Relative scheduling formulation

Scheduling problems are defined and solved on graphs with fixed delay operations. We extend this notion to graphs with data-dependent delay vertices. For a data-dependent delay vertex the execution delay is not known statically, and can assume any integer value from 0 to oo. For this reason, we define a subset of the vertices, called anchors, that serve as reference points for specifying the start times of operations. 

Definition 6.2.1 The anchors of a constraint grr h G V, E) consist of the source vertex vq and all vertices with data-dependent delay, and are denoted by AC V. 

The source votex vo is treated as an anchor since the activation of a sequencing gr h is analogous to the completion of a data-dependent delay source vertex, which is not known a priori. Therefore, all outgoing edges firom vo have data-dependent weight equal to 6(vo). 

It is important to point out that the definition of anchors above applies to both unbounded delay operations, where the delay is not known statically, and bounded delay operations, wh e the delay is bounded but not fixed, i.e., an operation requiring either 2 or 3 cycles to execute, depending on some condition, is an example of an anchor with bounded delay. It is possible to treat a bounded-delay anchor as a fixed-delay non-anchor by assuming its worst-case delay, at the expense of possibly increasing the overall latency. 

We extend the scheduling problem in the presence of data-dependent delay vertices by introducing the concept of offsets with respect to the anchors of the graph. Let 14 C be the subset of the vertices including a and all its successors. 

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The relative scheduling formulation provides a theoretical basis for analyzing redundancy in the synchronization of a given operation. Using synchronization redundancy can reduce the size of the corresponding control circuit, and algorithms are presented to remove all redundancies in a schedule. 

The main algorithmic contributions of this research are described in the next four chapters. Ch ter 6 presents the relative scheduling formulation that includes description of the algorithms and analysis of their prqterties. Chapto 7 describes conflict resolution under timing constraints. Chapter 8 describes the generation of the control circuit from a relative schedule. Chapter 9 describes the control resynchronization optimization that reduces the area of the control implementation under timing and synchronization constraints. 

Relative scheduling a scheduling formulation that supports synchronizations and timing constraints,... 

Relative scheduling. Once resource conflicts have been resolved, operations are assigned to control steps subject to synchronization and timing requirements. The formulation is based on relative scheduling. 

Conflict resolution, relative scheduling, relative control synthesis and optimization are formulated on a constraint graph model that is derived from the sequencing graph model under detailed timing constraints. Descriptions and analyses of these formulations are presented in subsequent chapters. 

The sequencing graph model is the underlying representation for design space exploration, which is described in the next chapter. Relative scheduling, constrained conflict resolution, and relative control synthesis and optimization are all formulated based on the constraint graph model. 

Organization of chapter. This chapter presents the formulation and algorithms for relative scheduling. Our approach can be described in a nutshell as follows. In relative scheduling, we support both operations with fixed delay and operations with data-dependent delay data-dependent delay operations represent points of synchronization. We uniformly model both types of operations as vertices in the constraint graph model. We assume in this cluq)ter that resource binding and conflict resolution have been performed prior to scheduling. 

Note that if there are no data-dependent delay vertices in the graph, then the start times of all operations will be specified in terms of time offsets from the source vertex, which reduces to the traditional scheduling formulation. We define the relative scheduling problem as follows. 

Relative scheduling provides the framewtx k for analyzing consistency of timing constraints, which is used extensively in the conflict resolution formulation. 

A mathematical formulation based on uneven discretization of the time horizon for the reduction of freshwater utilization and wastewater production in batch processes has been developed. The formulation, which is founded on the exploitation of water reuse and recycle opportunities within one or more processes with a common single contaminant, is applicable to both multipurpose and multiproduct batch facilities. The main advantages of the formulation are its ability to capture the essence of time with relative exactness, adaptability to various performance indices (objective functions) and its structure that renders it solvable within a reasonable CPU time. Capturing the essence of time sets this formulation apart from most published methods in the field of batch process integration. The latter are based on the assumption that scheduling of the entire process is known a priori, thereby specifying the start and/or end times for the operations of interest. This assumption is not necessary in the model presented in this chapter, since water reuse/recycle opportunities can be explored within a broader scheduling framework. In this instance, only duration rather start/end time is necessary. Moreover, the removal of this assumption allows problem analysis to be performed over an unlimited time horizon. The specification of start and end times invariably sets limitations on the time horizon over which water reuse/recycle opportunities can be explored. In the four scenarios explored in... 

Incidents of vincristine overdosage have been reported relatively frequently in the medical literature. Some of these have involved inadvertent administration of the intravenous formulation into the central nervous system by the intrathecal route this produces devastating results by a combination of chemical damage to sensitive neuronal tissue as well as biochemical perturbations. Two representative cases of vincristine overdose were described (46) involving administration of vincristine to patients scheduled to receive vinblastine. In one patient toxicity initially involved vomiting and diarrhea with subsequent constipation and paralytic ileus (inhibition of motor activity in the small intestine). Muscle pain... 

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