Dynamic Scheduling in a Partially Fluid, Partially Lossy Queueing System

Streaming media applications represent an important class of applications for embedded systems. Recent advances in design-space exploration of architectures for such applications have pointed towards the suitability of Multiprocessor System on Chip (SoC) solutions. Multiprocessor SoCs not only offer higher performance, but can also lead to solutions which are cheaper cost wise. A typical synthesis methodology for such architectures would require a validation stage at the end of final system integration. The wide availability of cheap and large FPGA devices, advances in automatic synthesis from VHDL/Verilog and abundance of high performance computing platforms enables the design of a generic validation system for such Multiprocessor SoCs.In this paper we present the design and implementation of Srijan Multiprocessor Prototyping System (SMPS). SMPS is a system for rapid prototyping and validation of single chip application specific multiprocessor systems. The individual computing elements are RISC processors, coprocessors which lie in the processor pipeline, and ASICs which connect directly to system bus. The system is a tightly coupled multiprocessor with shared memory and shared address space. A Real-time Operating System (RTOS) provides task scheduling and access to shared resources. The system is presented as a parameterized VHDL based on the open source Sparc~V8 compliant LEON processor and a homegrown light-weight RTOS, RtKer-MP. The entire VHDL is configurable using a GUI, has support for cache coherency, choice of arbitration policy and easy integration of custom processing engines. RtKer-MP allows for a pluggable scheduler, dynamic and static scheduling policies, static and dynamic task migrations domains and variable interruption frequencies for separate processors. The pluggable scheduler interface allows for quick exploration of various scheduling policies for a feedback to the estimation systems.

Traditional public transportation mostly uses fixed schedules to meet society’s needs reliably. Alternatively, one can design a dynamic policy to update the schedule according to the state of the network. Using such policy, any dynamic changes in demand, travel times, traffic, geometry, or emergency modes will be reflected in the real-time scheduling. In this study, the application of reinforcement learning for public transportation scheduling and routing is proposed considering electric vehicles. Reinforcement learning is a right choice for online decision-making in a time-variant setting. Reflecting electric vehicles’ characteristics on public transportation scheduling supports the necessity of considering a dynamic scheduling policy, such as vehicle-to-grid transaction capability or dynamic charging strategies. The proposed scheduling methodology is evaluated for a customary six-stop network. The trained agent takes actions based on the number of waiting people, the drop-off requests, battery level, time, and the current location. The assumed models for the traffic load effect, the passenger flow per stops, and the electricity price add nonlinearity to the problem in which this algorithm will behave more conveniently compared to a fixed schedule setting. Using this method, the electric bus can choose the next destination, the optimal driving speed for each interval, and the amount of electricity to charge or to sell for optimal financial gain when connected to the charging infrastructure. The proposed environment is built numerically, and a learning-based agent is trained for this purpose. Our study supports that the optimal dynamic agent outperforms a fixed schedule policy in different modes of network performance, particularly, when the network undergoes abrupt demand changes.KeywordsReinforcement LearningRoutingPublic transitOptimizationSAC (soft actor-critic)Electric vehicle

The increasing demand for data services has given rise to efficient utilization of available resources (e.g., energy) in modern wireless communication. In order to address the energy requirements a wireless powered communication network (WPCN) with separate energy source (ES) and access point (AP) is considered in this work. The transmitters here adopt harvest-then-transmit (HTT) protocol for transmission to AP. An optimal dynamic time allocation and scheduling policy is considered which maximizes the throughput of the system. The throughput maximization problem formulated is convex in nature and solved using convex optimization techniques. The fairness of proposed policy is compared with max-min policy which use harvest-or-transmit (HOT) protocol in terms of Jain's fairness index. Simulation results highlights the trade-off between throughput and fairness and show that the proposed policy is more reliable for the overcrowded scenario.

