Abstract: Implementation of a commercial application to a
grid infrastructure introduces new challenges in managing the
quality-of-service (QoS) requirements, most stem from the fact
that negotiation on QoS between the user and the service provider
should strictly be satisfied. An interesting commercial application
with a wide impact on a variety of fields, which can benefit from
the computational grid technologies, is three–dimensional (3-D)
rendering. In order to implement, however, 3-D rendering to a
grid infrastructure, we should develop appropriate scheduling
and resource allocation mechanisms so that the negotiated (QoS)
requirements are met. Efficient scheduling schemes require
modeling and prediction of rendering workload. In this paper
workload prediction is addressed based on a combined fuzzy
classification and neural network model. Initially, appropriate
descriptors are extracted to represent the synthetic world. The
descriptors are obtained by parsing RIB formatted files, which
provides a general structure for describing computer-generated
images. Fuzzy classification is used for organizing rendering
descriptor so that a reliable representation is accomplished which
increases the prediction accuracy. Neural network performs
workload prediction by modeling the nonlinear input-output
relationship between rendering descriptors and the respective
computational complexity. To increase prediction accuracy, a
constructive algorithm is adopted in this paper to train the neural
network so that network weights and size are simultaneously
estimated. Then, a grid scheduler scheme is proposed to estimate
the queuing order that the tasks should be executed and the
most appopriate processor assignment so that the demanded
QoS are satisfied as much as possible. A fair scheduling policy is
considered as the most appropriate. Experimental results on a real
grid infrastructure are presented to illustrate the efficiency of the
proposed workload prediction — scheduling algorithm compared
to other approaches presented in the literature.

Abstract: The management of Grid resources requires scheduling of both computation and communication tasks at various levels. In this study, we consider the two constituent sub-problems of Grid scheduling, namely: (i) the scheduling of computation tasks to processing resources and (ii) the routing and scheduling of the data movement in a Grid network. Regarding computation tasks, we examine two typical online task scheduling algorithms that employ advance reservations and perform full network simulation experiments to measure their performance when implemented in a centralized or distributed manner. Similarly, for communication tasks, we compare two routing and data scheduling algorithms that are implemented in a centralized or a distributed manner. We examine the effect network propagation delay has on the performance of these algorithms. Our simulation results indicate that a distributed architecture with an exhaustive resource utilization update strategy yields better average end-to-end delay performance than a centralized architecture.

Abstract: In this paper, we propose an efficient non-linear task workload prediction mechanism incorporated with a fair scheduling algorithm
for task allocation and resource management in Grid computing. Workload prediction is accomplished in a Grid middleware approach
using a non-linear model expressed as a series of finite known functional components using concepts of functional analysis. The coefficient
of functional components are obtained using a training set of appropriate samples, the pairs of which are estimated based on
a runtime estimation model relied on a least squares approximation scheme. The advantages of the proposed non-linear task workload
prediction scheme is that (i) it is not constrained by analysis of source code (analytical methods), which is practically impossible to be
implemented in complicated real-life applications or (ii) it does not exploit the variations of the workload statistics as the statistical
approaches does. The predicted task workload is then exploited by a novel scheduling algorithm, enabling a fair Quality of Service oriented
resource management so that some tasks are not favored against others. The algorithm is based on estimating the adjusted fair
completion times of the tasks for task order selection and on an earliest completion time strategy for the grid resource assignment. Experimental
results and comparisons with traditional scheduling approaches as implemented in the framework of European Union funded
research projects GRIA and GRIDLAB grid infrastructures have revealed the outperformance of the proposed method.

Abstract: About this book
This state-of-the-art survey features papers that were selected after an open call following the International Dagstuhl Seminar on Algorithmic Methods for Railway Optimization held in Dagstuhl Castle, Germany, in June 2004. The second part of the volume constitutes the refereed proceedings of the 4th International Workshop on Algorithmic Methods and Models for Optimization of Railways held in Bergen, Norway, in September 2004.
The volume covers algorithmic methods for analyzing and solving problems arising in railway optimizations, with a special focus on the interplay between railway and other public transportation systems. Beside algorithmics and mathematical optimization, the relevance of formal models and the influence of applications on problem modeling are also considered. In addition, the papers address experimental studies and useful prototype implementations.
The 17 full papers presented here were carefully reviewed and selected from numerous submissions and are organized into topical sections covering network and line planning, timetabling and timetable information, rolling stock and crew scheduling, and real-time operations.

