Approximation Algorithms for Layered Multicast Scheduling

Multi-chip scheduler implementation in IQ switches are suited to reduce the hardware complexity in very large, high-speed, switches. However, this implies introducing a RTTs (Round Trip Time) among input and output selectors used to determine a matching due to inter-chip latency. This delay requires modifications to scheduling algorithms to allow a fully distributed implementation while keeping good performance. We propose a novel multicast scheduler, named IMRR, an extension of a previously proposed multicast scheduling algorithm named mRRM, making it suitable to a multi-chip implementation, and examine its performance by simulation.

In this paper, we consider scheduling in multicast switching networks, which aims to minimize the multicast latency for a set of multicast requests. Such a problem has been proved to be NP-complete. We propose a simple, fast greedy multicast scheduling algorithm and derive a lower bound and an upper bound on the performance of the algorithm. As can be seen, while a lower bound is fairly straightforward, the upper bound is much more difficult to obtain. By translating the multicast scheduling problem into a graph theory problem and employing a random graph approach, we are able to obtain a probabilistic upper bound on the performance of the multicast scheduling algorithm. Our analytical and simulation results show that the performance of the proposed multicast scheduling algorithm is quite close to the lower bound and is statistically guaranteed by the probabilistic upper bound.

Summary form only given. Multicast communication, which involves transmitting information from one node to multiple nodes, is a vital operation in both broadband integrated services digital networks (BISDN) and scalable parallel computers. Among different multicast switching networks, much work has been centered around the crossbar switches due to the simplicity of implementation. However, crossbars have the maximum number of crosspoints and implementation complexity among all switching fabrics. Multistage interconnect networks (MINs) such as Clos networks have attracted many attentions in recent years due to the nonblocking property as the crossbars, while at the same time possessing many advantages over crossbars. However, no multicast scheduling and routing algorithm have been applied to Clos network. This paper explores this aspect - we study some existing multicast scheduling and routing algorithms and apply them to Clos networks. Moreover, we propose two packet scheduling strategies to improve the system performance in terms of switch blocking probability and throughput, as shown by simulations.

Multirate multicast is a powerful methodology of multimedia communication in heterogenous networks. A variant of multirate multicast motivated by scalable multimedia streaming is layered multicast, where the transmitted signal is presented in successive data layers. With recent advances of network coding theory, many layered multicast schemes using network coding have been proposed to improve the performance of traditional routing-based layered multicast. They divide the network into different layers and construct a unirate multicast network code for each layer. However, these schemes do not perform network coding between data layers, and consequently cannot realize the full potential of network coding. In this paper, we propose a novel approach to layered multicast that allows network coding of data in different layers. This relaxation lends the proposed scheme greater flexibility in optimizing the data flow than previous layered solutions, and thus achieves higher throughput.

Recent developments in networking technologies, coupled with the advent of high-capacity storage devices and improved coding schemes, will make it feasible to provide many advanced multimedia communications services. Among future telecommunication services, the VOD (Video On Demand) service is emerging as one of the most promising services. In this paper, we propose a new VOD service scheme that utilizes the dynamic multicasting capabilities of future networks. We first describe an overall VOD service architecture that consists of CPEs (Customer Premise Equipments), SCCs (Service Control Centers), and ISs (Information Stores). Based on the assumptions that each subscriber has local storage space and the video transfer speed is faster than the playback speed, we develop a new service scheme where video signals are multicasted to multiple subscribers simultaneously. To realize the potential benefits of multicasting, we propose two scheduling algorithms: EDS (Earliest Deadline Scheduling) and MMS (Most Multicasting Scheduling). Finally, we study the performance of multicasting scheme and compare the performance of the two scheduling algorithms via computer simulation. The simulation results show that multicasting increases the service capacity of an SCC significantly.

