Performance Evaluation最新文献

Suppose sender–receiver transmission links in a downlink network at a given data rate are subject to fading, path loss, and inter-cell interference, and that transmissions either pass, suffer loss, or incur retransmission delay. We introduce a method to obtain the average activity level of the system required for handling the buffered work and from this derive the resulting coverage probability and key performance measures. The technique involves a family of stationary buffer distributions which is used to solve iteratively a nonlinear balance equation for the unknown busy-link probability and then identify throughput, loss probability, and delay. The results allow for a straightforward numerical investigation of performance indicators, are in special cases explicit and may be easily used to study the trade-off between reliability, latency, and data rate.

Distributed Join-Idle-Queue load balancing is known to achieve vanishing waiting times in the large-scale limit provided that the number of dispatchers remains fixed, while the number of servers tends to infinity. When the number of dispatchers $m$ scales to infinity together with the number of servers $n$, such that $r=n/m$ remains fixed, the large-scale performance of Join-Idle-Queue load balancing is less clear as waiting times no longer vanish.

In this paper we first discuss some existing mean field models for distributed Join-Idle-Queue load balancing with $r=n/m$ fixed and explain why the well-known model introduced in Lu et al. (2011) is not exact in the large-scale limit. The inexactness is caused by mixing two variants of distributed Join-Idle-Queue load balancing: a variant with and one without token withdrawals. Next we introduce mean field models for Join-Idle-Queue load balancing with and without token withdrawals, where an idle server places a token at a dispatcher with the shortest among $d$ randomly chosen dispatchers.

The introduced mean field models in case of token withdrawals imply that for phase type distributed service times and a total job arrival rate of $\lambda n<n$, the response time of a job corresponds to that in a standard M/PH/1 queue with load $\lambda q_0$. The value of $q_0$ can be determined numerically and depends on $\lambda ,r$ and $d$, but not on the job size distribution (apart from its mean). This simple behavior is lost if token withdrawals do not take place. For the models without withdrawals we develop fast numerical algorithms to determine the performance. We present simulation experiments that suggest that the unique fixed point of the introduced mean field models provides exact results in the large-scale limit.

The most energy-hungry parts of mobile networks are the base station sites, which consume around $60-80\text{\%}$ of their total energy. One of the approaches for relieving this energy pressure on the electricity grid infrastructure and reducing the Operational Expenditures (OPEX) is to power base stations with renewable energy. However, the design of a green mobile network requires the dimensioning of the energy harvesting and storage systems through the estimation of the network’s energy demand. Therefore, this paper develops a diffusion-based modelling framework for solar-powered green off-grid base station sites. We apply this framework to evaluate the energy performance of homogeneous and hybrid energy storage systems supplied by harvested solar energy. We present the complete analysis, with numerical examples, to study the relationship between the design parameters and the energy performance metrics. The numerical computations demonstrate how the proposed framework can be applied to evaluate homogeneous and unconventional hybrid energy storage systems.

Markov reward models are commonly used in the analysis of systems by integrating a reward rate to each system state. Typically, rewards are defined based on system states and reflect the system’s perspective. From a user’s point of view, it is important to consider the changing system conditions and dynamics while the user consumes a service. The key contributions of this paper are proper definitions for (i) system-centric reward and (ii) user-centric reward of the Erlang loss model M/M/n-0 and M/M(x)/n with state-dependent service rates, as well as (iii) the analysis of the relationships between those metrics. Our key result allows a simple computation of the user-centric rewards. The differences between the system-centric and the user-centric rewards are demonstrated for a real-world cloud gaming use case. To the best of our knowledge, this is the first analysis showing the relationship between user-centric rewards and system-centric rewards. This work gives relevant and important insights in how to integrate the user’s perspective in the analysis of Markov reward models and is a blueprint for the analysis of other services beyond cloud gaming while also considering user engagement.

We consider a Markovian retrial queueing system with customer collisions and abandonment in the context of carrier-sense multiple access systems. Using $z$-transform techniques, we find a set of first-order differential equations for the probability generating functions of the orbit size when the server is empty, busy, or in the collision phase. We then rely on series expansion techniques to extract approximations for relevant performance measures from this set of differential equations. More precisely, we construct a numerical algorithm to calculate the terms in the series expansions of various factorial moments of the orbit size. To improve the accuracy of our series expansion approach, we apply Wynn’s epsilon algorithm which not only speeds up convergence, but also extends the region of convergence. We illustrate the accuracy of our approach by means of some numerical examples, and find that the method is both fast and accurate for a wide range of the parameter values.

This paper introduces TorchAxf¹, a framework for fast simulation of diverse approximate deep neural network (DNN) models, including spiking neural networks (SNNs). The proposed framework utilizes various approximate adders and multipliers, supports industrial standard reduced precision floating-point formats, such as bfloat16, and accommodates user-customized precision representations. Leveraging GPU acceleration on the PyTorch framework, TorchAxf accelerates approximate DNN training and inference. In addition, it allows seamless integration of arbitrary approximate arithmetic algorithms with C/C++ behavioral models to emulate approximate DNN hardware accelerators.