Abstract: Grid Infrastructures have been used to solve large scale scientific problems that do not have special requirements on QoS. However, the introduction and success of the Grids in commercial applications as well, entails the provision of QoS mechanisms which will allow for meeting the special requirements of the users-customers. In this paper we present an advanced Grid Architecture which incorporates appropriate mechanisms so as to allow guarantees of the diverse and contradictory usersrsquo QoS requirements. We present a runtime estimation model, which is the heart of any scheduling and resource allocation algorithm, and we propose a scheme able to predict the runtime of submitted jobs for any given application on any computer by introducing a general prediction model. Experimental results are presented which indicate the robustness and reliability of the proposed architecture. The scheme has been implemented in the framework of GRIA IST project (Grid Resources for Industrial Applications).

Abstract: In this paper, a novel configuration is proposed for
the implementation of an almost all-optical switch architecture
called the scheduling switch, which when combined with appropriate
wait-for-reservation or tell-and-go connection and flow
control protocols provides lossless communication for traffic
that satisfies certain smoothness properties. An all-optical 2 2
exchange/bypass (E/B) switch based on the nonlinear operation
of a semiconductor optical amplifier (SOA) is considered as the
basic building block of the scheduling switch as opposed to active
SOA-based space switches that use injection current to switch
between ON and OFF states. The experimental demonstration of
the optically addressable 2 2 E/B, which is summarized for
10–Gb/s data packets as well as synchronous digital hierarchy
(SDH)/STM-64 data frames, ensures the feasibility of the proposed
configuration at high speeds, with low switching energy and low
losses during the scheduling process. In addition, it provides
reduction of the number of required components for the construction
of the scheduling switch, which is calculated to be 50% in the
number of active elements and 33% in the fiber length.

Abstract: We examine the problem of assigning n independent jobs to m unrelated parallel machines, so that each job is processed without interruption on one of the machines, and at any time, every machine processes at most one job. We focus on the case where m is a fixed constant, and present a new rounding approach that yields approximation schemes for multi-objective minimum makespan scheduling with a fixed number of linear cost constraints. The same approach gives approximation schemes for covering problems like maximizing the minimum load on any machine, and for assigning specific or equal loads to the machines.

Abstract: We study the problem of scheduling permanent jobs on un-
related machines when the objective is to minimize the Lp
norm of the machine loads. The problem is known as load
balancing under the Lp norm. We present an improved up-
per bound for the greedy algorithm through simple analy-
sis; this bound is also shown to be best possible within the
class of deterministic online algorithms for the problem. We
also address the question whether randomization helps on-
line load balancing under Lp norms on unrelated machines;
this is a challenging question which is open for more than a
decade even for the L2 norm. We provide a positive answer
to this question by presenting the ¯rst randomized online
algorithms which outperform deterministic ones under any
(integral) Lp norm for p = 2; :::; 137. Our algorithms es-
sentially compute in an online manner a fractional solution
to the problem and use the fractional values to make ran-
dom choices. The local optimization criterion used at each
step is novel and rather counterintuitive: the values of the
fractional variables for each job correspond to °ows at an ap-
proximate Wardrop equilibrium for an appropriately de¯ned
non-atomic congestion game. As corollaries of our analysis
and by exploiting the relation between the Lp norm and the
makespan of machine loads, we obtain new competitive algo-
rithms for online makespan minimization, making progress
in another longstanding open problem.

Abstract: We study the problem of scheduling permanent jobs on un-
related machines when the objective is to minimize the Lp
norm of the machine loads. The problem is known as load
balancing under the Lp norm. We present an improved up-
per bound for the greedy algorithm through simple analy-
sis; this bound is also shown to be best possible within the
class of deterministic online algorithms for the problem. We
also address the question whether randomization helps on-
line load balancing under Lp norms on unrelated machines;
this is a challenging question which is open for more than a
decade even for the L2 norm. We provide a positive answer
to this question by presenting the ¯rst randomized online
algorithms which outperform deterministic ones under any
(integral) Lp norm for p = 2; :::; 137. Our algorithms es-
sentially compute in an online manner a fractional solution
to the problem and use the fractional values to make ran-
dom choices. The local optimization criterion used at each
step is novel and rather counterintuitive: the values of the
fractional variables for each job correspond to °ows at an ap-
proximate Wardrop equilibrium for an appropriately de¯ned
non-atomic congestion game. As corollaries of our analysis
and by exploiting the relation between the Lp norm and the
makespan of machine loads, we obtain new competitive algo-
rithms for online makespan minimization, making progress
in another longstanding open problem.