Traditional macro-cell networks are experiencing an explosion of data traffic, and small-cell can efficiently solve this problem by efficiently offloading the traffic from macro-cells. Given massive small-cells deployed in each over-crowed macro-cell, their aggregate power consumption (though low for an individual) can be larger than that of a macro-cell. To reduce the total power consumption of a whole heterogeneous network (HetNet) including macro-cells and small-cells, we dynamically schedule the operating modes of all small-cells (active or sleeping) in each macro-cell, while keeping the macro-cell active to avoid any service failure in coverage. When mobile users (MUs) are homogeneously distributed in a macro-cell according to a Poisson point process (PPP), we optimally propose small-cell location-based scheduling scheme to progressively decide the states of small-cells according to their distances to the corresponding macro-cell base station. Finally, we turn to a more general case where MUs are heterogeneously distributed in different small-cells. We first prove that the optimal scheduling problem is NP-hard and then propose a location-and-coverage-based scheduling algorithm which gives a suboptimal solution in polynomial-time. Simulation results show that the performance loss of our proposed algorithm is less than 1 percentage from the perspective of network power consumption.

We consider the minimum-delay multicast scheduling problem for switched beamforming systems. A salient characteristic of mmWave links, reflection, is considered, which enables opportunistic reduction of data dissemination delay. We formulate the problem as a mixed integer nonlinear programming, which is difficult to solve directly. Instead, we decompose the problem into a set of subproblems, by allocating a fixed path to each receiver for data reception. The optimal solution to each subproblem has a contiguous structure, and hence can be computed using a dynamic programming-based approach. We propose an optimal algorithm for the original problem based on the solutions to the subproblems. By simulation we show the outperformance of our algorithm over an optimal multicast scheduling policy without leveraging reflections and a broadcast baseline scheme.

This paper addresses the problem of scheduling real-time wireless flows under dynamic network conditions and general traffic patterns. The objective is to maximize the fraction of packets of each flow to be delivered within their deadlines, referred to as timely-throughput. The scheduling problem under restrictive frame-based traffic models or greedy maximal scheduling schemes like LDF has been extensively studied so far, but scheduling algorithms to provide deadline guarantees on packet delivery for general traffic under dynamic network conditions are very limited. We propose two scheduling algorithms using deep reinforcement learning approach to optimize timely-throughput for general traffic in dynamic wireless networks: RL-Centralized scheduling algorithm and RL-Decentralized scheduling algo-rithm. Specifically, we formulate the centralized scheduling problem as a Markov Decision Process (MDP) and a multi-environments double deep Q-network (ME-DDQN) structure is proposed to adapt to the dynamic network conditions. The decentralized scheduling problem is formulated as a Partially Observable Markov Decision Process (POMDP) and an expert-apprentice centralized training and decentralized execution (EA-CTDE) structure is designed to accelerate the training speed and achieve the optimal timely-throughput. The extensive results show that the proposed scheduling algorithms converge fast and adapt well to network dynamics with superior performance compared to baseline policies. Finally, experimental tests confirm simulation results and also show that the proposed algorithms are feasible in practice on resource limited platforms.

