A four-stage index 2 Diagonally Implicit Runge-Kutta method

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.

Intra-type migrative scheduling of implicit-deadline sporadic tasks on two- type heterogeneous multiprocessor

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a two-type heterogeneous multiprocessor platform. Each processor is either of type-1 or type-2 with each task having different execution time on each processor type. Jobs can migrate between processors of same type (referred to as intra-type migration) but cannot migrate between processors of different types. We present a new scheduling algorithm namely, LP-Relax(THR) which offers a guarantee that if a task set can be scheduled to meet deadlines by an optimal task assignment scheme that allows intra-type migration then LP-Relax(THR) meets deadlines as well with intra-type migration if given processors 1/THR as fast (referred to as speed competitive ratio) where THR <= 2/3.

Conjecture about global fixed-priority preemptive multiprocessor scheduling of implicit-deadline sporadic tasks: the utilization bound of SM-US(sqrt(2)-1) is sqrt(2)-1

Consider global fixed-priority preemptive multiprocessor scheduling of implicit-deadline sporadic tasks. I conjecture that the utilization bound of SM-US(√2−1) is √2-1.

An implicit GTS allocation mechanism in IEEE 802.15.4 for time-sensitive wireless sensor networks: theory and practice

Timeliness guarantee is an important feature of the recently standardized IEEE 802.15.4 protocol, turning it quite appealing for Wireless Sensor Network (WSN) applications under timing constraints. When operating in beacon-enabled mode, this protocol allows nodes with real-time requirements to allocate Guaranteed Time Slots (GTS) in the contention-free period. The protocol natively supports explicit GTS allocation, i.e. a node allocates a number of time slots in each superframe for exclusive use. The limitation of this explicit GTS allocation is that GTS resources may quickly disappear, since a maximum of seven GTSs can be allocated in each superframe, preventing other nodes to benefit from guaranteed service. Moreover, the GTS may be underutilized, resulting in wasted bandwidth. To overcome these limitations, this paper proposes i-GAME, an implicit GTS Allocation Mechanism in beacon-enabled IEEE 802.15.4 networks. The allocation is based on implicit GTS allocation requests, taking into account the traffic specifications and the delay requirements of the flows. The i-GAME approach enables the use of one GTS by multiple nodes, still guaranteeing that all their (delay, bandwidth) requirements are satisfied. For that purpose, we propose an admission control algorithm that enables to decide whether to accept a new GTS allocation request or not, based not only on the remaining time slots, but also on the traffic specifications of the flows, their delay requirements and the available bandwidth resources. We show that our approach improves the bandwidth utilization as compared to the native explicit allocation mechanism defined in the IEEE 802.15.4 standard. We also present some practical considerations for the implementation of i-GAME, ensuring backward compatibility with the IEEE 801.5.4 standard with only minor add-ons. Finally, an experimental evaluation on a real system that validates our theoretical analysis and demonstrates the implementation of i-GAME is also presented

Online robust optimization framework for QoS guarantees in distributed soft real-time systems

In distributed soft real-time systems, maximizing the aggregate quality-of-service (QoS) is a typical system-wide goal, and addressing the problem through distributed optimization is challenging. Subtasks are subject to unpredictable failures in many practical environments, and this makes the problem much harder. In this paper, we present a robust optimization framework for maximizing the aggregate QoS in the presence of random failures. We introduce the notion of K-failure to bound the effect of random failures on schedulability. Using this notion we define the concept of K-robustness that quantifies the degree of robustness on QoS guarantee in a probabilistic sense. The parameter K helps to tradeoff achievable QoS versus robustness. The proposed robust framework produces optimal solutions through distributed computations on the basis of Lagrangian duality, and we present some implementation techniques. Our simulation results show that the proposed framework can probabilistically guarantee sub-optimal QoS which remains feasible even in the presence of random failures.

i-GAME: an implicit GTS allocation mechanism in IEEE 802.15.4 for time-sensitive wireless sensor networks

The IEEE 802.15.4 Medium Access Control (MAC) protocol is an enabling technology for time sensitive wireless sensor networks thanks to its Guaranteed-Time Slot (GTS) mechanism in the beacon-enabled mode. However, the protocol only supports explicit GTS allocation, i.e. a node allocates a number of time slots in each superframe for exclusive use. The limitation of this explicit GTS allocation is that GTS resources may quickly disappear, since a maximum of seven GTSs can be allocated in each superframe, preventing other nodes to benefit from guaranteed service. Moreover, the GTSs may be only partially used, resulting in wasted bandwidth. To overcome these limitations, this paper proposes i-GAME, an implicit GTS Allocation Mechanism in beacon-enabled IEEE 802.15.4 networks. The allocation is based on implicit GTS allocation requests, taking into account the traffic specifications and the delay requirements of the flows. The i-GAME approach enables the use of a GTS by multiple nodes, while all their (delay, bandwidth) requirements are still satisfied. For that purpose, we propose an admission control algorithm that enables to decide whether to accept a new GTS allocation request or not, based not only on the remaining time slots, but also on the traffic specifications of the flows, their delay requirements and the available bandwidth resources. We show that our proposal improves the bandwidth utilization compared to the explicit allocation used in the IEEE 802.15.4 protocol standard. We also present some practical considerations for the implementation of i-GAME, ensuring backward compatibility with the IEEE 801.5.4 standard with only minor add-ons.

The role of implicit contracts: Building public works in the 1840s in Portugal

Business History, Vol 50 No 2, p147-162

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising two different types of processors—such a platform is referred to as two-type platform. We present two low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

Generalized Extraction of Real-Time Parameters for Homogeneous Synchronous Dataflow Graphs

23rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP 2015). 4 to 6, Mar, 2015. Turku, Finland.

Optimal job design in the presence of implicit contracts

We characterize the optimal job design in a multitasking environment when the firms rely on implicit incentive contracts (i.e., bonus payments). Two natural forms of job design are compared: (i) individual accountability, where each agent is assigned to a particular job and assumes full responsibility for its outcome; and (ii) team accountability, where a group of agents share responsibility for a job and are jointly accountable for its outcome. The key trade-off is that team accountability mitigates the multitasking problem but may weaken the implicit contracts. The optimal job design follows a cut-off rule: firms with high reputation concerns opt for team accountability, whereas firms with low reputation concerns opt for individual accountability. Team accountability is more likely the more acute the multitasking problem is. However, the cut-off rule need not hold if the firm combines implicit incentives with explicit pay-per-performance contracts.

The role of guarantees in pension plan design: Pension saving decisions

This study centers on the assessment of psychological value of guarantees in pension products and the behavior biases associated with choice. When a guarantee on a product increases from 99% to 99,5% less than half of respondents show willingness to pay in contrast with 73% when going from 99,5% to 100%. Out of 105 respondents, 55 show that their choices concerning pension products are inconsistent with classic utility theory. Financial background proves insignificant thus pointing to behavioral biases. As individuals make choices that leave them worse-off, we argue that pension plan design would highly benefit from public policy interventions.

Implicit sequence learning in recurrent neural networks

Magdeburg, Univ., Fak. für Elektrotechnik, Diss., 2013