The Consensus Scheduling Model: Negotiation among Peers

The Consensus Schedufing Model (CSM) is introduced a way to accommodate negotiation in over-constrained, distributed scheduling problems. The CSM is appropriate for negotiation among a group of peers and is also applicable to a manager that must balance conflicting views of its workers. The distributed scheduling algorithm that is used selects a candidate from the priority list of resource requests and inserts that candidate into the evolving timetable. Two protocols ere required. The minimax protocol assures equitable power among the peers. The bumping protocol allows reactive scheduling by using a request’s total worth to dictate when a new request can seize a previously assigned resource. A request’s total worth is the sum of its priority value, its ordering value, and any bonus points received by previous negotiations. Three styles of negotiation are examined: unilateral, verbose, and periodic. In cases where a problem is over-constrained, no solution is possible unless the system relaxes the constraints. Inclusion of negotiation within the communication protocol allows the system to adjust its constraints in an intelligent way. In a distributed environment hese relaxation choices may be made by multiple users, and the users need to negotiate about relaxing some constraints. The main goal of this work is to determine appropriate models for negotiation among peers. This goal generates the following criteria on which the design of CSM is based: (1) the schedule’s evaluation and the decision to relax constraints are distributed; (2) the human peers are able to give their constraints and preferences to the system without being bound to the tedious communication and negotiation processes; (3) the system goal is to maximize the total worth of the system; (4) the implementation for scheduling has been modularized into four components: accumulation of resources, communication, scheduling, and negotiation; (5) the protocol is one form of equitable scheduling among peers; (6) variations in the calculations of a constraint’s worth are provided; (7) the model can deal with multiple, independent schedules being constructed and negotiated simultaneously; and (8) only requests that require the shared resources are made public. The CSM begins with a committee of peers and adds a Virtual Chair (VC). VC does not dictate to the committee members as is customary in a hierarchical structure, but acts as secretary of the committee by (1) performing all scheduling of the shared resources, (2) incorporating individuai members’ objections to proposed schedules, and (3) accommodating members’ changing constraints and utilities. The collection of requirements and associated utilities that the committee members present to VC is the public knowledge. Each request for a shared resource has a priority value assigned to it by the requestor. VC begins scheduling by randomly selecting one member after the other, with no repetitions, until each department has been selected once. VC holds a tab for each member as follows: when a resource with priority P is scheduled, add to the member’s tab the cost P/(10N) where N is the total number of requests and P __. 10. Until all resources are assigned, repeat (a) use the minimax protocol to select the next member and assigned its highest rated, unassigned request, and (b) insen the resources into the schedule and adjust the member’s tab; the bumping protocol may be required here. The minimax protocol chooses the next member to schedule based on the minimal current tab and from that department’s request list of unassigned resources, chooses the request with the maximum priority. The bmpmg protocol allows transference of an already-amigoed resource to .a later req .u~tor and re~bednling of the original request. This transfer m bumping and can occur only if the request being added is worth more than the request being transferred. The worth of a request is the weighted sum of its priority value, its ordering value, and any bonus points received by previous negotiations. In the unilateral negotiation style committee members agree that no negotiation will take place when the sTstem is over-~:onstralncd. This style is also used in conjunction with other styles as a last resort after other styles of negotiation have failed to resolve a dispute. Whim negotiation between VC and the members begins in the middle of scheduling, all requests of lesser priority have to wait. This style of negotiation is verbose. Two different reward types are considered for verbose negotiation. The group-ra:e reward affects all unscheduled request of the rewarded memb~ by changing its tab calculations. The coupon reward asks that a specific number of unscheduled courses he given bonus priority points. In per/od/c uegotimions, VC fills as many request as possible, notes the unfilled requests, and continues constructing the schedule. The members ale asked to help aocommo0~h-~ the unfilled requests after the current schedule and unfilled requests are presented. VC can reward a chosen compfiant member by attempting to upgrade all of the compliant member’s requests by adding points to each request’s worth. All styles have been implemented and tested using the Parallel Virtual Machine on a SUN network. One possible expansion allows the requests to include constraints; a request may include priorities together with other consWaints about time or location. Other styles of negotiation that look promising are either those based on timing or those based on smmmre. For example, another appropriate structure-based style of negotiation for large systems may be a delay style, which lies between the periodic and the verbose styles Day, W. 1994. Planning Model Implementation in CLP. Technical Report, RL-TR-94-49, Rome Laboratory, Griffiss AFB, NY. Liu, J. and Sycara, K. P. 1994. Distributed ConstraintDirected Meeting Scheduling. Presented at Workshop on Coordinated Design and Planning at the Tenth ~ Conf. on AI for Applications, San Antonio, TX, March 1994. Tsang, E. 1993. Foundations of Constraint Satisfaction, New York: Academic Press. 444 ICMAS-95 From: Proceedings of the First International Conference on Multiagent Systems. Copyright © 1995, AAAI (www.aaai.org). All rights reserved.