Abstract: Divisible load scenarios occur in modern media server applications since most multimedia applications typically require access to continuous and discrete data. A high performance Continuous Media (CM) server greatly depends on the ability of its disk IO subsystem to serve both types of workloads efficiently. Disk scheduling algorithms for mixed media workloads, although they play a central role in this task, have been overlooked by related research efforts. These algorithms must satisfy several stringent performance goals, such as achieving low response time and ensuring fairness, for the discrete-data workload, while at the same time guaranteeing the uninterrupted delivery of continuous data, for the continuous-data workload. The focus of this paper is on disk scheduling algorithms for mixed media workloads in a multimedia information server. We propose novel algorithms, present a taxonomy of relevant algorithms, and study their performance through experimentation. Our results show that our algorithms offer drastic improvements in discrete request average response times, are fair, serve continuous requests without interruptions, and that the disk technology trends are such that the expected performance benefits can be even greater in the future.

Abstract: In this work we examine a task scheduling and data migration problem for Grid Networks, which we refer to as the Data Consolidation (DC) problem. DC arises when a task needs for its execution two or more pieces of data, possibly scattered throughout the Grid Network. In such a case, the scheduler and the data manager must select the data replicas to be used and the site where these will accumulate for the task to be executed. The policies for selecting the data replicas and the data consolidating site comprise the Data Consolidation problem. We propose and experimentally evaluate a number of DC techniques. Our simulation results brace our belief that DC is an important technique for Data Grids since it can substantially improve task delay, network load and other performance related parameters.

Abstract: We describe our experiences from implementing and integrating a new job scheduling algorithm in the gLite Grid middleware and present experimental results that compare it to the existing gLite scheduling algorithms. It is the first time that gLite scheduling algorithms are put under test and compared with a new algorithm under the same conditions. We describe the problems that were encountered and solved, going from theory and simulations to practice and the actual implementation of our scheduling algorithm. In this work we also describe the steps one needs to follow in order to develop and test a new scheduling algorithm in gLite. We present the methodology followed and the testbed that was set up for the comparisons. Our research sheds light on some of the problems of the existing gLite scheduling algorithms and makes clear the need for the development of new.

Abstract: Two important performance parameters of distributed, rate-based flow control algorithms are their locality and convergence complexity. The former is characterized by the amount of global knowledge that is available to their scheduling mechanisms, while the latter is defined as the number of update operations performed on rates of individual sessions until max-min fairness is reached. Optimistic algorithms allow any session to intermediately receive a rate larger than its max-min fair rate; bottleneck algorithms finalize the rate of a session only if it is restricted by a certain, highly congested link of the network. In this work, we present a comprehensive collection of lower and upper bounds on convergence complexity, under varying degrees of locality, for optimistic, bottleneck, rate-based flow control algorithms. Say that an algorithm is oblivious if its scheduling mechanism uses no information of either the session rates or the network topology. We present a novel, combinatorial construction of a capacitated network, which we use to establish a fundamental lower bound of dn 4 + n 2 on the convergence complexity of any oblivious algorithm, where n is the number of sessions laid out on a network, and d, the session dependency, is a measure of topological dependencies among sessions. Moreover, we devise a novel simulation proof to establish that, perhaps surprisingly, the lower bound of dn 4 + n 2 on convergence complexity still holds for any partially oblivious algorithm, in which the scheduling mechanism is allowed to use information about session rates, but is otherwise unaware of network topology. On the positive side, we prove that the lower bounds for oblivious and partially oblivious algorithms are both tight. We do so by presenting optimal oblivious algorithms, which converge after dn 2 + n 2 update operations are performed in the worst case. To complete the picture, we show that linear convergence complexity can indeed be achieved if information about both session rates and network topology is available to schedulers. We present a counterexample, nonoblivious algorithm, which converges within an optimal number of n update operations. Our results imply a surprising convergence complexity collapse of oblivious and partially oblivious algorithms, and a convergence complexity separation between (partially) oblivious and nonoblivious algorithms for optimistic, bottleneck rate-based flow control.

