The on-demand activation of frequency bands in radio access networks can lead to a significant reduction of energy consumption, but risks to adversely impact performance. This approach to frequency band management can be applied either to a group of co-located base stations whose operators adopt a network sharing approach or to a single base station that uses multiple frequency bands. We develop a stochastic model based on the Matrix Analytic Method for the quantification of system performance and energy consumption in the case of coexisting streaming and elastic services. By computing numerical results in a specific setting, we show that the on-demand (de)activation, possibly combined with the adaptation of the data rate of streaming services, succeeds in greatly reducing energy consumption with respect to the case in which frequency bands are always active, with limited impact on the performance experienced by users. We also show that the introduction of a hysteresis in the frequency band activation/deactivation process allows the optimization of the energy/performance trade-off. Finally, we show that performance is not drastically altered by the burstiness of the elastic service request arrival process, and we prove that the separate analysis of streaming and elastic services provides quite optimistic results with respect to the joint analysis made possible by our model.
In many IoT systems, network gateways and servers must handle traffic from a vast number of devices. The incoming traffic typically exhibits high variance and autocorrelation. Moreover, as load increases, servers and gateways slow down and may even completely crash. Consequently, long periods of overload may be observed leading to long response times or even instability of the system. To prevent such situations, incoming traffic must be regulated through traffic shaping schemes. This paper analyzes a class traffic shaping schemes under stochastic assumptions and demonstrates how their parameters can be optimized to reduce the population and response time of the system without discarding incoming traffic. The analysis is based on matrix geometric methods and a new approach to analyze the stability of infinite Markov chains.
We consider the moments and the distribution of the hitting times and cover times of the star graph composed of m arms each of length n . We obtain recurrence relations for the distribution and higher-order moments of both the hitting times of the leaves and the cover times for various initial states. We use the recurrence relations on the moments to analyze the asymptotic behavior of the cover times distribution when the number of arms m m, which may depend on the length n of the arms, tends to infinity as n tends to infinity. We call this new graph, composed of an infinite number of arms each of infinite length, the sun graph.
Classical queueing models rely on the work conservation principle, which assumes that whenever a server completes a service and there are waiting customers, the server immediately begins serving the next customer. However, in many service systems, servers may become temporarily unavailable after service—for example, due to after-call work or unscheduled breaks—violating this assumption. In this paper, we study an Erlang C system with server unavailability and customer abandonment and formulate it as a level-dependent quasi-birth-and-death (LDQBD) process. By leveraging the LDQBD structure, we first show that the rate matrices are element-wise non-increasing beyond a certain level. Then, we extend an existing algorithm from the literature to compute steady-state probabilities within any desired error tolerance. Through numerical experiments, we calibrate model parameters using data from the call center of a non-profit organization, illustrating how staffing levels and agent unavailability affect customer waiting times and overall system performance.
We study moment properties of counting processes for certain subclasses of Markovian arrival processes (MAPs). We focus on the class of Markovian transition counting processes (MTCPs) which counts all the transitions of the background Markov chain. While Markov modulated Poisson processes (MMPPs) are often used to model bursty traffic, MTCPs deliver similar modelling capability and reduce the mathematical and computational complexity. To support the suggested use of MTCPs as alternatives to MMPPs, we establish an equivalence in terms of first and second moments of counts with a sub-class of MMPPs which we refer to as slow MMPPs (SMMPPs). For this we construct matched MTCPs (MMTCPs), where an MMTCP is parameterized with the same basic parameters as an SMMPP. In the course of this study, we summarize and derive general results about moment matrices of MAPs by using deviation matrix representations in novel forms that have not appeared in the existing literature.
