorithm for ORC-GPS with one for GPS in terms of schedulable region and computational complexity.

Mobility of Mobile Station in Voice Priority Queue Scheduler for VoIPWLANs

Voice over Internet Protocol (VoIP) is growing rapidly during this decade. VoIP is seen as a short-term and long-trem transmission for voice and audio traffic. Meanwhile, VoIP is moving on Wireless Local Area Networks (WLANs) based on IEEE 802.11 standards. Currently, many packet scheduling algorithms like Weighted Fair Queuing (WFQ), was mainly designed to provide the bandwidth reservation. The Strict Priority (SP) is low-cost to maintain the delay sensitive voice traffic. Also, a number of research scheduling solutions have been proposed like General processor sharing (GPS), Deficit Round Robin (DRR), Contention-Aware Temporally fair Scheduling (CATS). Unfortunately, the current scheduling will not be able to handle the VoIP packets with the proper manner and they have some drawbacks over real-time applications. The objective of this research is to propose a new Voice Priority Queue (VPQ) packet scheduling and algorithm to ensure more throughput, fairness and efficient packet scheduling for VoIP performance of queues and traffics. A new scheduler flexible which is capable of satisfying the VoIP traffic flows. Experimental topologies on NS-2 network simulator were analyzed for voice traffic. Preliminary results show that this can achieve maximum and more accurate VoIP quality throughput and fairness index in mobility of mobile station. We verified and validated VPQ an extensive experimental simulation study under various traffic flows over WLANs.

Asymptotic Analysis of Two Coupled Queues with Vastly Different Arrival Rates and Finite Customer Capacities

We consider two coupled queues, with each having a finite capacity of customers. When both queues are nonempty they evolve independently, but when one becomes empty the service rate in the other changes. Such a model corresponds to a generalized processor sharing (GPS) discipline. We study the joint distribution p(m, n) of finding (m, n) customers in the (first, second) queue, in the steady state. We study the problem in an asymptotic limit of “heavy traffic,” where also the arrival rate to the second queue is assumed to be small relative to that of the first. The capacity of the first queue is scaled to be large, while that of the second queue is held constant. We consider several different scalings, and in each case obtain limiting differential and/or difference equation for p(m, n), and these we explicitly solve. We show that our asymptotic approximations are quite accurate numerically. This work supplements previous investigations into this GPS model, which assumed infinite capacities/buffers. The present model corresponds to a random walk in a lattice rectangle, where p(m, n) satisfies a different boundary condition on each edge.

Energy-aware capacity scaling in virtualized environments with performance guarantees

We investigate the trade-off between performance and power consumption in servers hosting virtual machines running IT services. The performance behavior of such servers is modeled through Generalized Processor Sharing (GPS) queues enhanced with a green speed-scaling mechanism that controls the processing capacity to use depending on the number of active virtual machines. When the number of virtual machines grows large, we show that the stochastic evolution of our model converges to a system of ordinary differential equations for which we derive a closed-form formula for its unique stationary point. This point is a function of the capacity and the shares that characterize the GPS mechanism. It allows us to show that speed-scaling mechanisms can provide large reduction in power consumption having only small performance degradation in terms of the delays experienced in the virtual machines. In addition, we derive the optimal choice for the shares of the GPS discipline, which turns out to be non-trivial. Finally, we show how our asymptotic analysis can be applied to the dimensioning and service partitioning in data-centers. Experimental results show that our asymptotic formulas are accurate even when the number of virtual machines is small.