Abstract: We present three new coordination mechanisms for schedul-
ing n sel¯sh jobs on m unrelated machines. A coordination
mechanism aims to mitigate the impact of sel¯shness of jobs
on the e±ciency of schedules by de¯ning a local schedul-
ing policy on each machine. The scheduling policies induce
a game among the jobs and each job prefers to be sched-
uled on a machine so that its completion time is minimum
given the assignments of the other jobs. We consider the
maximum completion time among all jobs as the measure
of the e±ciency of schedules. The approximation ratio of
a coordination mechanism quanti¯es the e±ciency of pure
Nash equilibria (price of anarchy) of the induced game. Our
mechanisms are deterministic, local, and preemptive in the
sense that the scheduling policy does not necessarily process
the jobs in an uninterrupted way and may introduce some
idle time. Our ¯rst coordination mechanism has approxima-
tion ratio O(logm) and always guarantees that the induced
game has pure Nash equilibria to which the system con-
verges in at most n rounds. This result improves a recent
bound of O(log2 m) due to Azar, Jain, and Mirrokni and,
similarly to their mechanism, our mechanism uses a global
ordering of the jobs according to their distinct IDs. Next
we study the intriguing scenario where jobs are anonymous,
i.e., they have no IDs. In this case, coordination mechanisms
can only distinguish between jobs that have diffeerent load
characteristics. Our second mechanism handles anonymous
jobs and has approximation ratio O
¡ logm
log logm
¢
although the
game induced is not a potential game and, hence, the exis-
tence of pure Nash equilibria is not guaranteed by potential
function arguments. However, it provides evidence that the
known lower bounds for non-preemptive coordination mech-
anisms could be beaten using preemptive scheduling poli-
cies. Our third coordination mechanism also handles anony-
mous jobs and has a nice \cost-revealing" potential func-
tion. Besides in proving the existence of equilibria, we use
this potential function in order to upper-bound the price of stability of the induced game by O(logm), the price of an-
archy by O(log2 m), and the convergence time to O(log2 m)-
approximate assignments by a polynomial number of best-
response moves. Our third coordination mechanism is the
¯rst that handles anonymous jobs and simultaneously guar-
antees that the induced game is a potential game and has
bounded price of anarchy.

Abstract: We examine a task scheduling and data migration problem for grid networks, which we refer to as the Data Consolidation (DC) problem. DC arises when a task concurrently requests multiple pieces of data, possibly scattered throughout the grid network, that have to be present at a selected site before the task¢s execution starts. In such a case, the scheduler and the data manager must select (i) the data replicas to be used, (ii) the site where these data will be gathered for the task to be executed, and (iii) the routing paths to be followed; this is assuming that the selected datasets are transferred concurrently to the execution site. The algorithms or policies for selecting the data replicas, the data consolidating site and the corresponding paths comprise a Data Consolidation scheme. We propose and experimentally evaluate several DC schemes of polynomial number of operations that attempt to estimate the cost of the concurrent data transfers, to avoid congestion that may appear due to these transfers and to provide fault tolerance. Our simulation results strengthen our belief that DC is an important problem that needs to be addressed in the design of data grids, and can lead, if performed efficiently, to significant benefits in terms of task delay, network load and other performance parameters.

Abstract: In this work we study the problem of scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds.
We present the preemptive algorithm "Save-Energy" that given a schedule of tasks it post processes it to improve the energy efficiency without any deterioration of the makespan. In terms of time efficiency, we show that preemptive scheduling in an asymmetric system can achieve the same or better optimal makespan than in a symmetric system. Motivited by real multiprocessor systems, we investigate architectures that exhibit limited asymmetry: there are two essentially different speeds. Interestingly, this special case has not been studied in the field of parallel computing and scheduling theory; only the general case was studied where processors have K essentially different speeds. We present the non-preemptive algorithm "Remnants'' that achieves almost optimal makespan. We provide a refined analysis of a recent scheduling method. Based on this analysis, we specialize the scheduling policy and provide an algorithm of (3 + o(1)) expected approximation factor. Note that this improves the previous best factor (6 for two speeds). We believe that our work will convince researchers to revisit this well studied scheduling problem for these simple, yet realistic, asymmetric multiprocessor architectures.

Abstract: We propose a fair scheduling algorithm for Computational Grids, called Fair Execution Time Estimation (FETE) algorithm. FETE assigns a task to the computation resource that minimizes what we call its fair execution time estimation. The fair execution time of a task on a certain resource is an estimation of the time by which a task will be executed on the resource, assuming it gets a fair share of the resource’s computational power. Though space-shared scheduling is used in practice, the estimates of the fair execution times are obtained assuming that a time-sharing discipline is used. We experimentally evaluate the proposed algorithm and observe that it outperforms other known scheduling algorithms. We also propose a version of FETE, called Simple FETE (SFETE), which requires no a-priori knowledge of the tasks workload and in most cases has similar performance to that of FETE.