Service function chaining (SFC) plays a critical role in modern communication networks. Network function virtualization (NFV) provides a flexible paradigm to implement and instantiate SFC on demand at any time and any location. However, few existing works address multicriteria routing for Pareto optimality in NFV networks. Considering the importance of computing and network resources in NFV networks, we define the bandwidth-capacity optimal SFC (BCoSFC) problem and prove its NP-hardness. By leveraging the label setting (LS) algorithmic framework in multicriteria optimization, we design a suite of algorithms, consisting of an upper-bound algorithm (BCoSFC-UB) and a lower-bound algorithm (BCoSFC-LB); both of which can efficiently generate feasible routing paths. When their solutions converge, the exact optimum is achieved. Otherwise, BCoSFC-UB yields a non-tight, overestimated performance pair, while BCoSFC-LB, with tunable operation modes, produces a (near-)optimal solution. Simulation results demonstrate that BCoSFC-UB and BCoSFC-LB typically converge either to the exact optimum or to a narrow performance gap efficiently under realistic configurations. From the perspective of service providers, the derived bandwidth-capacity plane, analogous to a Pareto front, provides a panoramic view of service provisioning capability, and also facilitates flexible trade-offs within it. The proposed solution can be readily extended to support diverse resource types in NFV/SFC scenarios and also to support various QoS metrics.
The half-duplex constraint in 5G Integrated Access and Backhaul (IAB) networks, where nodes cannot transmit and receive simultaneously, presents a significant challenge for accurate packet-level performance modeling. Existing analytical models often oversimplify this crucial operational dynamic. To address this gap, we introduce and solve an analytical non-symmetric polling system with cyclic server routing that provides a novel and effective way to capture the half-duplex constraint through a state-dependent arrival mechanism, where packet reception is gated by the node’s transmission state. Using the Laplace-Stieltjes Transform (LST), we derive exact closed-form expressions for the full probability distributions of packet sojourn times for the system with an arbitrary number of queues, providing a precise and computationally efficient tool for system analysis.Our results reveal a fundamental performance trade-off in traffic management. While balanced traffic is shown to minimize mean sojourn times, our quantile-based analysis demonstrates that an unbalanced traffic strategy is optimal for achieving the lowest possible best-case (low-quantile) latency. Conversely, traffic balancing is essential for controlling tail latencies and ensuring robust worst-case Quality of Service (QoS). Moreover, this trade-off becomes even more critical as the number of queues grows, making traffic balancing essential for performance in larger, denser networks. In addition to latency analysis of the packet transmission process in IAB systems, these results also facilitate optimization of the complex metrics of interest such as the Age of Information (AoI), which is critically important for multi-hop IAB systems.
Crowdsensed data trading (CDT) solves the problem of data resource scarcity and data source homogeneity faced in conventional data trading, which is more cost-effective and time-efficient than deploying sensors. In CDT, data requesters can incentive multiple data workers to perform data acquisition tasks in specified areas, and data workers can get payoff by providing data report embedded privacy formation which they may be unwilling to expose. Thus, there are some studies focusing on privacy protection, such as differential privacy and federated learning. Nevertheless, Data workers involved in CDT may still face potential privacy leakage due to the exposure of information provided to data requesters. In this paper, we advocate a novel mechanism to unleash the value of dispersive and diversiform data. Designing such scheme involves several challenges. First, it is difficult to determine the privacy budget that data workers should choose for data requesters, since they have conflicting objectives and private information. Second, it is difficult to achieve a social agreement owing to each participant is self-interested. Therefore, we propose an auction-based crowdsensed data trading (ACDT) mechanism to address these challenges and achieve socially optimization. The ACDT relies on a broker to orchestrate and coordinate the interactions between multiple data requesters and multiple data workers with any prior knowledge, and induce actual information in an iterative fashion for enabling the market to function efficiently. Extensive theoretical and simulation analysis show that the proposed scheme satisfies the expected economic properties and has commendable performance in terms of social welfare.