We utilize the proposed TorchAxf framework to assess twelve popular DNN models under approximate multiply-and-accumulate (MAC) operations. Through comprehensive experiments, we determine the suitable degree of floating-point arithmetic approximation for these DNN models without significant accuracy loss and offer the optimal reduced precision formats for each DNN model. Additionally, we demonstrate that approximate-aware re-training can rectify errors and enhance pre-trained DNN models under reduced precision formats. Furthermore, TorchAxf, operating on GPU, remarkably reduces simulation time for complex DNN models using approximate arithmetic by up to 131.38$\times$ compared to the baseline optimized CPU implementation. Finally, we compare the proposed framework with state-of-the-art frameworks to highlight its superiority.

Energy Packet Networks (EPNs) model the interaction between renewable sources generating energy following a random process and communication devices that consume energy. This network is formed by cells and, in each cell, there is a queue that handles energy packets and another queue that handles data packets. We assume Poisson arrivals of energy packets and of data packets to all the cells and exponential service times. We consider an EPN model with a dynamic load balancing where a cell without data packets can poll other cells to migrate jobs. This migration can only take place when there is enough energy in both interacting cells, in which case a batch of data packets is transferred and the required energy is consumed (i.e. it disappears). We consider that data packet also consume energy to be routed to the next station. Our main result shows that the steady-state distribution of jobs in the queues admits a product form solution provided that a stable solution of a fixed point equation exists. We prove sufficient conditions for irreducibility. Under these conditions and when the fixed point equation has a solution, the Markov chain is ergodic. We also provide sufficient conditions for the existence of a solution of the fixed point equation. We then focus on layered networks and we study the polling rates that must be set to achieve a fair load balancing, i.e., such that, in the same layer, the load of the queues handling data packets is the same. Our numerical experiments illustrate that dynamic load balancing satisfies several interesting properties such as performance improvement or fair load balancing.

Network slicing is a key component of 5G-and-beyond networks but induces many questions related to an associated business model and its need to be regulated due to its difficult co-existence with the network neutrality debate. We propose in this paper a slicing model in the case of heterogeneous users/applications where a service provider may purchase a slice in a wireless network and offer a “premium” service where the improved quality stems from higher prices leading to less demand and less congestion than the basic service offered by the network owner, a scheme known as Paris Metro Pricing. We obtain thanks to game theory the economically-optimal slice size and prices charged by all actors. We also compare with the case of a unique “pipe” (no premium service) corresponding to a fully-neutral scenario and with the case of vertical integration to evaluate the impact of slicing on all actors and identify the “best” economic scenario and the eventual need for regulation.

Motivated by real-life applications, a special research-work interest has been recently directed towards the prioritized status update systems, which prioritize the update streams according to their timeliness constraints. The preferential service treatment between priority classes is commonly based on classical disciplines, preemption and non-preemption. However, both disciplines fail to give an even satisfaction between all classes. In our work, an interruption-based hybrid preemptive/non-preemptive discipline is proposed under a single-buffer system modeled as an M/M/1/2 priority queueing system. Each class being served (resp. buffered) can be preempted unless its recorded number of service preemptions reaches the predetermined in-service (resp. in-waiting) threshold. All thresholds between classes are the controlling parameters of the whole system’s performance. Using the stochastic hybrid system approach, the age of information (AoI) performance metric is analyzed in terms of its statistical average along with the higher-order moments, considering a general number of priority classes. Closed-form results are also obtained for some special cases, giving analytical insights about the AoI stability in heavy loading conditions. The average AoI and its dispersion are numerically investigated for the case of a three-class network. The significance of the proposed model is manifested in achieving a compromise satisfaction between all priority classes by a thorough adjustment of its threshold parameters. Two approaches are proposed to clarify the adjustment of these parameters. It turned out that the proposed hybrid discipline compensates for the limited buffer resource, achieving more promising performance with low design complexity and low cost. Moreover, the proposed scheme can operate under a wider span of the total offered load, through which the whole network satisfaction can be optimized under some legitimate constraints on the age-sensitive classes.

Model transformation languages are domain-specific languages used to define transformations of models. These transformations consist of the translation from one modeling formalism into another or just the updating of a given model. Such transformations are often described declaratively and are often implemented based on very small models that cover the language of the input model. As a result, transformation developers are often unable to assess the time required to transform a larger model.

Hence, we propose a prediction approach based on machine learning which uses a set of model characteristics as input and provides a prediction of the execution time of a transformation defined in the Atlas Transformation Language (ATL). In our previous work (Groner et al., 2023), we already showed that support vector regression in combination with a model characterization based on the number of model elements, the number of references, and the number of attributes is the best choice in terms of usability and prediction accuracy for the transformations considered in our experiments.

A major weakness of our previous approach is that it fails to predict the performance of transformations that also transform attribute values of arbitrary length, such as string values. Therefore, we investigate in this work whether an extension of our feature sets that describes the average size of string attributes can help to overcome this weakness.

Our results show that the random forest approach in combination with model characterizations based on the number of model elements, the number of references, the number of attributes, and the average size of string attributes filtered by the 85th percentile of their variance is the best choice in terms of the simple way to describe a model and the quality of the obtained prediction. With this combination, we obtained a mean absolute percentage error (MAPE) of 5.07% over all modules and a MAPE of 4.82% over all modules excluding the transformation for which our previous approach failed. Whereas, we obtained previously a MAPE of 38.48% over all modules and a MAPE of 4.45% over all modules excluding the transformation for which our previous approach failed.