Abstract: Wireless networks are nowadays widely used and constantly evolving; we are constantly surrounded by numerous such networks. A modern idea is to exploit this variety and aggregate all available connections together towards improving Internet connectivity. In this paper we present our design of a networking system that enables participating entities to connect with each other and share their possible broadband connections. Every connected entity will gain broadband connection access from the ones that have and share one, independently from how many connections are available and how fast they are. Our goal is to improve the broadband connections' utilization and aim towards fault tolerance on these connections. To this end, the system is built on top of a peer-to-peer network, where the participating entities share their connections according to various scheduling algorithms.

Abstract: This paper presents results from the IST Phosphorus project that studies and implements an optical Grid test-bed. A significant part of this project addresses scheduling and routing algorithms and dimensioning problems of optical grids. Given the high costs involved in setting up actual hardware implementations, simulations are a viable alternative. In this paper we present an initial study which proposes models that reflect real-world grid application traffic characteristics, appropriate for simulation purposes. We detail several such models and the corresponding process to extract the model parameters from real grid log traces, and verify that synthetically generated jobs provide a realistic approximation of the real-world grid job submission process.

Abstract: In this paper we present a multicost algorithm for the joint
time scheduling of the communication and computation
resources that will be used by a task. The proposed
algorithm selects the computation resource to execute the
task, determines the path to route the input data, and finds
the starting times for the data transmission and the task
execution, performing advance reservations. We initially
present an optimal scheme of non-polynomial complexity
and by appropriately pruning the set of candidate paths we
also give a heuristic algorithm of polynomial complexity. We
evaluate the performance of our algorithm and compare it to
that of algorithms that handle only the computation or
communication part of the problem separately. We show that
in a Grid network where the tasks are CPU- and dataintensive
important performance benefits can be obtained by
jointly optimizing the use of the communication and
computation resources.

Abstract: A key problem in Grid networks is how to efficiently manage the available infrastructure, in order to
satisfy user requirements and maximize resource utilization. This is in large part influenced by the
algorithms responsible for the routing of data and the scheduling of tasks. In this paper,wepresent several
multi-cost algorithms for the joint scheduling of the communication and computation resources that
will be used by a Grid task. We propose a multi-cost scheme of polynomial complexity that performs
immediate reservations and selects the computation resource to execute the task and determines the
path to route the input data. Furthermore, we introduce multi-cost algorithms that perform advance
reservations and thus also find the starting times for the data transmission and the task execution. We
initially present an optimal scheme of non-polynomial complexity and by appropriately pruning the set
of candidate paths we also give a heuristic algorithm of polynomial complexity. Our performance results
indicate that in a Grid network in which tasks are either CPU- or data-intensive (or both), it is beneficial
for the scheduling algorithm to jointly consider the computational and communication problems. A
comparison between immediate and advance reservation schemes shows the trade-offs with respect to
task blocking probability, end-to-end delay and the complexity of the algorithms.

Abstract: We present an architecture for implementing optical
buffers, based on the feed-forward-buffer concept, that can truly
emulate input queuing and accommodate asynchronous packet
and burst operation. The architecture uses wavelength converters
and fixed-length delay lines that are combined to form either a
multiple-input buffer or a shared buffer. Both architectures are
modular, allowing the expansion of the buffer at a cost that grows
logarithmically with the buffer depth, where the cost is measured
in terms of the number of switching elements, and wavelength
converters are employed. The architectural design also provides
a tradeoff between the number of wavelength converters and their
tunability. The buffer architectures proposed are complemented
with scheduling algorithms that can guarantee lossless communication
and are evaluated using physical-layer simulations to
obtain their performance in terms of bit-error rate and achievable
buffer size.

Abstract: We present an architecture for implementing optical
buffers, based on the feed-forward-buffer concept, that can truly
emulate input queuing and accommodate asynchronous packet
and burst operation. The architecture uses wavelength converters
and fixed-length delay lines that are combined to form either a
multiple-input buffer or a shared buffer. Both architectures are
modular, allowing the expansion of the buffer at a cost that grows
logarithmically with the buffer depth, where the cost is measured
in terms of the number of switching elements, and wavelength
converters are employed. The architectural design also provides
a tradeoff between the number of wavelength converters and their
tunability. The buffer architectures proposed are complemented
with scheduling algorithms that can guarantee lossless communication
and are evaluated using physical-layer simulations to
obtain their performance in terms of bit-error rate and achievable
buffer size.