In 1985, Grassmann et al. (1985) published their celebrated paper, in which they introduced a numerically stable algorithm for computing the stationary probabilities of a finite-state Markov chain, one of the key performance quantities in both theory and applications. This algorithm later became the well-known GTH algorithm (or the state-reduction method) in the literature, becoming one of the standard algorithms in applied probability. In the early 1990s, motivated by queueing applications, this algorithm was extended to deal with the stationary distributions of block-structured Markov chains with repeating rows by Grassmann and Heyman (1990, 1993). In this paper, we focus on the block-form GTH algorithm and organize it into two parts. In the first part, we connect the block-form GTH algorithm to censored Markov chains and the block-form RG-factorization. We show that the forward block-elimination and back block-form substitution of the block-form GTH algorithm are equivalent to solving a system formulated using the RG-factorization in two steps. We also show that this connection remains valid when the block-form GTH algorithm is extended to infinite-state Markov chains. It is well known that censoring an infinite-state Markov chain to a finite state space yields a stationary distribution that provides a best approximation to the stationary distribution of the original infinite-state Markov chain. In the second part, we first derive an explicit expression for the censored Markov chain from the infinite state space to a finite space for Markov chains of M/G/1 type. Based on this expression, we propose a renormalized approximated censored transition matrix (RA-CM). The resulting stationary distribution is shown to be asymptotically optimal in terms of approximation error. We compare the approximation error of the RA-CM with the error arising from the last-block-column augmentation.
The increasing complexity of next-generation services demands efficient orchestration across the edge-to-cloud continuum to balance computational intensity, latency constraints, and resource availability. These services are typically decomposed into interdependent sub-tasks, requiring careful synchronization to meet stringent completion time requirements. The challenge is further amplified in heterogeneous and resource-constrained edge environments, where multiple providers dynamically compete for sub-task execution. This paper introduces a game-theoretic stochastic framework that optimizes system welfare from both users' and providers' perspectives, ensuring efficient task allocation across distributed computing resources. We propose a Cumulative Distribution Function (CDF)-driven game, where edge nodes serve as intermediaries between users and cloud/edge service providers. The framework is structured as a two-level mechanism: (i) a matching game governing the user-to-edge node association, and (ii) a nested Vickrey-Clarke-Groves auction selecting the optimal provider, based on a CDF-driven assessment of service completion times. To enhance feasibility in decentralized edge computing environments, provider bids are represented as uniform CDFs, establishing a dominance relation that mitigates strategic manipulation. We theoretically analyze cheating strategies, showing that truthful bidding is a rational provider behavior and that the resulting user-edge matching satisfies a suitable stability notion. Extensive simulations compare the proposed approach against a full-knowledge-based allocation, conventional game-theoretic models, and a heuristic recently proposed in the literature, evaluating the price of anarchy, system welfare, and outage probability. The results demonstrate the effectiveness of our framework in achieving resilient, cost-efficient, and low-latency orchestration across the edge-to-cloud continuum in heterogeneous edge deployments.
Response time analysis (RTA) is an effective method for analyzing the schedulability of real-time tasks. Most existing RTAs focus on improving the accuracy of their evaluation results at the expense of execution efficiency. In order to adapt to complex system environments with large-scale tasks and processors, as well as some iterative co-design where the RTAs are run over and over, it is necessary to study how to improve the execution efficiency of RTAs without affecting their accuracy. In this paper, we propose an efficient execution framework for existing RTAs for tasks under global earliest-deadline-first (G-EDF) scheduling. Unlike existing RTA methods, which calculate the Worst-Case Response Time (WCRT) of the target task under each busy period length, we improve the efficiency of existing RTA methods by identifying meaningful busy period lengths to reduce unnecessary computations. The theoretical analysis results prove the correctness of the new framework. The simulation results show that the new framework can reduce the runtime of the existing RTAs by more than half.
