Robert D. van der Mei

A prediction method for job runtimes on shared processors: Survey, statistical analysis and new avenues

Grid computing is an emerging technology by which huge numbers of processors over the world create a global source of processing power. Their collaboration makes it possible to perform computations that are too extensive to perform on a single processor. On a grid, processors may connect and disconnect at any time, and the load on the computers can be highly bursty. These characteristics raise the need for the development of techniques that make grid applications robust against the dynamics of the grid environment. In particular, applications that use significant amounts of processor power for running jobs need effective predictions of the expected computation times of those jobs on remote hosts. Currently, there are no effective prediction methods available that cope with the ever-changing running times of jobs on a grid environment. Motivated by this, we develop the Dynamic Exponential Smoothing (DES) method to predict running times in a grid environment. The main idea behind DES is that it dynamically adapts its prediction strategy to the height of the fluctuations in those running times. We have performed extensive experiments in a real global-scale grid environment to compare the effectiveness of DES. The results demonstrate that DES strongly and consistently outperforms existing prediction methods.

Towards a unifying theory on branching-type polling systems in heavy traffic

Abstract For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper it is shown that for this class of polling models the vector that describes the state of the system at these polling instants, say X=(X1,…,XM), satisfies the following heavy-traffic behavior (under mild assumptions): 1

Optimal File Splitting for Wireless Networks with Concurrent Access

\label{eq01}(1-\rho)\underline{X}\rightarrow_{d}\underline{\gamma}~\Gamma(\alpha,\mu)\quad (\rho\uparrow1),

The impact of scheduling policies on the waiting-time distributions in polling systems

where γ is a known M-dimensional vector, Γ(α,μ) has a gamma-distribution with known parameters α and μ, and where ρ is the load of the system. This general and powerful result is shown to lead to exact—and in many cases even closed-form—expressions for the Laplace-Stieltjes Transform (LST) of the complete asymptotic queue-length and waiting-time distributions for a broad class of branching-type polling models that includes many well-studied polling models policies as special cases. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models.

On two-queue Markovian polling systems with exhaustive service

Grids functionally combine globally distributed computers and information systems for creating a universal source of computing power and information A key characteristic of grids is that resources (e.g., CPU cycles and network capacities) are shared among numerous applications, and therefore, the amount of resources available to any given application highly fluctuates over time In this paper we analyze the impact of the fluctuations in the processing speed on the performance of grid applications Extensive lab experiments show that the burstiness in processing speeds has a dramatic impact on the running times, which heightens the need for dynamic load balancing schemes to realize good performance Our results demonstrate that a simple dynamic load balancing scheme based on forecasts via exponential smoothing is highly effective in reacting to the burstiness in processing speeds.

Resource optimization in distributed real-time multimedia applications

The fundamental limits on channel capacity form a barrier to the sustained growth on the use of wireless networks. To cope with this, multi-path communication solutions provide a promising means to improve reliability and boost Quality of Service (QoS) in areas that are covered by a multitude of wireless access networks. Today, little is known about how to effectively exploit this potential. Motivated by this, we consider N parallel communication networks, each of which is modeled as a processor sharing (PS) queue that handles two types of traffic: foreground and background. We consider a foreground traffic stream of files, each of which is split into N fragments according to a fixed splitting rule (*** 1 ,...,*** N ), where *** *** i = 1 and *** i *** 0 is the fraction of the file that is directed to network i . Upon completion of transmission of all fragments of a file, it is re-assembled at the receiving end. The background streams use dedicated networks without being split. We study the sojourn time tail behavior of the foreground traffic. For the case of light foreground traffic and regularly varying foreground file-size distributions, we obtain a reduced-load approximation (RLA) for the sojourn times, similar to that of a single PS-queue. An important implication of the RLA is that the tail-optimal splitting rule is simply to choose *** i proportional to c i *** ρ i , where c i is the capacity of network i and ρ i is the load offered to network i by the corresponding background stream. This result provides a theoretical foundation for the effectiveness of such a simple splitting rule. Extensive simulations demonstrate that this simple rule indeed performs well, not only with respect to the tail asymptotics, but also with respect to the mean sojourn times. The simulations further support our conjecture that the same splitting rule is also tail-optimal for non-light foreground traffic. Finally, we observe near-insensitivity of the mean sojourn times with respect to the file-size distribution.

Internet performance and control of network systems

Many Internet applications employ multi-tier software architectures. The performance of such multi-tier Internet applications is typically measured by the end-to-end response times. Most of the earlier works in modeling the response times of such systems have limited their study to modeling the mean. However, since the user-perceived performance is highly influenced by the variability in response times, the variance of the response times is important as well. We first develop a simple model for the end-to-end response times for multi-tiered Internet applications. We validate the model by real data from two large-scale applications that are widely deployed on the Internet. Second, we derive exact and approximate expressions for the mean and the variance, respectively, of the end-to-end response times. Extensive numerical validation shows that the approximations match very well with simulations. These observations make the results presented highly useful for capacity planning and performance prediction of large-scale multi-tiered Internet applications.

Waiting times in queueing networks with a single shared server

We consider polling models consisting of a single server that visits the queues in a cyclic order. In the vast majority of papers that have appeared on polling models, it is assumed that at each of the individual queues, the customers are served on a first-come-first-served (FCFS) basis. In this paper, we study polling models where the local scheduling policy is not FCFS but instead is varied as last-come-first-served (LCFS), random order of service (ROS), processor sharing (PS), and shortest-job-first (SJF). The service policies are assumed to be either gated or globally gated. The main result of the paper is the derivation of asymptotic closed-form expressions for the Laplace–Stieltjes transform of the scaled waiting-time and sojourn-time distributions under heavy-traffic assumptions. For FCFS service, the asymptotic sojourn-time distribution is known to be of the form