The Shortest-Remaining-Processing-Time (SRPT) scheduling policy has long been known to be optimal for minimizing mean response time (sojourn time). Despite this fact, SRPT scheduling is rarely used in practice. It is believed that the performance improvements of SRPT over other scheduling policies stem from the fact that SRPT unfairly penalizes the large jobs in order to help the small jobs. This belief has led people to instead adopt “fair ” scheduling policies such as Processor-Sharing (PS), which produces the same expected slowdown for jobs of all sizes. This paper investigates formally the problem of unfairness in SRPT scheduling as compared with PS scheduling. The analysis assumes an M/G/1 model, and emphasizes job size distributions with a heavy-tailed property, as are characteristic of empirical workloads. The analysis shows that the degree of unfairness under SRPT is surprisingly small. The M/G/1/SRPT and M/G/1/PS queues are also analyzed under overload and closed-form expressions for mean response time as a function of job size are proved in this setting.

Is it possible to reduce the expected response time ofevery request at a web server, simply by changing the order in which we schedule the requests? That is the question we ask in this paper. This paper proposes a method for improving the performance of web servers servicing static HTTP requests. The idea is to give preference to those requests which are short, or have small remaining processing requirements, in accordance with the SRPT (Shortest Remaining Processing Time) scheduling policy. The implementation is at the kernel level and in-volves controlling the order in which socket buffers are drained into the network.Experiments are executed both in a LAN and a WAN environment. We use the Linux operating system and the Apache and Flash web servers. Results indicate that SRPT-based scheduling of connections yields significant reductions in delay at the web server. These result in a substantial reduction inmean response time, mean slowdown, and variance in response time for both the LAN and WAN environments. Significantly, and counter to intuition, the large requests are only negligibly penalized or not at all penalized as a result of SRPT-based scheduling.

It is common to classify scheduling policies based on their mean response times. Another important, but sometimes opposing, performance metric is a scheduling policy’s fairness. For example, a policy that biases towards short jobs so as to minimize mean response time, may end up being unfair to long jobs. In this paper we define three types of unfairness and demonstrate large classes of scheduling policies that fall into each type. We end with a discussion on which jobs are the ones being treated unfairly. 1

Internet measurements show that the size distribution of Web-based transactions is usually very skewed; a few large requests constitute most of the total traffic. Motivated by the advantages of scheduling algorithms which favor short jobs, we propose to perform differentiated control over Web-based transactions to give preferential service to short web requests. The control is realized through service semantics provided by Internet Traffic Managers, a Diffserv-like architecture. To evaluate the performance of such a control system, it is necessary to have a fast but accurate analytical method. To this end, we model the Internet as a time-shared system and propose a numerical approach which utilizes Kleinrock's conservation law to solve the model. The numerical results are shown to match well those obtained by packet-level simulation, which runs orders of magnitude slower than our numerical method.

Abstract Previous studies have shown that giving preferential treatment to short jobs helps reduce the average system response time, especially when the job size distribution possesses the heavytailed (HT) property. Since it has been shown that the TCP flow length distribution also has the same property, it is natural to let short TCP flows enjoy better service inside the network. Analyzing such discriminatory system requires modification to traditional job scheduling models since usually network traffic managers do not have detailed knowledge about individual flows such as their lengths. The Multi-Level queue, proposed by Kleinrock, can be used to to characterize such system. In this paper, we perform an approximate analysis on the Multi-Level queueing system to obtain closed-form solution of the average system response time function. 1 Introduction Previous job scheduling studies indicate that providing rapid response to interactive jobs which place frequent but small demands, can reduce the overall system average response time [1]. Such size-aware discriminatory scheduling algorithms have been shown, both experimentally and analytically (see [2] and references therein), to work extremely well when the job size distribution possesses the heavytailed (HT) property1. Since data transfer in a network can be modeled as a flow scheduling problem, and the HT property has been observed in the length of Internet transactions, especially Web file transfers, it is natural to design a network system that favors short file transfers.