We introduce a methodology for training deep neural networks (DNNs) to compute an approximation for the limiting distribution of the queue length in the GI/G/K queue. This work extends Baron et al. (2024) to multi-server systems, with its key contribution being an effective algorithm for generating training samples with exact labels. The algorithm, based on matrix-analytic methods, computes the limiting distribution of the queue length in continuous/discrete time PH/PH/K queues, which are dense in the set of GI/G/K queues. Specifically, the algorithm integrates the quasi birth-and-death process (QBD), the count-server-for-phase (CSFP) method, and the matrix-geometric solution to generate large-scale exact training data for neural networks analyzing GI/G/K queues with a moderate number of servers. We train three DNN variants using continuous time, discrete time, or mixed PH/PH/K samples and compare their performance on PH/PH/K and GI/M/K queues with those of existing methods to evaluate trained DNNs. The results demonstrate that DNNs are effective analytical tools for queueing models, with prediction (i.e., the limiting distribution of queue length) quality depending on traffic intensity and training sample diversity. This study sheds light on training neural networks for complex stochastic systems.
6G networks aim to offer users ultra-efficient access to networked services based on seamless integration of the network with low latency solutions such as the Multi-access Edge Computing. To achieve this goal, the 6G edge orchestration should support smart decisions based on the learned user mobility behaviour. In this paper, we focus on the handover prediction problem that is an essential component to implement proactive service migration in 6G networks, particularly when migration delays require reliable forecasts several seconds ahead. We analyse three novel models based on Long Short-Term Memory (LSTM) neural networks aiming to improve the handover prediction performances when working with a wider prediction horizon. The architectures include: a parallel multi-output model that produces all outputs simultaneously, a multi-output model with the addition of a Bahdanau attention mechanism that works by iterative prediction of future time points, and an ensemble of single-output models that incorporates previous predictions into future steps. Our results show that the single-output ensemble models provide stable results over the entire prediction horizon, although prediction time costs must be assumed. The iterative attention model achieves a balance in mid-range predictions, while the parallel multi-output model stands out for its excels in early-horizon prediction. These findings highlight a clear trade-off between predictive accuracy and computational cost, indicating that the MEC orchestrator should choose an architecture guided by the requirements of the targeted MEC service and the lead time available for proactive migration.
Dispatching policies shape delay and throughput in multi-server data centers, yet the fidelity of classical queueing models under production workloads remains unclear. We combine analytical modeling with trace-driven simulation to reassess Round Robin (RR), Join-Idle-Queue (JIQ), and Least-Work-Left (LWL) using job-level and task-level views of Google ClusterData v3 and Alibaba Cluster Trace v2018. Under controlled Poisson arrivals with Weibull service times, the analytical models match the simulation closely. We then examine model-trace discrepancies through controlled manipulations: shuffling inter-arrival times, replacing arrivals with a Poisson process, shuffling task Central Processing Unit (CPU) times, and trimming the top 0.1% of service demands. Hidden dependence and rare very large jobs explain most gaps; when both sequences are randomized and outliers removed, job-level predictions align with simulation. At the task level, where jobs decompose into independently dispatched tasks, policy ordering may change: in a production trace case, JIQ often matches or surpasses LWL, while RR remains weakest. We also introduce a simple analytical approximation for JIQ that is easy to evaluate and accurate in the controlled setting. Overall, the study clarifies when analytical models hold, identifies workload features that break them, and informs dispatcher choice under production conditions.