Abstract: In this paper a performanse analysis of the packet scheduling switch uses a series of feed forward delays interconnected with elementary optical switches. This series of programmable delay blocks constitute an optical buffer of depth T, whose purpose is to delay/re-arrange incoming packets that request packet contention.Performance results have been obtained for random Bernoulli traffic, Pareto traffic, as well as for smooth with an upper bound of inherent burstiness.

Abstract: A performance analysis of an optically interconnected packet-scheduling switch network is presented. The scheduling switch uses a branch of feed-forward delays for each input port, interconnected with elementary optical switches to resolve contention. The scheduling switch is guaranteed to be lossless under a certain smoothness property condition. We investigate the packet-loss performance of the switch when the smoothness property condition does not hold, as well as the packet delay impairments at the edge of a scheduling switch interconnected network when this property is enforced.

Abstract: We consider in this paper the problem of scheduling a set of independent
parallel tasks (jobs) with respect to two criteria, namely,
the makespan (time of the last finishing job) and the minsum (average
completion time). There exist several algorithms with a good
performance guaranty for one of these criteria. We are interested
here in studying the optimization of both criteria simultaneously.
The numerical values are given for the moldable task model, where
the execution time of a task depends on the number of processors
alloted to it. The main result of this paper is to derive explicitly
a family of algorithms guaranteed for both the minsum and the
makespan. The performance guaranty of these algorithms is better
than the best algorithms known so far. The Guaranty curve
of the family is the set of all points (x; y) such that there is an
algorithm with guarantees x on makespan and y on the minsum.
When the ratio on the minsum increases, the curve tends to the
best ratio known for the makespan for moldable tasks (3=2). One
extremal point of the curves is a (3;6)-approximation algorithm.
Finally a randomized version is given, which improves this results
to (3;4.08).

Abstract: Grids offer a transparent interface to geographically scattered computation, communication, storage and
other resources. In this chapter we propose and evaluate QoS-aware and fair scheduling algorithms for
Grid Networks, which are capable of optimally or near-optimally assigning tasks to resources, while taking
into consideration the task characteristics and QoS requirements. We categorize Grid tasks according to
whether or not they demand hard performance guarantees. Tasks with one or more hard requirements are
referred to as Guaranteed Service (GS) tasks, while tasks with no hard requirements are referred to as Best
Effort (BE) tasks. For GS tasks, we propose scheduling algorithms that provide deadline or computational
power guarantees, or offer fair degradation in the QoS such tasks receive in case of congestion. Regarding
BE tasks our objective is to allocate resources in a fair way, where fairness is interpreted in the max-min fair
share sense. Though, we mainly address scheduling problems on computation resources, we also look at
the joint scheduling of communication and computation resources and propose routing and scheduling
algorithms aiming at co-allocating both resource type so as to satisfy their respective QoS requirements.

Abstract: We propose information aggregation as a method for summarizing the resource-related information, used by the task scheduler. Through this method the information of a set of resources can be uniformly represented, reducing at the same time the amount of information transferred in a Grid network. A number of techniques are described for aggregating the information of the resources belonging to a hierarchical Grid domain. This information includes the cpu and storage capacities at a site, the number of tasks queued, and other resource-related parameters. The quality of the aggregation scheme affects the efficiency of the scheduler{\^a}€™s decisions. We use as a metric of aggregation efficiency the Stretch Factor (SF), defined as the ratio of the task delay when the task is scheduled using complete resource information over the task delay when an aggregation scheme is used. The simulation experiments performed show that the proposed aggregation schemes achieve large information reduction, while enabling good task scheduling decisions as indicated by the SF achieved.

Abstract: A key problem in networks that support advance reservations is the routing and time scheduling of connections with flexible starting time and known data transfer size. In this paper we present a multicost routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the data should start and end transmission at each link so as to minimize the reception time at the destination, or optimize some other performance criterion. The utilization profiles of the network links, the link propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm. We initially present a scheme of non-polynomial complexity to compute a set of so called non-dominated candidate paths, from which the optimal path can be found. We then propose two mechanisms to appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of polynomial complexity. We examine the performance of the algorithms in the special case of an Optical Burst Switched network. Our results indicate that the proposed polynomial-time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network propagation delays and link-state update policies have on performance.

