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# Sequencing of a Set of Partially Independent Processes

IP.com Disclosure Number: IPCOM000079767D
Original Publication Date: 1973-Sep-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 3 page(s) / 49K

IBM

## Related People

Chroust, G: AUTHOR [+5]

## Abstract

A control method is described which guarantees save and optimal sequencing of an enumerable-set of processes {P(1),P(2),...,P(n)} with the sequencing constraints, that process P(i) can only be initiated after completion of processes P(i-d(1)), P(i-d(2)),...,P(i-d(n)) (d(i) > 0). Additionally, the method described has been proved to use the minimum number of shared control fields.

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Sequencing of a Set of Partially Independent Processes

A control method is described which guarantees save and optimal sequencing of an enumerable-set of processes {P(1),P(2),...,P(n)} with the sequencing constraints, that process P(i) can only be initiated after completion of processes P(i-d(1)), P(i-d(2)),...,P(i-d(n)) (d(i) > 0). Additionally, the method described has been proved to use the minimum number of shared control fields.

The set of integers {d(1),d(2),...,d(n)} is called the distance set D. From D a reduced distance set E can be determined by eliminating all elements which can be represented as a linear combination of other elements d(i) = alpha(j*)d(j) with (alpha(j) >/- 0). This reduced set E = {e1,e(2),...,e(m)} determines the control mechanism required. In the following, E be an increasingly ordered array, i.e., e(1) < e(2) < ... e(m).

The minimal number of control fields s can be determined as s = minimal common element of S(1), S(2), S(3), ..., S(m) where S(j(e)) = {e(i)+sigma alpha(j)*| alpha >/-0} is the set of all possible sums, having the elements e(j) as summand an arbitrary number of times and e. at least once. In fact, any common elements of S(1), S(2), ..., S(m) could be used as a dimension of the array of control fields, e.g., sigma/m/(j-1) e(i). From the totality of all processes, only control fields s are considered at any one time as candidates for starting?

Each of these s processes is controlled by two control fields (Fig.
1): ID(i) identifies the process

W(i) contains the wait count.

When a wait count W(i) becomes zero, the process identified by ID(i) can be started. The processes are controlled by the...