Significant progress has been made in optimizing LLVM compiler option sequences to improve non-functional attributes such as code size, execution time, and energy consumption. However, complex interactions-among options, between options and objectives, and among objectives themselves-make it challenging to efficiently identify non-dominated sequences across multiple objectives within the vast search space. This paper proposes IMOOM, an Interaction-aware Multi-Objective Optimization Method targeting execution time and energy consumption in embedded programs. IMOOM operates in two stages. In the first stage, IMOOM-SL captures option interactions using Latin Hypercube Sampling, partitions samples via non-dominated sorting and hypervolume metrics, and confirms selected options through a decision table, thereby reducing the search space while preserving solution quality. In the second stage, IMOOM-SQ constructs an Item Interaction Graph (IIG) that encodes interaction frequencies and objective annotations to predict both objectives, and integrates this predictive model with NSGA-II to efficiently obtain high-quality non-dominated sequences. Extensive evaluation on eight embedded programs across five domains demonstrates that IMOOM outperforms four state-of-the-art methods in hypervolume, coverage rate, and inverted generational distance. IMOOM-SL achieves 94.5% selection accuracy with 80.6% space reduction, while the effectiveness of IIG-based optimization in IMOOM-SQ is empirically validated.
In this article we classify discrete-time queues based on scheduling rules and observation epochs combinations. This classification leads to coherent, sub-coherent, and super-coherent systems when observed waiting times are, respectively equal to, less than, or larger than actual waiting times. We then explore the consequences of this classification. Specifically, we discuss invariant properties of coherent systems including queue-lengths, waiting times, servers’ busy times, and other common characteristics. An important consequence is that a performance characteristic of a system with specific scheduling rule and observation epoch combination extends to the entire class. An unresolved issue in the literature is the assertion that Little’s law does not apply for discrete-time queues that incorporate certain scheduling rules. Using this classification, we reconcile the generality of Little’s law and its applicability to all discrete-time queues regardless of scheduling rules.
In order to better solve the underdetermined anti-collision problem of RFID system, this paper optimizes the blind source separation algorithm from the initial mixing matrix. Since the mixing matrix determines the linear mapping relationship between the source signal and the observed signal, it directly affects the convergence of the separation algorithm and the quality of the separation results. Therefore, the selection of the initial mixing matrix is crucial to the performance and effectiveness of the algorithm. This paper adopts the successive non-negative projection algorithm (SNPA) to calculate the initial mixing matrix, abandons the traditional random initialization, and avoids the algorithm from falling into the local optimal solution. Then the bounded component analysis (BCA) algorithm is used to separate the mixed signal. The algorithm completes the separation of the mixed tag source signal without considering the arrangement and phase uncertainty of the source signal estimation. The simulation results show that the algorithm can effectively separate the tag source signal and has higher accuracy than the existing algorithms under both low and high signal-to-noise ratio conditions. Its low bit error rate also shows that the system can effectively handle interference and noise during data transmission or reception, thereby reducing the occurrence of data errors.
We study revenue optimisation for a Markovian queueing model with two observable parallel queues. Customers are heterogeneous in the sense that they value the service differently and strategically choose which queue to join depending on which queue offers the greatest expected utility. To join a queue, customers must pay a predetermined fee, which the provider sets to optimise revenue. We consider both a scenario where customers must always choose a queue and one where customers have the option to balk. In both scenarios, we use a power series approximation method accelerated by Wynn's epsilon-method to efficiently solve the balance equations.
We consider the offloading of tasks in edge-cloud computing systems using a renewal input modified batch service queue. Tasks are processed using a modified batch service policy with a minimum batch size of L and a maximum batch size of K in an edge-cloud computing system. Bulk services combine several tasks from many Internet of Things devices and offload them to the edge or cloud for concurrent execution. The updated batch service rule allows tasks to be offloaded for variable batch sizes, smaller batches when network circumstances are favorable, and bigger batches when the network is congested to reduce transmission overhead. In addition, if the server has commenced the processing and there are fewer than K tasks, we let the tasks join. Furthermore, the batches’ processing rates are presumed to depend on the batch size. We derive the analytic results for the marginal and joint probability distribution of the number of tasks in the queue/system and with the server. We show the influence of light-tailed and heavy-tailed inter-arrival time distributions on the system model with numerical examples. Dynamic service rates adjust processing speeds at edge or cloud servers based on workload, network latency, and available resources. It reduces latency, balances computational load, and improves system adaptability to changing conditions.
