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With the development of 5 G communication and Internet of Things (IoT) technology, increasing data is generated by a large number of IoT devices at edge networks. Therefore, increasing need for distributed Data Centers (DCs) are seen from enterprises and building elastic applications upon DCs deployed over decentralized edge infrastructures is becoming popular. Nevertheless, it remains a great difficulty to effectively schedule computational tasks to appropriate DCs at the edge end with low energy consumption and satisfactory user-perceived Quality of Service. It is especially true when DCs deployed over an edge environment, which can be highly inhomogeneous in terms of resource configurations and computing capabilities. To this end, we develop an edge task scheduling method by synthesizing a M/G/1/PR queuing model for characterizing the workload distribution and a Deep Deterministic Policy Gradient algorithm for yielding high-quality schedules with low energy cost. We conduct extensive numerical analysis as well and show that our proposed method outperforms state-of-the-art methods in terms of average task response time and energy consumption.

The performance analysis of the classical M / G / 1 queue, under a general mixed joining/balking strategy was carried out recently by Kerner (Stoch Mod 24:364–375, 2008), who used an analytic approach based on the supplementary variable method. The tractability of the corresponding queueing system with state-dependent arrival rates is particularly significant, as it has important applications in situations where the customers are strategic. In this paper, we present an alternative path for the analysis of the same system, using purely probabilistic arguments.

Vehicular Ad Hoc Networks (VANETs) employ multichannel to provide a variety of safety and non-safety applications, based on the IEEE 802.11p and IEEE 1609.4 protocols. The safety applications require timely and reliable transmissions, while the non-safety applications require efficient and high throughput. In the IEEE 1609.4 protocol, operating interval is divided into alternating Control Channel (CCH) interval and Service Channel (SCH) interval with an identical length. During the CCH interval, nodes transmit safety-related messages and control messages, and Enhanced Distributed Channel Access (EDCA) mechanism is employed to allow four Access Categories (ACs) within a station with different priorities according to their criticality for the vehicle’s safety. During the SCH interval, the non-safety massages are transmitted. An analytical model is proposed in this paper to evaluate performance, reliability and efficiency of the IEEE 802.11p and IEEE 1609.4 protocols. The proposed model improves the existing work by taking serval aspects and the character of multichannel switching into design consideration. Extensive performance evaluations based on analysis and simulation help to validate the accuracy of the proposed model and analyze the capabilities and limitations of the IEEE 802.11p and IEEE 1609.4 protocols, and enhancement suggestions are given.

This study introduces an approximate solution for the M/G/1 queueing model in scenarios where the service time distribution follows a pure mixture distribution. The derivation of the proposed approximation leverages the analytical tractability of the variance for certain mixture distributions. By incorporating this variance into the Pollaczek–Khinchine equation, an approximate closed-form expression for the M/G/1 queue is obtained. The formulation is extended to service-time distributions composed of two or more components, specifically Gamma, Gaussian, and Beta mixtures. To assess the accuracy of the proposed approach, a discrete-event simulation of an M/G/1 system was conducted using random variates generated from these mixture distributions. The comparative analysis reveals that the approximation yields results in close agreement with simulation outputs, with particularly high accuracy observed for Gaussian mixture cases.

Consider a stable M/G/1 system in which, at time t=0, there are exactly n customers with residual service times equal to v1,v2,…,vn. In addition, assume that there is an extra customer c who arrives at time t=0 and has a service requirement of x. The externalities which are created by c are equal to the total waiting time that others will save if her service requirement is reduced to zero. In this work, we study the joint distribution (parameterized by n,v1,v2,…,vn,x) of the externalities created by c when the underlying service distribution is either last-come, first-served with preemption or first-come, first-served. We start by proving a decomposition of the externalities under the above-mentioned service disciplines. Then, this decomposition is used to derive several other results regarding the externalities: moments, asymptotic approximations as x→∞, asymptotics of the tail distribution, and a functional central limit theorem.

This paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous arrival; or the service time of a customer depends on her waiting time. In each case, we derive and solve a fixed-point equation for the Laplace–Stieltjes transform of a key performance measure of the model, like waiting time or ruin time.

In recent years, there is a growing attention towards queueing models with customers who choose their service durations. The model assumptions in the existing literature imply that every customer knows his service demand when he enters into the service position. Clearly, this property is not consistent with some real-life situations. Motivated by this issue, the current work includes a single-server queueing model with customers who dynamically choose their service durations. In this setup, the main result is existence of a quadratic price function which (1) implies an optimal resource allocation from a social point of view and (2) internalizes the externalities in the system. In addition, it is explained how to compute its parameters efficiently.

Road capacity, traffic safety, and energy efficiency can be extremely improved by forming platoons with a small intra-vehicle spacing. Automated controllers obtain vehicle speed, acceleration, and position through vehicular ad hoc networks (VANETs), which allows the performance of platoon communication to make a significant impact on the stability of the platoon. To the best of our knowledge, there is not much research relating to packet delay and packet dropping rate of platoon communication based on the IEEE 802.11p broadcasting. In this paper, we introduce platoon structure model, vehicle control model, and communication model for a single platoon scenario. By utilizing Markov process and M/G/1/K queuing theory, we put forward an analytical model to assess the property of intra-vehicle communication. The analytical model is validated by simulations and the influence of communication parameters on intra-vehicle communication performance are discussed. In addition, the experimental results demonstrate that the IEEE 802.11p-based intra-vehicle communication guarantee the stability of platoon.

We consider the optimal scheduling problem in the M/G/1 queue. While this is a thoroughly studied problem when the target is to minimize the mean delay, there are still open questions related to some other objective functions. In this paper, we focus on minimizing mean slowdown among non-anticipating polices, which may utilize the attained service of the jobs but not their remaining service time when making scheduling decisions. By applying the Gittins index approach, we give necessary and sufficient conditions for the jobs’ service time distribution under which the well-known scheduling policies first come first served and foreground background are optimal with respect to the mean slowdown. Furthermore, we characterize the optimal non-anticipating policy in the multi-class case for certain types of service time distributions. In fact, our results cover a more general objective function than just the mean slowdown, since we allow the holding costs for a job to depend on its own service time S via a generic function c(S). When minimizing the mean slowdown, this function reads as c(x)=1/x.

We consider Md-M/G/1 processes, which are irreducible discrete-time Markov chains consisting of two components. The first component is a nonnegative integer vector, while the second component indicates the state (or phase) of the external environment. The level of a state is defined by the minimum value in its first component. The matrix G of the process represents the conditional probabilities that, starting from a given state of a certain level, the Markov chain will first reach a lower level in a specific state. This study aims to develop an effective algorithm for computing matrices G for Md-M/G/1 processes.