With a view on improving user perceived performance on networks supporting best effort flows, e.g., multimedia/data file transfers, we propose a family of bandwidth allocation criteria that depends on the residual work of on-going transfers. Analysis and simulations show that allocating bandwidth in this fashion can significantly improve the user perceived delay, bit transmission delay, and throughput over traditional approaches, e.g., by 58% on an 80% loaded linear network. A simple implementation based on TCP Reno, exemplifies how one might approach practically realizing such gains. We discuss several other advantages of incorporating such differentiation at the transport level. In particular we make the case that favoring small transfers combined with user impatience or peak rate constraints, both of which are natural mechanisms for users to express the utility of completing transfers, offers a lightweight approach to achieving good overall network goodput and/or utility for best effort networks.

Abstract — With a view on improving user perceived performance on networks supporting elastic flows, e.g., multimedia/data file transfers, we identify the key properties that an online dynamic bandwidth allocation policy should have. We then propose a family of bandwidth allocation criteria which depends on the residual work of on-going transfers. Analysis and simulations show that allocating bandwidth in this fashion can improve the user perceived average bit transmission delay (BTD), i.e., delay/flow size, by up to 70 % at 80 % traffic load over traditional approaches. A simple implementation based upon TCP Reno, exemplifies how one might approach practically realizing such gains. Further studies on simple network topologies show that as the penetration of the proposed transport mechanism increases, users will have the proper incentives to upgrade from TCP Reno, and that the overall performance is better for all users once the penetration exceeds 20%. I.

We present the rst approximation schemes for minimizing weighted ow time on a single machine with preemption. Our rst result is an algorithm that computes a (1+)-approximate solution for any instance of weighted ow time in O(n time; here P is the ratio of maximum job processing time to minimum job processing time, and W is the ratio of maximum job weight to minimum job weight. This result directly gives a quasi-PTAS for weighted ow time when P and W are polybounded, and a PTAS when they are both O(1). We strengthen the former result to show that in order to get a quasi-PTAS it suces to have just one of P and W to be poly-bounded. Our result provides strong evidence to the hypothesis that the weighted ow time problem has a PTAS. We note that the problem is strongly NP-hard even when P and W are O(1). We next consider two important special cases of weighted ow time, namely, when P is O(1) and W is arbitrary, and when the weight of a job is inverse of its processing time referred to as the stretch metric. For both of the above special cases we obtain a (1 + )-approximation for any > 0 by using a randomized partitioning scheme to reduce an arbitrary instance to several instances all of which have P and W bounded by a constant that depends only on .

Abstract This paper uses a probe-based sampling approach to study the behavioural properties of Web server scheduling strategies, such as Processor Sharing (PS) and Shortest Remaining Processing Time (SRPT). The approach is general purpose, in that it can be used to estimate the mean and variance of the job response time, for arbitrary arrival processes, scheduling policies, and service time distributions.

An Architecture for Highly Concurrent, Well-Conditioned Internet Services by Matthew David Welsh Doctor of Philosophy in Computer Science University of California at Berkeley Professor David Culler, Chair This dissertation presents an architecture for handling the massive concurrency and load conditioning demands of busy Internet services. Our thesis is that existing programming models and operating system structures do not adequately meet the needs of complex, dynamic Internet servers, which must support extreme concurrency (on the order of tens of thousands of client connections) and experience load spikes that are orders of magnitude greater than the average. We propose a new software framework, called the staged event-driven architecture (or SEDA), in which applications are constructed as a network of event-driven stages connected with explicit queues. In this model, each stage embodies a robust, reusable software component that performs a subset of request processing. By performing admission control on each event queue, the service can be well-conditioned to load, preventing resources from being overcommitted when demand exceeds service capacity. SEDA employs dynamic control to tune runtime parameters (such as the scheduling parameters of each stage) automatically, as well as to manage load, for example, by performing adaptive load shedding.