Schedule vector

In case of a systolic array, the schedule vector A specifies that the AST node at index point 7 is to be executed at time step A 7. The vector A also specifies that the data which are transmitted over an edge defined by a dependence vector di is delayed A di time steps, so that the data will arrive in time at the node of the DG by which they are to be processed. In case of a wavefront processor array, the schedule vector A only specifies the ordering of the computations and the data storage capacity of the edges. Furthermore, the node at index point 7 will be mapped onto the processor at index point P j during the array synthesis step. Note that the S-T transformation only defines the S-T allocation... 

The first n — 3 rows of the transformation matrix are called the multidimensional scheduling vectors. 

The vector 11 -2 is the low-level scheduling vector, corresponding to the conventional time assignment [12, 15]. 

Multidimensional scheduling can be interpreted as follows the first scheduling vector Hi partitions the index space D into subdomains Di by using the relation Ui X I = i. Each of these subdomains can be further partitioned by the other multidimensional scheduling vectors. This results in a set of three-dimensional subdomains Each of these can be executed in parallel on a 2-D... 

Some of the production decisions of the aggregated scheduling problem are provided to the detailed scheduler. These decisions have to be taken before any observation of the outcome of the uncertain parameters is available. Thus, they correspond to the first-stage decisions of the two-stage stochastic problem. Consequently, the vector of first-stage decisions x consists of all production decisions of the short-term horizon N >rp and Zy, for i e 1,..., If. ... 

All remaining decisions can be made after the observation of the outcome of uncertain parameters, either in the detailed scheduler or by decisions of the aggregated problem which are taken later. Thus, these decisions are considered as second-stage decisions. Consequently, the vector of second-stage decisions ya consists of all production decisions of the periods i > h and all continuous variables of the cost model for all periods. 

To make the proj)a.ga.tor run concurrently at hi st use was made of MPI and of a Task Farm model [41]. In the startup phase the Master jirocess distributes the rows of C using a cyclic policy. This implies that in the startup phase if j = i mod M (with M being the number of scheduled Workers) the vector Raiv j. C) is sent to the worker W,. At the end of the startup phase each Worker has stored the rows received from the Master in a local (unshared) secondary space storage hereafter called Dataset Wi- C). Similarly, all the elements of the matrices A and B referred by the Worker IP) arc stored in an analogous Dataset during the wavepacket initialization (immediately before the hrst step t = 0). 

Figure 10.1-10. Gantt chart for production scheduling of one batch of adenoviral vector. The top and bottom charts show the duration of each operation in the cell culture and downstream processing sections, respectively. The total process time is 405 hours. The arrow indicates the start of a new batch at 264 hours.

Captain Layia slotted the starship into the spaceport approach vector which traffic control assigned her, then spent a further twenty minutes datavising the Sll fleet operations office, explaining why their scheduled return flight from Norfolk had been delayed. 

The systolic answer to the problem is to localize the broadcasts in the DG before scheduling and mapping its nodes [15], so as to synthesize an architecture where all communications are made local. Such a derivation process is well understood. Some recent synthesis results are discussed in chapter 6. The natural idea is to replace the broadcast of a variable by its pipelined propagation along the direction of the dependence vector. In this way, we obtain the DG of figure 3. 

The column-vector 7 contains the skewing parameter ja- This parameter determines how much the calculation of a variable A i) is delayed relatively to the scheduling determined by t. This permits dealing with potentially complex processing elements that contain, for instance, internal pipelining. 

In the next phase, the scheduled flow graph is partitioned, i.e., all operations belonging to one partition are mapped onto the same CBB. In this step, the vector information of the scheduler is used to take into account mutually exclusive operations. 

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