Abstract: We propose QoS-aware scheduling algorithms for Grid Networks that are capable of optimally or near-optimally
assigning computation and communication tasks to grid resources. The routing and scheduling algorithms to be
presented take as input the resource utilization profiles and the task characteristics and QoS requirements, and
co-allocate resources while accounting for the dependencies between communication and computation tasks.
Keywords: communication and computation utilization profiles, multicost routing and scheduling, grid
computing.

Abstract: A key problem in networks that support advance reservations is the routing and time scheduling of
connections with flexible starting time and known data transfer size. In this paper we present a multicost
routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the
data should start and end transmission at each link so as to minimize the reception time at the destination,
or optimize some other performance criterion. The utilization profiles of the network links, the link
propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm.
We initially present a scheme of non-polynomial complexity to compute a set of so-called non-dominated
candidate paths, from which the optimal path can be found. We then propose two mechanisms to
appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of
polynomial complexity. We examine the performance of the algorithms in the special case of an Optical
Burst Switched network. Our results indicate that the proposed polynomial time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network
propagation delays and link-state update policies have on performance.

Abstract: A key problem in networks that support advance
reservations is the routing and time scheduling of connections
with flexible starting time. In this paper we present a multicost
routing and scheduling algorithm for selecting the path to be
followed by such a connection and the time the data should start
so as to minimize the reception time at the destination, or some
other QoS requirement. The utilization profiles of the network
links, the link propagation delays, and the parameters of the
connection to be scheduled form the inputs to the algorithm. We
initially present a scheme of non-polynomial complexity to
compute a set of so-called non-dominated candidate paths, from
which the optimal path can be found. By appropriately pruning
the set of candidate paths using path pseudo-domination
relationships, we also find multicost routing and scheduling
algorithms of polynomial complexity. We examine the
performance of the algorithms in the special case of an Optical
Burst Switched network. Our results indicate that the proposed
polynomial time algorithms have performance that it is very close
to that of the optimal algorithm.

Abstract: We consider information aggregation as a method for reducing the information exchanged in a Grid network and used by the resource manager in order to make scheduling decisions. In this way, information is summarized across nodes and sensitive or detailed information can be kept private, while resources are still publicly available for use. We present a general framework for information aggregation, trying to identify issues that relate to aggregation in Grids. In this context, we describe a number of techniques, including single point and intra-domain aggregation, define appropriate grid-specific domination relations and operators for aggregating static and dynamic resource information, and discuss resource selection optimization functions. The quality of an aggregation scheme is measured both by its effects on the efficiency of the scheduler¢s decisions and also by the reduction it brings on the amount of resource information recorded, a tradeoff that we examine in detail. Simulation experiments demonstrate that the proposed schemes achieve significant information reduction, either in the amount of information exchanged, or in the frequency of the updates, while at the same time maintaining most of the value of the original information as expressed by a stretch factor metric we introduce.

Abstract: In this work we study the problem of scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds. We examine the energy-efficiency and time efficiency of scheduling in an asymmetric system.

Abstract: We study a problem of scheduling client requests to servers. Each client has a particular latency requirement at each server and may choose either to be assigned to some server in order to get serviced provided that her latency requirement is met, or not to participate in the assignment at all. From a global perspective, in order to optimize the performance of such a system, one would aim to maximize the number of clients that participate in the assignment. However, clients may behave selfishly in the sense that, each of them simply aims to participate in an assignment and get serviced by some server where her latency requirement is met with no regard to overall system performance. We model this selfish behavior as a strategic game, show how to compute pure Nash equilibria efficiently, and assess the impact of selfishness on system performance. We also show that the problem of optimizing performance is computationally hard to solve, even in a coordinated way, and present efficient approximation and online algorithms.

Abstract: We study a problem of scheduling client requests to servers.
Each client has a particular latency requirement at each server and may
choose either to be assigned to some server in order to get serviced provided
that her latency requirement is met or not to participate in the
assignment at all. From a global perspective, in order to optimize the
performance of such a system, one would aim to maximize the number
of clients that participate in the assignment. However, clients may behave
selfishly in the sense that each of them simply aims to participate
in an assignment and get serviced by some server where her latency requirement
is met with no regard to the overall system performance. We
model this selfish behavior as a strategic game, show how to compute
equilibria efficiently, and assess the impact of selfishness on system performance.
We also show that the problem of optimizing performance is
computationally hard to solve, even in a coordinated way, and present
efficient approximation and online algorithms.

