Scheduling Packets with Values and Deadlines in Size-bounded Buffers

Motivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of multiple size-bounded buffers such that at any time, the number of packets residing in each individual buffer cannot exceed its capacity. Packets arrive at the network switch over time; they have values, deadlines, and designated buffers. In each time step, at most one pending packet is allowed to be sent and this packet can be from any buffer. The objective is to maximize the total value of the packets sent by their respective deadlines. A 9.82-competitive online algorithm has been provided for this model (Azar and Levy. SWAT 2006), but no offline algorithms have been known yet. In this paper, We study the offline setting of the multi-buffer model. Our contributions include a few optimal offline algorithms for some variants of the model. Each variant has its unique and interesting algorithmic feature. These offline algorithms help us understand the model better in designing online algorithms.Comment: 7 page

Bounded Delay Scheduling with Packet Dependencies

A common situation occurring when dealing with multimedia traffic is having large data frames fragmented into smaller IP packets, and having these packets sent independently through the network. For real-time multimedia traffic, dropping even few packets of a frame may render the entire frame useless. Such traffic is usually modeled as having {\em inter-packet dependencies}. We study the problem of scheduling traffic with such dependencies, where each packet has a deadline by which it should arrive at its destination. Such deadlines are common for real-time multimedia applications, and are derived from stringent delay constraints posed by the application. The figure of merit in such environments is maximizing the system's {\em goodput}, namely, the number of frames successfully delivered. We study online algorithms for the problem of maximizing goodput of delay-bounded traffic with inter-packet dependencies, and use competitive analysis to evaluate their performance. We present competitive algorithms for the problem, as well as matching lower bounds that are tight up to a constant factor. We further present the results of a simulation study which further validates our algorithmic approach and shows that insights arising from our analysis are indeed manifested in practice

Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc

Measuring the Impact of Adversarial Errors on Packet Scheduling Strategies

In this paper we explore the problem of achieving efficient packet transmission over unreliable links with worst case occurrence of errors. In such a setup, even an omniscient offline scheduling strategy cannot achieve stability of the packet queue, nor is it able to use up all the available bandwidth. Hence, an important first step is to identify an appropriate metric for measuring the efficiency of scheduling strategies in such a setting. To this end, we propose a relative throughput metric which corresponds to the long term competitive ratio of the algorithm with respect to the optimal. We then explore the impact of the error detection mechanism and feedback delay on our measure. We compare instantaneous error feedback with deferred error feedback, that requires a faulty packet to be fully received in order to detect the error. We propose algorithms for worst-case adversarial and stochastic packet arrival models, and formally analyze their performance. The relative throughput achieved by these algorithms is shown to be close to optimal by deriving lower bounds on the relative throughput of the algorithms and almost matching upper bounds for any algorithm in the considered settings. Our collection of results demonstrate the potential of using instantaneous feedback to improve the performance of communication systems in adverse environments

A New Competitive Ratio for Network Applications with Hard Performance Guarantee

Online algorithms are used to solve the problems which need to make decisions without future knowledge. Competitive ratio is used to evaluate the performance of an online algorithm. This ratio is the worst-case ratio between the performance of the online algorithm and the offline optimal algorithm. However, the competitive ratios in many current studies are relatively low and thus cannot satisfy the need of the customers in practical applications. To provide a better service, a practice for service provider is to add more redundancy to the system. Thus we have a new problem which is to quantify the relation between the amount of increased redundancy and the system performance. In this dissertation, to address the problem that the competitive ratio is not satisfactory, we ask the question: How much redundancy should be increased to fulfill certain performance guarantee? Based on this question, we will define a new competitive ratio showing the relation between the system redundancy and performance of online algorithm compared to offline algorithm. We will study three applications in network applications. We propose online algorithms to solve the problems and study the competitive ratio. To evaluate the performances, we further study the optimal online algorithms and some other commonly used algorithms as comparison. We first study the application of online scheduling for delay-constrained mobile offloading. WiFi offloading, where mobile users opportunistically obtain data through WiFi rather than through cellular networks, is a promising technique to greatly improve spectrum efficiency and reduce cellular network congestion. We consider a system where the service provider deploys multiple WiFi hotspots to offload mobile traffic with unpredictable mobile users’ movements. Then we study online job allocation with hard allocation ratio requirement. We consider that jobs of various types arrive in some unpredictable pattern and the system is required to allocate a certain ratio of jobs. We then aim to find the minimum capacity needed to meet a given allocation ratio requirement. Third, we study online routing in multi-hop network with end-to-end deadline. We propose reliable online algorithms to schedule packets with unpredictable arriving information and stringent end-to-end deadline in the network