This paper is concerned with the problem of optimally scheduling a multiclass open queueing network with four single-server stations in which dynamic control policies are permitted. Under the assumption that the system is heavily loaded, the original scheduling problem can be approximated by a dynamic control problem involving Brownian motion. We reformulate and solve this problem and, from the interpretation of the solution, we obtain two dynamic scheduling policies for our queueing network. We compare the performance of these policies with two static scheduling policies and a lower bound via simulation. Our results suggest that under either dynamic policy the system, at least when heavily loaded, exhibits the form of resource pooling given by the solution to the approximating control problem. Furthermore, even when lightly loaded the system performs better under the dynamic policies than under either static policy.

Many researchers have studied variants of queueing systems with vacations. Most of them have dealt with M/G/1 systems and have explicitly analyzed some of their performance measures, such as queue length, waiting time, and so on. Recently, studies on queueing systems whose arrival processes are not Poissonian have appeared. We consider a single server queueing system with multiple vacations and E-limited service discipline, where messages arrive to the system according to a switched Poisson process. First, we consider the joint probability density functions of the queue length and the elapsed service time or the elapsed vacation time. We derive the equations for these pdf's, which include a finite number of unknown values. Using Rouche's theorem, we determine the values from boundary conditions. Finally, we derive the transform of the stationary queue length distribution explicitly.

Motivated by dynamic scheduling control for queueing networks, Chen and Yao [8] developed a systematic method to generate dynamic scheduling control policies for a fluid network, a simple and highly aggregated model that approximates the queueing network. This study addresses the question of how good these fluid policies are as heuristic scheduling policies for queueing networks. Using simulation on some examples these heuristic policies are compared with traditional simple scheduling rules. The results show that the heuristic policies perform at least comparably to classical priority rules, regardless of the assumptions made about the traffic intensities and the arrival and service time distributions. However, they are certainly not always the best and, even when they are, the improvement is seldom dramatic. The comparative advantage of these policies may lie in their application to nonstationary situations such as might occur with unreliable machines or nonstationary demand patterns.

Departure process of a single server queueing system with Markov renewal input and general service time distribution

Mobile cloud computing (MCC) as an emerging and prospective computing paradigm, can significantly enhance computation capability and save energy of smart mobile devices (SMDs) by offloading computation-intensive tasks from resource-constrained SMDs onto the resource-rich cloud. However, how to achieve energy-efficient computation offloading under the hard constraint for application completion time remains a challenge issue. To address such a challenge, in this paper, we provide an energy-efficient dynamic offloading and resource scheduling (eDors) policy to reduce energy consumption and shorten application completion time. We first formulate the eDors problem into the energy-efficiency cost (EEC) minimization problem while satisfying the task-dependency requirements and the completion time deadline constraint. To solve the optimization problem, we then propose a distributed eDors algorithm consisting of three subalgorithms of computation offloading selection, clock frequency control and transmission power allocation. More importantly, we find that the computation offloading selection depends on not only the computing workload of a task, but also the maximum completion time of its immediate predecessors and the clock frequency and transmission power of the mobile device. Finally, our experimental results in a real testbed demonstrate that the eDors algorithm can effectively reduce the EEC by optimally adjusting the CPU clock frequency of SMDs based on the dynamic voltage and frequency scaling (DVFS) technique in local computing, and adapting the transmission power for the wireless channel conditions in cloud computing.

We consider queueing systems in which the service rate is the controlled variable. The cost depends on the queue length and selected rate. The objective is to choose the service rate dynamically, based on the state of the system so as to minimize the average cost over an infinite horizon. Six classes, either known in the literature or new, are studied in detail: queueing systems with vacations, single-server queueing systems with and without switching costs, and tandem queueing systems with and without service costs. A novel approach is presented here using fuzzy control to solve these problems. Simulation shows that the approach is efficient and promising, especially in cases where analytical solutions do not exist.

In this paper we assume that the customers arrive at a single server queueing system according to Markovian Arrival process. When the system is empty, the server goes for vacation and produces inventory for future use during this period. The maximum processed inventory at a stretch is L. The inventory processing time follows phase type distribution. These are required for the service of customers-one for each customer. The server returns from vacation when there are N customers in the system. The service time follows two distinct phase type distributions depending on whether there is processed items or no processed item available at service commencement epoch. We analyse the distributions of time till the number of customers hit N or the inventory level reaches L, idle time, the distribution of time until the number of customers hit N and also the distribution of the number of inventory processed before the arrival of first customer. Also we provide the distribution of a busy cycle, LSTs of busy cycles in which no item is left in the inventory and at least one item is left in the inventory. We perform some numerical experiments to evaluate the expected idle time, standard deviation and coefficient of variation of idle time of the server.