Abstract: Efficient task scheduling is fundamental for the success of the Grids,
since it directly affects the Quality of Service (QoS) offered to the users. Efficient
scheduling policies should be evaluated based not only on performance
metrics that are of interest to the infrastructure side, such as the Grid resources
utilization efficiency, but also on user satisfaction metrics, such as the percentage
of tasks served by the Grid without violating their QoS requirements. In this
paper, we propose a scheduling algorithm for tasks with strict timing requirements,
given in the form of a desired start and finish time. Our algorithm aims
at minimizing the violations of the time constraints, while at the same time
minimizing the number of processors used. The proposed scheduling method
exploits concepts derived from spectral clustering, and groups together for assignment
to a computing resource the tasks so to a) minimize the time overlapping
of the tasks assigned to a given processor and b) maximize the degree of
time overlapping among tasks assigned to different processors. Experimental
results show that our proposed strategy outperforms greedy scheduling algorithms
for different values of the task load submitted.

Abstract: Efficient task scheduling is fundamental for the success of the Grids,
since it directly affects the Quality of Service (QoS) offered to the users. Efficient
scheduling policies should be evaluated based not only on performance
metrics that are of interest to the infrastructure side, such as the Grid resources
utilization efficiency, but also on user satisfaction metrics, such as the percentage
of tasks served by the Grid without violating their QoS requirements. In this
paper, we propose a scheduling algorithm for tasks with strict timing requirements,
given in the form of a desired start and finish time. Our algorithm aims
at minimizing the violations of the time constraints, while at the same time
minimizing the number of processors used. The proposed scheduling method
exploits concepts derived from spectral clustering, and groups together for assignment
to a computing resource the tasks so to a) minimize the time overlapping
of the tasks assigned to a given processor and b) maximize the degree of
time overlapping among tasks assigned to different processors. Experimental
results show that our proposed strategy outperforms greedy scheduling algorithms
for different values of the task load submitted.

Abstract: Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [E. Koutsoupias, C. Papadimitriou, Worst-case equilibria, in: 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS, vol. 1563, 1999, pp. 404-413; T. Roughgarden, E. Tardos, How bad is selfish routing? in: 41st IEEE Annual Symposium of Foundations of Computer Science, FOCS, 2000, pp. 93-102]. A Leader can decrease the coordination ratio by assigning flow {\'a}r on M, and then all Followers assign selfishly the (1-{\'a})r remaining flow. This is a Stackelberg Scheduling Instance(M,r,{\'a}),0≤{\'a}≤1. It was shown [T. Roughgarden, Stackelberg scheduling strategies, in: 33rd Annual Symposium on Theory of Computing, STOC, 2001, pp. 104-113] that it is weakly NP-hard to compute the optimal Leader's strategy. For any such network M we efficiently compute the minimum portion @b"M of flow r>0 needed by a Leader to induce M's optimum cost, as well as her optimal strategy. This shows that the optimal Leader's strategy on instances (M,r,@a>=@b"M) is in P. Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling {\'a}r flow can induce ≤1/{\'a} times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example. Finally, we extend this result to k commodities. A conference version of this paper has appeared in [A. Kaporis, P. Spirakis, The price of optimum in stackelberg games on arbitrary single commodity networks and latency functions, in: 18th annual ACM symposium on Parallelism in Algorithms and Architectures, SPAA, 2006, pp. 19-28]. Some preliminary results have also appeared as technical report in [A.C. Kaporis, E. Politopoulou, P.G. Spirakis, The price of optimum in stackelberg games, in: Electronic Colloquium on Computational Complexity, ECCC, (056), 2005].

Abstract: Digital optical logic circuits capable of performing bit-wise signal processing are critical building blocks for the realization of future high-speed packet-switched networks. In this paper, we present recent advances in all-optical processing circuits and examine the potential of their integration into a system environment. On this concept, we demonstrate serial all-optical Boolean AND/XOR logic at 20 Gb/s and a novel all-optical packet clock recovery circuit, with low capturing time, suitable for burst-mode traffic. The circuits use the semiconductor-based ultrafast nonlinear interferometer (UNI) as the nonlinear switching element. We also present the integration of these circuits in a more complex unit that performs header and payload separation from short synchronous data packets at 10 Gb/s. Finally, we discuss a method to realize a novel packet scheduling switch architecture, which guarantees lossless communication for specific traffic burstiness constraints, using these logic units.