Many applications involve the concepts of scheduling, such as communications, packet routing, production planning [Zhai et al., 2006], classroom arrangement [Mathaisel & Comm, 1991], aircrew scheduling [Chang, 2002], nurse scheduling [Ohki et al., 2006], food industrial [Simeonov & Simeonovova, 2002], control system [Fleming & Fonseca, 1993], resource-constrained scheduling problem [Chen, 2007] and grid computing. There are many different types of scheduling problems such as real-time, job-shop, permutation flow-shop, project scheduling and other scheduling problems have been studied intensively. However, in this work, the studied grid task scheduling problem is much more complex than above stated classic task scheduling problems. Restated, a grid application is regarded as a task scheduling problem involving tasks with inter-communication and distributed homogeneous or heterogeneous resources, and can be represented by a task interaction graph (TIG). Grid is a service for sharing computing power and data storage capacity over the Internet. The grid systems outperform simple communication between computers and aims ultimately to turn the global network of computers into one vast computational resource. Grid computing can be adopted in many applications, such as high-performance applications, large-output applications, data-intensive applications and community-centric applications. These applications major concern to efficiently schedule tasks over the available multi-processor environment provided by the grid. A grid is a collaborative environment in which one or more tasks can be submitted without knowing where the resources are or even who owns the resources [Foster et al., 2001]. The efficiency and effectiveness of grid resource management greatly depend on the scheduling algorithm [Lee et al., 2007]. Generally, in the grid environment, these resources are different over time, and such changes will affect the performance of the tasks running on the grid. In grid computing, tasks are assigned among grid system [Salman, 2002]. The purpose of task scheduling in grid is to find optimal task-processor assignment and hence minimize application completion time (total cost). Most scheduling problems in these applications are categorized into the class of NP-complete problems. This implies that it would take amount of computation time to obtain an optimal solution, especially for a large-scale scheduling problem. A variety of approaches have been applied to solve scheduling problems, such as

Multirate multicast is a powerful methodology of multimedia communication in heterogenous networks. With recent advances of network coding theory, many multirate multicast techniques using network coding have been proposed and they hold promises of improving information multicast efficiency over the traditional application-layer multicast protocols. However, all these network coding based multirate multicast solutions adopted a layered coding technique and involves computationally expensive optimization to decide the amount of information transmitted in each multicast layer. In this paper, we propose a novel multirate multicast framework for lossy networks, which uses both the uneven erasure protection (UEP) technique and linear network codes. The new multicast framework not only simplifies the construction of the multicast codes, but also guarantees the strict fairness among clients of different bandwidths.

More and more applications of grid have been achieved. How to support Quality of Service (QoS) to meet different users' demand has raised an outstanding challenge. Currently, several QoS policies of resource have been widely used in Grid. Thus, how to use them freely and efficiently is a serious problem. In this study, we illustrated three QoS policies of resources: best effort, real time, and competing, and explain their mechanisms. Following this, we proposed a new QoS policy, namely Free QoS policy, to help the user who is not very familiar with QoS polices. The first step is that we can get the matrix of QoS parameters of each resource from the Policy Pool in which all the information about QoS policies of resources in “virtual organizations” could be obtained. Second, we will calculate every resource's P adjugment value by a comparison algorithm. Finally, the QoS policy matching the maximum value of P adjugment value is the user's decision. After choosing a suitable resource with a clear QoS policy, the next question is how to achieve an optimum quality under the given policy, which is the problem of scheduling. Min_Min algorithm has been widely used as a higher efficiency and simple algorithm. However, it has a serious problem: load unbalance. In order to solve the problem, we propose a novel task scheduling algorithm, called the Heuristic task scheduling algorithm based on Min-Min and Max-Min (H-MM) in the best effort of the QoS policy, which is merged with the high efficiency of the traditional Min-Min scheduling algorithm and the load balance of the traditional Max-Min scheduling algorithm. Through plenty of experiments, we know that the performance of Max-Min is better than that of Min-Min in the condition that the values of ETC are not uniform, and the performance of Min-Min is a priority to Max-Min when there are many tasks in which the value of ETC are uniform. In this paper, we take the relative standard deviation value of ETC matrix's Min_Time as the criterion to judge whether the set of tasks is uniform or not. Finally, the scheduler selects the Max-Min or Min-Min to assign tasks. The experiments have shown that the H-MM algorithm overweighs traditional algorithms a lot in the makespan and the scalability of the scheduling algorithm.