We consider a single server queueing system where each customer visits the queue a fixed number of times before departure. A customer on his j th visit to the queue is defined to be a class-j -customer. We obtain the joint probability generating function for the number of class-j-customers and also obtain the Laplace-Stieltjes transform for the total response time of a customer.

We present a multiplicative multifractal process to model traffic which exhibits long‐range dependence. Using traffic trace data captured by Bellcore from operations across local and wide area networks, we examine the interarrival time series and the packet length sequences. We also model the frame size sequences of VBR video traffic process. We prove a number of properties of multiplicative multifractal processes that are most relevant to their use as traffic models. In particular, we show these processes to characterize effectively the long‐range dependence properties of the measured processes. Furthermore, we consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by our multifractal processes (the latter forming a MFe/MFg/1 queueing system model). In comparing the performance of both systems, we demonstrate our models to effectively track the behaviour exhibited by the system driven by the actual traffic processes. We show the multiplicative multifractal process to be easy to construct. Through parametric dependence on one or two parameters, this model can be calibrated to fit the measured data. We also show that in simulating the packet loss probability, our multifractal traffic model provides a better fit than that obtained by using a fractional Brownian motion model. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper, we consider two queueing models. Model I is on a single-server queueing system in which the arrival process follows MAP with representation D = (D0,D1) of order m and service time follows phase-type distribution (β, S) of order n. When a customer enters into service, a generalized Erlang clock is started simultaneously. The clock has k stages. The pth stage parameter is θp for 1 ≤ p ≤ k. If a customer completes the service in between the realizations of stages k1 and k2 (1 < k1 < k2 < k) of the clock, it is a perfect one. On the other hand, if the service gets completed either before the kth1 stage realization or after the kth2 stage realization, it is discarded because of imperfection. We analyse this model using the matrix-geometric method. We obtain the expected service time and expected waiting time of a tagged customer. Additional performance measures are also computed. We construct a revenue function and numerically analyse it. In Model II, a single server queueing system in which all assumptions are the same as in Model I except the assumption on service time, is considered. Up to stage k1 service time follows phase-type distribution (α′ , T′) of order n1 and beyond stage k1, the service time follows phase type distribution (β′ , S′) of order n2. We compare the values of the revenue function of the two models

We consider a single server queueing system M/G/1 in which customers arrive in a Poisson process with mean λt, and the service time has distribution dB(t), 0 < t < ∞. Let W(t) be the virtual waiting time process, i.e., the time that a potential customer arriving at the queueing system at time t would have to wait before beginning his service. We also let the random variable denote the first busy period initiated by a waiting time u at time t = 0.

Optimal scheduling in single-server queueing systems is a classic problem in queueing theory. The Gittins index policy is known to be the optimal nonanticipating policy minimizing the mean delay in the M/G/1 queue. While the Gittins index is thoroughly characterized for ordinary jobs whose state is described by the attained service, it is not at all the case with jobs that have more complex structure. Recently, a class of such jobs, multistage jobs, were introduced, and it was shown that the computation of Gittins index of a multistage job decomposes into separable computations for the individual stages. The characterization is, however, indirect in the sense that it relies on the recursion for an auxiliary function (the so-called SJP—single-job profit—function) and not for the Gittins index itself. In this paper, we focus on sequential multistage jobs, which have a fixed sequence of stages, and prove that, for them, it is possible to compute the Gittins index directly by recursively combining the Gittins indices of its individual stages. In addition, we give sufficient conditions for the optimality of the FCFS and SERPT disciplines for scheduling sequential multistage jobs. On the other hand, we demonstrate that, for nonsequential multistage jobs, it is better to compute the Gittins index by utilizing the SJP functions.