How many small cell (SC) access points (APs) are required to guarantee a chosen quality of service in a heterogeneous network? In this chapter, we answer this question considering two different network models. The first is the downlink of a finite-area SC network where the locations of APs within the chosen area are uniformly distributed. A key step in obtaining the closed-form expressions is to generalize the well-accepted moment matching approximation for the linear combination of lognormal random variables. For the second model, we focus on a two-layer downlink heterogeneous network with frequency reuse-1 hexagonal macro cells (MCs), and SC APs that are placed at locations that do not meet a chosen quality of service from macro base stations (BSs). An important property of this model is that the SC AP locations are coupled with the MC coverage. Here, simple bounds for the average total interference within an MC makes the formulation possible for the percentage of MC area in outage, as well as the required average number of SCs (per MC) to overcome outage, assuming isolated SCs. Introduction Heterogeneous cellular networks (HCNs) are being considered as an efficient way to improve system capacity as well as effectively enhance network coverage [1, 2]. Comprising multiple layers of access points (APs), HCNs encompass a conventional macro cellular network (first layer) overlaid with a diverse set of small cells (SCs) (higher layers). Cell deployment is an important problem in heterogeneous networks, both in terms of the number and positioning of the SCs. Traditional network models are either impractically simple (such as the Wyner model [3]) or excessively complex (e.g., the general case of random user locations in a hexagonal lattice network [4]) to accurately model SC networks. A useful mathematical model that accounts for the randomness in SC locations and irregularity in the cells uses spatial point processes, such as Poisson point process (PPP), to model the location of SCs in the network [5–10]. The independent placement of SCs from the MC layer, has the advantage of analytical tractability and leads to many useful SINR and/or rate expressions. However, even assuming that wireless providers would deploy SCs to support mobile broadband services, the dominant assumption remains that SCs are deployed randomly and independent of the MC layer [11].

We consider the scheduling problem in a new slotted optical network called TWIN. The TWIN architecture possesses interesting properties, which may offer solutions for next-generation optical networks. Besides, TWIN has the ability to support quality of service (QoS) by controlling two important parameters: queueing delay and delay variance. However, to the best of our knowledge, the existing scheduling algorithms in TWIN focused mainly on maximizing the throughput and ignored the consideration of QoS. We formulate the scheduling problem into an integer linear programming problem and propose a heuristic--virtual topology-based dynamic scheduling (VTBDS) algorithm to solve it fast and efficiently. Besides, we derive an analytical model for TWIN and investigate the performance of VTBDS in it. By means of simulations, we demonstrate that our model approximates the TWIN network very well, and VTBDS incurs smaller queueing delay and delay variance, which are advantageous for guaranteeing better QoS.

Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to be executed on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time.Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new input. For scheduling problems, the maximum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor.We design a strongly optimal algorithm with the migration factor \(1-\frac 1m\) for identical machines. Such algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is minimal lexicographically. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ℓ p norm (for p > 1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any ℓ p norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.

In a heterogeneous system, processor and network failure are inevitable and can have adverse effect on the complex applications executing on the systems. To reduce the rate of these failures, matching and scheduling algorithms should take into account the objectives of minimizing schedule length (makespan) and reducing the probability of failure. Equitable distribution of workload over resources contributes in reducing the probability of failure. The Heterogeneous Earliest Finish Time (HEFT) algorithm has been proved as a performance effective task scheduling algorithm, addressing the objective of minimizing makespan. Reliable Dynamic Level Scheduling (RDLS) algorithm is a bi-objective scheduling algorithm that maximizes the reliability more effectively. Though the reliable version of HEFT algorithm (RHEFT) considers failure rate in scheduling decision, the improvement in reliability is less, compared to that of RDLS. To overcome this deficiency, we propose to incorporate the task–processor pair finding step of RDLS in HEFT algorithm, since it meets both the objectives of minimizing the makespan and maximizing the reliability. We define the load on a processor as the amount of time the processor is engaged in completing the scheduled subtasks. In this paper, a modification to the HEFT is proposed as a new algorithm called Improved Reliable HEFT (IRHEFT) for minimizing the schedule length, balancing the load and maximizing the reliability of schedule. The algorithm is compared for its performance with RDLS algorithm for randomly generated task graphs and a real application task graph.